/brief historical perspective/

The greatness of a true scientist is not in the titles and awards with which he is marked or awarded by the world community, and not even in the recognition of his services to Humanity, but in the discoveries and theories that he left to the World. Unique discoveries made during our bright life, the famous scientist Isaac Newton is difficult to overestimate or underestimate.

Theories and discoveries

Isaac Newton formulated the basic laws of classical mechanics, was opened law of universal gravitation, theory developed movement celestial bodies , created fundamentals of celestial mechanics.

Isaac Newton(independently of Gottfried Leibniz) created theory of differential and integral calculus, opened light dispersion, chromatic aberration, studied interference and diffraction, developed corpuscular theory of light, gave a hypothesis that combined corpuscular And wave representations, built mirror telescope.

Space and time Newton considered absolute.

Historical formulations of Newton's laws of mechanics

Newton's first law

Every body continues to be maintained in a state of rest or uniform and rectilinear motion until and unless it is forced by applied forces to change this state.

Newton's second law

In an inertial reference frame, the acceleration that a material point receives is directly proportional to the resultant of all forces applied to it and inversely proportional to its mass.

The change in momentum is proportional to the applied driving force and occurs in the direction of the straight line along which this force acts.

Newton's third law

An action always has an equal and opposite reaction, otherwise the interactions of two bodies on each other are equal and directed in opposite directions.

Some of Newton's contemporaries considered him alchemist. He was the director of the Mint, established the coin business in England, and headed the society Prior-Zion, studied the chronology of ancient kingdoms. He devoted several theological works (mostly unpublished) to the interpretation of biblical prophecies.

Newton's works

– “A New Theory of Light and Colors”, 1672 (communication to the Royal Society)

– “Motion of bodies in orbit” (lat. De Motu Corporum in Gyrum), 1684

– “Mathematical principles of natural philosophy” (lat. Philosophiae Naturalis Principia Mathematica), 1687

- “Optics or a treatise on the reflections, refractions, bendings and colors of light” (eng. Opticks or a treatise of the reflections, refractions, inflections and colors of light), 1704

– “On the quadrature of curves” (lat. Tractatus de quadratura curvarum), supplement to "Optics"

– “Enumeration of lines of the third order” (lat. Enumeratio linearum tertii ordinis), supplement to "Optics"

– “Universal arithmetic” (lat. Arithmetica Universalis), 1707

– “Analysis using equations with an infinite number of terms” (lat. De analysi per aequationes numero terminorum infinitas), 1711

– “Method of Differences”, 1711

According to scientists around the world, Newton's work was significantly ahead of the general scientific level of his time and were little understood by his contemporaries. However, Newton himself said about himself: “ I don’t know how the world perceives me, but to myself I seem to be only a boy playing on the seashore, who amuses himself by occasionally finding a pebble more colorful than the others, or a beautiful shell, while the great ocean of truth spreads out before me. unexplored by me. »

But according to the conviction of no less a great scientist, A. Einstein “ Newton was the first to try to formulate elementary laws that determine the time course of a wide class of processes in nature with high degree completeness and accuracy" and “... with his works had a deep and strong influence on the entire worldview as a whole. »

Newton's grave bears the following inscription:

“Here lies Sir Isaac Newton, the nobleman who, with an almost divine mind, was the first to prove with the torch of mathematics the motion of the planets, the paths of comets and the tides of the oceans. He investigated the differences in light rays and the various properties of colors that appeared thereby, which no one had previously suspected. A diligent, wise and faithful interpreter of nature, antiquity and Holy Scripture, he affirmed with his philosophy the greatness of Almighty God, and with his disposition he expressed evangelical simplicity. Let mortals rejoice that such an adornment of the human race existed. »

Prepared Lazarus Model.

Sir Isaac Newton is an English physicist, mathematician, astronomer, creator of classical mechanics, who made the greatest scientific discoveries in the history of mankind.

Isaac Newton was born on January 4, 1643 (according to Gregorian calendar) in the village of Woolsthorpe in Lincolnshire. He received his name in honor of his father, who died 3 months before the birth of his son. Three years later, Isaac's mother, Anna Ayscough, remarried. Three more children were born into the new family. Isaac Newton was taken into the care of his uncle, William Ayscough.

Childhood

The house where Newton was born

Isaac grew up withdrawn and silent. He preferred reading to communicating with his peers. He loved making technical toys: kites, windmills, water clock.

At the age of 12, Newton began attending school in Grantham. He lived at that time in the house of the pharmacist Clark. Perseverance and hard work soon made Newton the best student in his class. But when Newton was 16 years old, his stepfather died. Isaac's mother brought him back to the estate and assigned him household responsibilities. But Newton did not like this at all. He did little housekeeping, preferring reading to this boring activity. One day, Newton's uncle, finding him with a book in his hands, was amazed to see that Newton was solving a mathematical problem. Both his uncle and the school teacher convinced Newton’s mother that such a capable young man should continue his studies.

Trinity College

Trinity College

In 1661, 18-year-old Newton was enrolled at Trinity College, Cambridge University, as a sizar student. Such students were not charged tuition fees. They had to pay their tuition by doing various jobs at the University or serving wealthy students.

In 1664, Newton passed the exams, became a student and began to receive a scholarship.

Newton studied, forgetting about sleep and rest. He studied mathematics, astronomy, optics, phonetics, and music theory.

In March 1663, the department of mathematics was opened at the college. It was headed by Isaac Barrow, a mathematician, future teacher and friend of Newton. In 1664 Newton discovered binomial expansion for an arbitrary rational exponent. This was Newton's first mathematical discovery. Newton would later discover a mathematical method for expanding a function into an infinite series. At the end of 1664 he received his bachelor's degree.

Newton studied the works of physicists: Galileo, Descartes, Kepler. Based on their theories, he created universal world system.

Newton’s programmatic phrase: “In philosophy there can be no sovereign except truth...”. Is this where the famous expression came from: “Plato is my friend, but the truth is dearer”?

Years of the Great Plague

The years 1665 to 1667 were the period of the Great Plague. Classes at Trinity College ceased and Newton went to Woolsthorpe. He took all his notebooks and books with him. During these difficult “plague years,” Newton did not stop studying science. Carrying out various optical experiments, Newton proved that white color is a mixture of all colors of the spectrum. Law of Gravity- this is Newton’s greatest discovery, made by him during the “plague years”. Newton finally formulated this law only after the discovery of the laws of mechanics. And these discoveries were published only decades later.

Scientific discoveries

Newton's telescope

At the beginning of 1672, the Royal Society demonstrated reflecting telescope, which made Newton famous. Newton became a member of the Royal Society.

In 1686 Newton formulated three laws of mechanics, described the orbits of celestial bodies: hyperbolic and parabolic, proved that the Sun also obeys the general laws of motion. All this was set out in the first volume of Mathematical Principles.

In 1669, Newton's world system began to be taught at Cambridge and Oxford. Newton also becomes a foreign member of the Paris Academy of Sciences. In the same year, Newton was appointed manager of the Mint. He leaves Cambridge for London.

In 1669 Newton was elected to parliament. He stayed there for only a year. But in 1701 he was elected there again. That same year, Newton resigned as professor at Trinity College.

In 1703, Newton became president of the Royal Society and remained in this position until the end of his life.

In 1704, the monograph “Optics” was published. And in 1705, Isaac Newton was awarded the title of knight for scientific achievements. This happened for the first time in the history of England.

The famous collection of lectures on algebra, published in 1707 and called “Universal Arithmetic,” laid the foundation for the birth numerical analysis.

In the last years of his life, he wrote the “Chronology of Ancient Kingdoms” and prepared a reference book on comets. Newton very accurately calculated the orbit of Halley's comet.

Isaac Newton died in 1727 in Kensington near London. Buried in Westminster Abbey.

Newton's discoveries allowed humanity to make a giant leap in the development of mathematics, astronomy, and physics.

Isaac Newton

English mathematician, physicist, alchemist and historian Isaac Newton was born in the town of Woolsthorpe in Lincolnshire into a farmer's family. Newton's father died shortly before his birth; the mother soon remarried a priest from a neighboring town and moved in with him, leaving her son with his grandmother in Woolsthorpe. Some researchers explain Newton's painful unsociability and bileness, which later manifested itself in his relationships with others, as a mental breakdown in childhood. At the age of 12, Newton began studying at Grantham School, and in 1661 he entered St. Trinity University of Cambridge as a subsizer (the so-called poor students who did the work of servants), where his teacher was the famous mathematician I. Barrow. After graduating from the university, Newton received a bachelor's degree in 1665. In 1665-1667, during the plague epidemic, he was in his home village of Woolsthorpe; These years were the most productive in Newton's scientific work. Here he developed mainly those ideas that led him to the creation of differential and integral calculus, to the invention of the reflecting telescope, the discovery of the law of universal gravitation, and here he conducted experiments on the decomposition of light. In 1668, Newton was awarded a master's degree, and in 1669, Barrow transferred to him the chair of physics and mathematics, which Newton occupied until 1701. In 1671, Newton built a second reflecting telescope - large in size and best quality. The demonstration of the telescope made a strong impression on his contemporaries, and soon after, in January 1672, Newton was elected a member of the Royal Society of London (he became its president in 1703). In the same year, he presented to the Society his research on the new theory of light and colors, which caused a sharp struggle with Robert Hooke (Newton’s inherent pathological fear of public discussions led to the fact that he published “Optics”, prepared in those years, only 30 years later, after Hooke's death). Newton owns ideas about monochromatic light rays and the periodicity of their properties, substantiated by the finest experiments, that underlie physical optics. In those same years, Newton was developing the foundations of mathematical analysis, which became widely known from the correspondence of European scientists, although Newton himself did not publish a single line on this subject: Newton’s first publication on the foundations of analysis was published only in 1704. In 1687, Newton published his grandiose work, “Mathematical Principles of Natural Philosophy,” which laid the foundation not only for rational mechanics, but also for the entire mathematical science. In 1695, Newton received the position of Superintendent of the Mint. Newton was entrusted with the leadership of the re-minting of all English coins. He managed to put the disordered coinage of England in order, for which in 1699 he received the highly paid lifelong title of Director of the Mint. In 1705, Queen Anne elevated him to a knighthood for his scientific works. In the last years of his life, Newton devoted a lot of time to theology and ancient, biblical history. Newton was buried in the English national pantheon - Westminster Abbey.

There is probably not a single person in the world who does not know who Isaac Newton is. One of the world's most outstanding scientists, who made discoveries in several fields of science at once, giving rise to scientific directions in mathematics, optics, astronomy, one of the founding fathers classical physics. So, who is Isaac Newton? Today it is widely known short biography and his discoveries.

In contact with

The story of a scientist and explorer

One could say about him in the words of the poet Nikolai Tikhonov: “I should make nails out of these people. There couldn’t be any stronger nails in the world.” Born before his due date, very small and weak, he lived 84 years in perfect health, until a ripe old age, devoting wholeheartedly to the development of science and studying state affairs. Throughout his life, the scientist adhered to strong moral principles, was a model of honesty, and did not strive for publicity and fame. Even the will of King James II did not break him.

Childhood

The scientist considered his birth on the eve of Catholic Christmas to be a special sign of providence. After all, he managed to accomplish his greatest discoveries. Like a new star of Bethlehem, he illuminated many directions in which science subsequently developed. Many discoveries have been made thanks to the planned they are on their way.

Newton's father, who seemed an eccentric and strange man to his contemporaries, never found out about the birth of his son. A successful farmer and good owner, who lived only a few months before the birth of his son, left the family a significant farm and money.

WITH teenage years Having had a tender affection for his mother all his life, Isaac could not forgive her decision to leave him in the care of his grandparents after she married for the second time. The autobiography, compiled by him as a teenager, tells of outbursts of despair and children's plans for revenge against his mother and stepfather. He could only trust paper with the story of his emotional experiences; in life, the famous scientist was closed, didn't have close friends and was never married.

At the age of 12 he was sent to Grantham School. His closed and unsociable disposition, as well as his internal focus, turned his peers against him. From childhood, the future scientist preferred studying the natural sciences to boyish pranks. He read a lot, was interested in designing mechanical toys, and solving mathematical problems. Conflict situation with classmates encouraged the proud Newton to become best student at school.

Studying at Cambridge

Having been widowed, Newton's mother really hoped that her 16-year-old son would begin to help her with farming. But through the joint efforts of the school teacher, the boy's uncle and especially Humphrey Babington, a member of Trinity College, she was able to convince her of the need for further education. In 1661, Newton took an exam in Latin and enters Trinity College at the University of Cambridge. It was in this institution that for 30 years he studied science, conducted experiments and made world discoveries.

Instead of paying for his studies at the college, where the young man first lived as a student-sizer, he had to carry out some errands for richer students and other economic work around the university. Just 3 years later, in 1664, Newton passed the exams with honors and received an advanced student category, as well as the right not only to free education, but also to a scholarship.

His studies fascinated and inspired him so much that, according to the recollections of his classmates, he could forget about sleep and food. Still engaged in mechanics and designed various things and tools, was interested in mathematical calculations, astronomical observations, research in optics, philosophy, even music theory and history.

Deciding to devote his years of life to science, he gives up love and plans to start a family. The young pupil of the pharmacist Clark, who has school years He lived, also did not marry, and retained a tender memory of Newton throughout his life.

First steps in scientific activity

The year 1664 was an inspiring year for the young scientist. He compiles a “Questionnaire” of 45 scientific problems and sets himself the goal of solving them all.

Thanks to the lectures of the famous mathematician I. Barrow, Newton made his first discovery of the binomial expansion, which allowed him to subsequently develop the method of differential calculus, which is used today in higher mathematics. He passes the exam successfully and receives a bachelor's degree.

Even the plague epidemic of 1665 - 1667 could not stop this inquisitive mind and force him to sit idle. During the rampant illness, Newton went home, where he continued to engage in scientific activities. Here, in the privacy of home, he does most of his great discoveries:

• establishes basic methods of types of calculus - integral and differential;
• deduces the theory of color and gives rise to the development of optical science;
• finds a method for finding roots of quadratic equations;
• derives a formula for the expansion of an arbitrary natural power of a binomial.

Important! The famous apple tree, the observations of which helped in the discovery, was preserved as a memorial bench for the scientist.

Major discoveries

Isaac Newton a brief description of his activities. He was not just a genius, a famous scientist, but a person with diverse interests in many areas of science and technology. What is he famous for and what did he discover? A keen mathematician and physicist, he was equally well versed in both the exact sciences and the humanities. Economics, alchemy, philosophy, music and history - in all these areas the genius of his talent worked. Here is just a brief description of the great discoveries of Isaac Newton:

• developed a theory of the movement of celestial bodies - determined that the planets revolve around;
• formulated three important laws of mechanics;
• developed the theory of light and color shades;
• built the world's first mirror;
• discovered the Law of Gravity, thanks to which he became famous.

According to existing legend, Newton discovered the famous law while observing apples falling from an apple tree in his garden. Biographer of the famous scientist William Stukeley describes this moment in a book dedicated to the memories of Newton, which was published in 1752. According to Stukeley, it was an apple falling from a tree that gave him the idea of attraction of cosmic bodies and gravity.

“Why do apples fall perpendicular to the ground?” - thought Newton and, reflecting, deduced a new law. In the garden of the University of Cambridge, students revere and carefully care for a tree considered to be a descendant of the same “Newton’s apple tree”.

The falling of the apple served only as an impetus for the famous discovery. Newton went to him for many years, studying the works Galileo, Bullialda, Hooke, other astronomers and physicists. The scientist considered Keller’s Third Law to be another impulse. True, he composed the modern interpretation of the Law of Universal Gravitation somewhat later, when he studied the laws of mechanics.

Other scientific developments

The basis of classical mechanics is Newton’s Laws, the most important in the field of mechanics, which were formulated in a scientific work on mathematics and the principles of philosophy, published in 1687:

• the first Law of uniform motion in a straight line if no other forces act on the body;
• the second Law is , which in differential form describes the influence of acting forces on acceleration;
• the third Law is about the force of interaction between two bodies at a certain distance.

Currently these Newton's laws are an axiom.

Astronomy

At the end of 1669, the scientist received one of the most prestigious positions in the world at Trinity College, the named Lucasian professor of mathematics and optics. In addition to a £100 salary, bonuses and scholarships, there is the opportunity to devote more time own scientific research activities. Doing experiments in optics and the theory of light, Newton creates his first reflecting telescope.

Important! The improved telescope became the main instrument for astronomers and navigators of the time. With its help, the planet Uranus was discovered and other galaxies were discovered.

Studying the celestial bodies through his reflector, the scientist developed a theory of celestial bodies and determined the movement of planets around the Sun. Using the calculations of my reflector and applying a scientific approach to Bible study, I made my own message about the end of the world. According to his calculations, this event will take place in 2060.

Government activities

1696 The great scientist holds the position of keeper of the Mint and moved to London, where he lived until 1726. Having carried out financial accounting and established order in the documentation, he becomes Montagu's co-author on carrying out monetary reform.

During the period of his activity, a branch network of the Mint was created, and the production of silver coins increased several times. Newton introduces technology, allowing you to get rid of counterfeiters.

1699 Becomes manager of the Mint. In this post he continues to fight counterfeiters. His actions as manager were as brilliant as during his scientific career. Thanks to the reforms carried out in England economic crisis was averted.

1698 A report on Newton's economic reform was presented. While in England, Tsar Peter met with the famous professor three times. In 1700, a monetary reform similar to the English one was carried out in Russia.

1689 -1690. He was a representative of Cambridge University in the country's parliament. From 1703 to 1725 he served as President of the Royal Society.

Attention! In 1705, Queen Anne of Great Britain knighted Isaac Newton. This was the only time in English history that knighthood was awarded for scientific achievements.

Biography of Newton, his discoveries

The life of the great scientist Isaac Newton

Completion of life's journey

The last months of his life the professor lived in Kensington. The great scientist died on March 20, 1727. He died in his sleep and was buried on the grounds of Westminster Abbey in the tomb of the kings and most prominent people of England. All the townspeople came to say goodbye to their famous contemporary. The funeral procession was led by the Lord Chancellor himself, followed in the funeral procession by British ministers.

Wikipedia has articles about other people with this surname, see Newton.

Sir Isaac Newton(or Newton) (English) Sir Isaac Newton, December 25, 1642 - March 20, 1727 according to the Julian calendar, which was in force in England until 1752; or January 4, 1643 - March 31, 1727 according to the Gregorian calendar) - English physicist, mathematician, mechanic and astronomer, one of the founders of classical physics. The author of the fundamental work “Mathematical Principles of Natural Philosophy,” in which he outlined the law of universal gravitation and the three laws of mechanics, which became the basis of classical mechanics. He developed differential and integral calculus, color theory, laid the foundations of modern physical optics, and created many other mathematical and physical theories.

Biography

early years

Woolsthorpe. The house where Newton was born.

Isaac Newton was born in the village of Woolsthorpe. Woolsthorpe, Lincolnshire) on the eve civil war. Newton's father, a small but successful farmer Isaac Newton (1606-1642), did not live to see the birth of his son. The boy was born prematurely and was sickly, so they did not dare to baptize him for a long time. And yet he survived, was baptized (January 1), and named Isaac in memory of his father. Newton considered the fact of being born on Christmas a special sign of fate. Despite poor health in infancy, he lived to be 84 years old.

Newton sincerely believed that his family went back to the Scottish nobles of the 15th century, but historians discovered that in 1524 his ancestors were poor peasants. By the end of the 16th century, the family became rich and became yeomen (landowners). Newton's father left an inheritance of a large sum of 500 pounds sterling at that time and several hundred acres of fertile land occupied by fields and forests.

In January 1646, Newton's mother, Anne Ayscough Hannah Ayscough) (1623-1679) married again. She had three children with her new husband, a 63-year-old widower, and began to pay little attention to Isaac. The boy's patron was his maternal uncle, William Ayscough. As a child, Newton, according to contemporaries, was silent, withdrawn and isolated, loved to read and make technical toys: a sundial and water clock, a mill, etc. All his life he felt lonely.

His stepfather died in 1653, part of his inheritance went to Newton’s mother and was immediately registered by her in Isaac’s name. The mother returned home, but focused most of her attention on the three youngest children and the extensive household; Isaac was still left to his own devices.

In 1655, 12-year-old Newton was sent to study at a nearby school in Grantham, where he lived in the house of the pharmacist Clark. Soon the boy showed extraordinary abilities, but in 1659 his mother Anna returned him to the estate and tried to entrust part of the management of the household to her 16-year-old son. The attempt was not successful - Isaac preferred reading books, writing poetry, and especially designing various mechanisms to all other activities. At this time, Stokes, Newton's school teacher, approached Anna and began to persuade her to continue the education of her unusually gifted son; This request was joined by Uncle William and Isaac's Grantham acquaintance (relative of the pharmacist Clark) Humphrey Babington, a member of Trinity College Cambridge. With their combined efforts, they eventually achieved their goal. In 1661, Newton successfully graduated from school and went to continue his education at Cambridge University.

Trinity College (1661-1664)

Trinity College Clock Tower

In June 1661, 18-year-old Newton arrived in Cambridge. According to the charter, he was given an examination of his knowledge of the Latin language, after which he was informed that he had been admitted to Trinity College (College of the Holy Trinity) of the University of Cambridge. More than 30 years of Newton’s life are associated with this educational institution.

The college, like the entire university, was experiencing hard time. The monarchy had just been restored in England (1660), King Charles II often delayed payments due to the university, and dismissed a significant part of the teaching staff appointed during the revolution. In total, 400 people lived at Trinity College, including students, servants and 20 beggars, to whom, according to the charter, the college was obliged to give alms. The educational process was in a deplorable state.

Newton was classified as a "sizer" student. sizar), from whom tuition fees were not charged (probably on Babington's recommendation). According to the norms of that time, the sizer was obliged to pay for his education through various works at the University, or by providing services to wealthier students. Very little documentary evidence and memories of this period of his life have survived. During these years, Newton's character was finally formed - the desire to get to the bottom, intolerance to deception, slander and oppression, indifference to public fame. He still had no friends.

In April 1664, Newton, having passed the exams, moved to a higher student category of “students” ( scholars), which made him eligible for a scholarship to continue his studies at college.

Despite Galileo's discoveries, science and philosophy at Cambridge were still taught according to Aristotle. However, Newton's surviving notebooks already mention Galileo, Copernicus, Cartesianism, Kepler and Gassendi's atomic theory. Judging by these notebooks, he continued to make (mainly scientific instruments), and was enthusiastically engaged in optics, astronomy, mathematics, phonetics, and music theory. According to the memoirs of his roommate, Newton devoted himself wholeheartedly to his studies, forgetting about food and sleep; probably, despite all the difficulties, this was exactly the way of life that he himself desired.

Isaac Barrow. Statue at Trinity College.

The year 1664 in Newton's life was rich in other events. Newton experienced a creative surge, began independent scientific activity and compiled a large-scale list (of 45 points) of unsolved problems in nature and human life ( Questionnaire, lat. Questions quaedam philosophicae ). In the future, similar lists appear more than once in his workbooks. In March of the same year, lectures began at the college's newly founded (1663) mathematics department by a new teacher, 34-year-old Isaac Barrow, a major mathematician, Newton's future friend and teacher. Newton's interest in mathematics increased sharply. He made the first significant mathematical discovery: binomial expansion for an arbitrary rational exponent (including negative ones), and through it he came to his main mathematical method - the expansion of a function into an infinite series. At the very end of the year, Newton became a bachelor.

Scientific support and inspiration for Newton's creativity to the greatest extent there were physicists: Galileo, Descartes and Kepler. Newton completed their work by combining universal system peace. Other mathematicians and physicists had a lesser but significant influence: Euclid, Fermat, Huygens, Wallis and his immediate teacher Barrow. In Newton's student notebook there is a program phrase:

In philosophy there can be no sovereign except truth... We must erect gold monuments to Kepler, Galileo, Descartes and write on each one: “Plato is a friend, Aristotle is a friend, but the main friend is truth.”

"The Plague Years" (1665-1667)

On Christmas Eve 1664 London houses Red crosses began to appear - the first marks of the Great Plague Epidemic. By summer, the deadly epidemic had expanded significantly. On 8 August 1665, classes at Trinity College were suspended and the staff disbanded until the end of the epidemic. Newton went home to Woolsthorpe, taking with him the main books, notebooks and instruments.

These were disastrous years for England - a devastating plague (a fifth of the population died in London alone), a devastating war with Holland, and the Great Fire of London. But Newton made a significant part of his scientific discoveries in the solitude of the “plague years.” From the surviving notes it is clear that the 23-year-old Newton was already fluent in the basic methods of differential and integral calculus, including series expansion of functions and what was later called the Newton-Leibniz formula. After conducting a series of ingenious optical experiments, he proved that white color is a mixture of the colors of the spectrum. Newton later recalled these years:

At the beginning of 1665, I found the method of approximate series and the rule for transforming any power of a binomial into such a series... in November I received the direct method of fluxions [differential calculus]; in January of the following year I received the theory of colors, and in May I began the inverse method of fluxions [integral calculus] ... At this time I was experiencing the best time of my youth and was more interested in mathematics and [natural] philosophy than at any time later.

But his most significant discovery during these years was the law of universal gravitation. Later, in 1686, Newton wrote to Halley:

In papers written more than 15 years ago (I cannot give the exact date, but, in any case, it was before the beginning of my correspondence with Oldenburg), I expressed the inverse quadratic proportionality of the gravitational pull of the planets towards the Sun depending on the distance and calculated the correct ratio terrestrial gravity and the conatus recedendi [striving] of the Moon towards the center of the Earth, although not entirely accurately.

The revered descendant of "Newton's Apple Tree". Cambridge, Botanic Garden.

The inaccuracy mentioned by Newton was caused by the fact that Newton took the dimensions of the Earth and the magnitude of the acceleration of gravity from Galileo’s Mechanics, where they were given with a significant error. Later, Newton received more accurate data from Picard and was finally convinced of the truth of his theory.

There is a well-known legend that Newton discovered the law of gravity by observing an apple falling from a tree branch. For the first time, “Newton’s apple” was briefly mentioned by Newton’s biographer William Stukeley (book “Memoirs of the Life of Newton”, 1752):

After lunch, the weather became warm, we went out into the garden and drank tea in the shade of the apple trees. He [Newton] told me that the idea of ​​gravity came to him while he was sitting under a tree in the same way. He was in a contemplative mood when suddenly an apple fell from a branch. “Why do apples always fall perpendicular to the ground?” - he thought.

The legend became popular thanks to Voltaire. In fact, as can be seen from Newton's workbooks, his theory of universal gravitation developed gradually. Another biographer, Henry Pemberton, gives Newton's reasoning (without mentioning the apple) in more detail: "by comparing the periods of the several planets and their distances from the sun, he found that ... this force must decrease in quadratic proportion as the distance increases." In other words, Newton discovered that from Kepler’s third law, which relates the orbital periods of planets to the distance to the Sun, it follows precisely the “inverse square formula” for the law of gravity (in the approximation of circular orbits). Newton wrote out the final formulation of the law of gravitation, which was included in textbooks, later, after the laws of mechanics became clear to him.

These discoveries, as well as many of the later ones, were published 20-40 years later than they were made. Newton did not pursue fame. In 1670 he wrote to John Collins: “I see nothing desirable in fame, even if I were capable of earning it. This would perhaps increase the number of my acquaintances, but this is exactly what I try most to avoid.” Your first treatise(October 1666), which outlined the basics of the analysis, he did not publish; it was found only 300 years later.

Beginning of scientific fame (1667-1684)

Newton in his youth

In March-June 1666, Newton visited Cambridge. However, in the summer new wave The plague forced him to go home again. Finally, early in 1667, the epidemic subsided, and Newton returned to Cambridge in April. On October 1 he was elected a fellow of Trinity College, and in 1668 he became a master. He was allocated a spacious separate room to live in, assigned a salary (2 pounds per year) and was given a group of students with whom he conscientiously studied standard academic subjects for several hours a week. However, neither then nor later did Newton become famous as a teacher; his lectures were poorly attended.

Having strengthened his position, Newton traveled to London, where shortly before, in 1660, the Royal Society of London was created - an authoritative organization of prominent scientific figures, one of the first Academies of Sciences. The publication of the Royal Society was the journal Philosophical Transactions. Philosophical Transactions).

In 1669, mathematical works using expansions in infinite series began to appear in Europe. Although the depth of these discoveries could not be compared with Newton's, Barrow insisted that his student fix his priority in this matter. Newton wrote a brief but fairly complete summary of this part of his discoveries, which he called “Analysis by Equations with an Infinite Number of Terms.” Barrow sent this treatise to London. Newton asked Barrow not to reveal the name of the author of the work (but he still let it slip). “Analysis” spread among specialists and gained some fame in England and abroad.

In the same year, Barrow accepted the king's invitation to become a court chaplain and left teaching. On 29 October 1669, the 26-year-old Newton was elected as his successor, professor of mathematics and optics at Trinity College, with a high salary of £100 per annum. Barrow left Newton an extensive alchemical laboratory; During this period, Newton became seriously interested in alchemy and conducted a lot of chemical experiments.

Newton reflector

At the same time, Newton continued experiments in optics and color theory. Newton studied spherical and chromatic aberration. To reduce them to a minimum, he built a mixed reflecting telescope: a lens and a concave spherical mirror, which he made and polished himself. The project of such a telescope was first proposed by James Gregory (1663), but this plan was never realized. Newton's first design (1668) was unsuccessful, but the next one, with a more carefully polished mirror, despite its small size, provided a 40-fold magnification of excellent quality.

Rumors about the new instrument quickly reached London, and Newton was invited to show his invention to the scientific community. At the end of 1671 - beginning of 1672, a demonstration of the reflector took place before the king, and then at the Royal Society. The device received universal rave reviews. The practical importance of the invention probably also played a role: astronomical observations served to precise definition time, which in turn was necessary for navigation at sea. Newton became famous and in January 1672 was elected a member of the Royal Society. Later, improved reflectors became the main tools of astronomers, with their help the planet Uranus, other galaxies, and red shift were discovered.

At first, Newton valued his communication with colleagues from the Royal Society, which included, in addition to Barrow, James Gregory, John Wallis, Robert Hooke, Robert Boyle, Christopher Wren and other famous figures of English science. However, tedious conflicts soon began, which Newton really did not like. In particular, a noisy controversy erupted over the nature of light. It began with the fact that in February 1672 Newton published in the Philosophical Transactions detailed description his classical experiments with prisms and his theory of color. Hooke, who had previously published his own theory, stated that he was not convinced by Newton's results; he was supported by Huygens on the grounds that Newton's theory "contradicts generally accepted views." Newton responded to their criticism only six months later, but by this time the number of critics had increased significantly.

An avalanche of incompetent attacks left Newton irritated and depressed. Newton asked the secretary of the Oldenburg Society not to send him any more critical letters and made a vow for the future: not to get involved in scientific disputes. In his letters, he complains that he is faced with a choice: either not to publish his discoveries, or to spend all his time and energy repelling unfriendly amateur criticism. In the end he chose the first option and announced his resignation from the Royal Society (8 March 1673). It was not without difficulty that Oldenburg persuaded him to stay, but scientific contacts with the Society were kept to a minimum for a long time.

In 1673 there were two important events. First: by royal decree, Newton's old friend and patron, Isaac Barrow, returned to Trinity, now as the head ("master") of the college. Second: Leibniz, known at that time as a philosopher and inventor, became interested in Newton’s mathematical discoveries. Having received Newton's 1669 work on infinite series and studied it deeply, he then independently began to develop his own version of analysis. In 1676, Newton and Leibniz exchanged letters in which Newton explained a number of his methods, answered Leibniz's questions, and hinted at the existence of even more general methods, not yet published (meaning general differential and integral calculus). The Secretary of the Royal Society, Henry Oldenburg, persistently asked Newton to publish his mathematical discoveries on analysis for the glory of England, but Newton replied that he had been working on another topic for five years and did not want to be distracted. Newton did not respond to Leibniz's next letter. The first brief publication on Newton's version of analysis appeared only in 1693, when Leibniz's version had already spread widely throughout Europe.

The end of the 1670s was sad for Newton. In May 1677, 47-year-old Barrow died unexpectedly. In the winter of the same year, a strong fire broke out in Newton's house, and part of Newton's manuscript archive burned down. In September 1677, the secretary of the Royal Society, Oldenburg, who favored Newton, died, and Hooke, who was hostile to Newton, became the new secretary. In 1679, mother Anna became seriously ill; Newton, leaving all his affairs, came to her and received Active participation in caring for the patient, but the mother’s condition quickly deteriorated and she died. Mother and Barrow were among the few people who brightened up Newton's loneliness.

"Mathematical principles of natural philosophy" (1684-1686)

Title page of Newton's Principia

Main article: Mathematical principles of natural philosophy

The history of the creation of this work, one of the most famous in the history of science, began in 1682, when the passage of Halley's comet caused a rise in interest in celestial mechanics. Edmond Halley tried to persuade Newton to publish his “general theory of motion,” which had long been rumored in the scientific community. Newton, not wanting to be drawn into new scientific disputes and bickering, refused.

In August 1684, Halley came to Cambridge and told Newton that he, Wren and Hooke had discussed how to derive the ellipticity of planetary orbits from the formula for the law of gravity, but did not know how to approach the solution. Newton reported that he already had such a proof, and in November he sent Halley the finished manuscript. He immediately appreciated the significance of the result and the method, immediately visited Newton again and this time managed to persuade him to publish his discoveries. On December 10, 1684, a historical entry appeared in the minutes of the Royal Society:

Mr. Halley... recently saw Mr. Newton in Cambridge, and he showed him an interesting treatise "De motu" [On Motion]. According to the wishes of Mr. Halley, Newton promised to send the said treatise to the Society.

Work on the book took place in 1684-1686. According to the recollections of Humphrey Newton, a relative of the scientist and his assistant during these years, at first Newton wrote “Principia” in between alchemical experiments, to which he paid the main attention, then he gradually became carried away and enthusiastically devoted himself to working on the main book of his life.

The publication was supposed to be carried out with funds from the Royal Society, but at the beginning of 1686 the Society published a treatise on the history of fish that was not in demand, and thereby depleted its budget. Then Halley announced that he would bear the costs of publication himself. The Society gratefully accepted this generous offer and, as partial compensation, provided Halley with 50 free copies of a treatise on the history of fish.

Newton's work - perhaps by analogy with Descartes's "Principles of Philosophy" (1644) or, according to some historians of science, as a challenge to the Cartesians - was called "Mathematical principles of natural philosophy" (lat. Philosophiae Naturalis Principia Mathematica ), that is, in modern language, “Mathematical foundations of physics”.

On April 28, 1686, the first volume of "Mathematical Principles" was presented to the Royal Society. All three volumes, after some editing by the author, were published in 1687. The circulation (about 300 copies) was sold out in 4 years - very quickly for that time.

A page from Newton's Principia (3rd ed., 1726)

Both the physical and mathematical level of Newton's work are completely incomparable with the work of his predecessors. It lacks Aristotelian or Cartesian metaphysics, with its vague reasoning and vaguely formulated, often far-fetched “first causes” of natural phenomena. Newton, for example, does not proclaim that the law of gravity operates in nature, he strictly proves this fact, based on the observed picture of the movement of the planets and their satellites. Newton's method is to create a model of a phenomenon, “without inventing hypotheses,” and then, if there is enough data, to search for its causes. This approach, which began with Galileo, meant the end of old physics. A qualitative description of nature has given way to a quantitative one - a significant part of the book is occupied by calculations, drawings and tables.

In his book, Newton clearly defined the basic concepts of mechanics, and introduced several new ones, including such important physical quantities as mass, external force and momentum. Three laws of mechanics are formulated. A rigorous derivation from the law of gravity of all three Kepler laws is given. Note that hyperbolic and parabolic orbits of celestial bodies unknown to Kepler were also described. The truth of Copernicus's heliocentric system is not directly discussed by Newton, but implied; it even estimates the deviation of the Sun from the solar system's center of mass. In other words, the Sun in Newton’s system, unlike Keplerian’s, is not at rest, but obeys the general laws of motion. The general system also included comets, the type of orbits of which caused great controversy at that time.

The weak point of Newton's theory of gravity, according to many scientists of that time, was the lack of explanation of the nature of this force. Newton outlined only the mathematical apparatus, leaving open questions about the cause of gravity and its material carrier. For the scientific community, brought up on the philosophy of Descartes, this was an unusual and challenging approach, and only the triumphant success of celestial mechanics in the 18th century forced physicists to temporarily reconcile with Newtonian theory. The physical basis of gravity became clear only more than two centuries later, with the advent of the General Theory of Relativity.

Newton built the mathematical apparatus and general structure of the book as close as possible to the then standard of scientific rigor - Euclid's Elements. He deliberately did not use mathematical analysis almost anywhere - the use of new, unusual methods would have jeopardized the credibility of the results presented. This caution, however, devalued Newton's method of presentation for subsequent generations of readers. Newton's book was the first work on new physics and at the same time one of the last serious works using old methods of mathematical research. All of Newton's followers already used the powerful methods of mathematical analysis he created. The largest direct successors of Newton's work were D'Alembert, Euler, Laplace, Clairaut and Lagrange.

Administrative activity (1687-1703)

The year 1687 was marked not only by the publication of the great book, but also by Newton’s conflict with King James II. In February, the king, consistently pursuing his line for the restoration of Catholicism in England, ordered the University of Cambridge to give a master's degree to the Catholic monk Alban Francis. The university leadership hesitated, not wanting to either break the law or irritate the king; Soon, a delegation of scientists, including Newton, was summoned for reprisals to the Lord Chief Justice, George Jeffreys, known for his rudeness and cruelty. George Jeffreys). Newton opposed any compromise that would impair university autonomy and persuaded the delegation to take a principled stand. As a result, the vice-chancellor of the university was removed from office, but the king’s wish was never fulfilled. In one of his letters these years, Newton outlined his political principles:

Every honest person, according to the laws of God and man, is obliged to obey the lawful orders of the king. But if His Majesty is advised to demand something that cannot be done by law, then no one should suffer if such a demand is neglected.

In 1689, after the overthrow of King James II, Newton was first elected to Parliament from Cambridge University and sat there for little more than a year. The second election took place in 1701-1702. There is a popular anecdote that he took the floor to speak in the House of Commons only once, asking that the window be closed to avoid a draft. In fact, Newton carried out his parliamentary duties with the same conscientiousness with which he treated all his affairs.

Around 1691, Newton became seriously ill (most likely, he was poisoned during chemical experiments, although there are other versions - overwork, shock after a fire, which led to the loss of important results, and age-related ailments). Those close to him feared for his sanity; the few surviving letters of his from this period do indicate mental disorder. Only at the end of 1693 did Newton's health fully recover.

In 1679, Newton met at Trinity an 18-year-old aristocrat, a lover of science and alchemy, Charles Montagu (1661-1715). Newton probably made a strong impression on Montagu, because in 1696, having become Lord Halifax, President of the Royal Society and Chancellor of the Exchequer (that is, the Minister of the Exchequer of England), Montagu proposed to the King that Newton be appointed Warden of the Mint. The king gave his consent, and in 1696 Newton took this position, left Cambridge and moved to London. From 1699 he became the manager (“master”) of the Mint.

To begin with, Newton thoroughly studied the technology of coin production, put the paperwork in order, and redid the accounting over the past 30 years. At the same time, Newton energetically and skillfully contributed to Montagu's monetary reform, restoring confidence in the English monetary system, which had been thoroughly neglected by his predecessors. In England during these years, almost exclusively inferior coins were in circulation, and in considerable quantities counterfeit coins were in circulation. Trimming the edges of silver coins became widespread. Now the coins began to be produced on special machines and there was an inscription along the rim, so that criminal grinding of the metal became almost impossible. Over the course of 2 years, the old, inferior silver coin was completely withdrawn from circulation and re-minted, the production of new coins increased to keep up with the need for them, and their quality improved. Previously, during such reforms, the population had to change old money by weight, after which the volume of cash decreased both among individuals (private and legal) and throughout the country, but interest and loan obligations remained the same, which is why the economy began stagnation. Newton proposed exchanging money at par, which prevented these problems, and the inevitable shortage of funds after this was made up for by taking loans from other countries (most of all from the Netherlands), inflation dropped sharply, but the external public debt grew by the middle of the century to levels unprecedented in the history of England sizes. But during this time, noticeable economic growth occurred, because of it, tax contributions to the treasury increased (equal in size to those of France, despite the fact that France was inhabited by 2.5 times more people), due to this, the national debt was gradually paid off.

However, an honest and competent person at the head of the Mint did not suit everyone. From the very first days, complaints and denunciations rained down on Newton, and inspection commissions constantly appeared. As it turned out, many denunciations came from counterfeiters, irritated by Newton's reforms. Newton, as a rule, was indifferent to slander, but never forgave if it affected his honor and reputation. He was personally involved in dozens of investigations, and more than 100 counterfeiters were tracked down and convicted; in the absence of aggravating circumstances, they were most often sent to the North American colonies, but several leaders were executed. The number of counterfeit coins in England has decreased significantly. Montagu, in his memoirs, highly appreciated the extraordinary administrative abilities shown by Newton and ensured the success of the reform. Thus, the reforms carried out by the scientist not only prevented an economic crisis, but also, decades later, led to a significant increase in the country’s well-being.

In April 1698, the Russian Tsar Peter I visited the Mint three times during the “Great Embassy”; Unfortunately, the details of his visit and communication with Newton have not been preserved. It is known, however, that in 1700 a monetary reform similar to the English one was carried out in Russia. And in 1713, Newton sent the first six printed copies of the 2nd edition of the Principia to Tsar Peter in Russia.

Newton's scientific triumph was symbolized by two events in 1699: the teaching of Newton's world system began at Cambridge (from 1704 at Oxford), and the Paris Academy of Sciences, the stronghold of his Cartesian opponents, elected him as a foreign member. All this time Newton was still listed as a member and professor of Trinity College, but in December 1701 he officially resigned from all his posts at Cambridge.

In 1703, the President of the Royal Society, Lord John Somers, died, having attended the meetings of the Society only twice during the 5 years of his presidency. In November, Newton was elected as his successor and ruled the Society for the rest of his life - more than twenty years. Unlike his predecessors, he was personally present at all meetings and did everything to ensure that the British Royal Society took an honorable place in the scientific world. The number of members of the Society grew (among them, in addition to Halley, one can highlight Denis Papin, Abraham de Moivre, Roger Coates, Brooke Taylor), interesting experiments were carried out and discussed, the quality of journal articles improved significantly, financial problems were mitigated. The society acquired paid secretaries and its own residence (on Fleet Street); Newton paid the moving expenses out of his own pocket. During these years, Newton was often invited as a consultant to various government commissions, and Princess Caroline, the future Queen of Great Britain, spent hours talking with him in the palace on philosophical and religious topics.

Last years

One of the last portraits of Newton (1712, Thornhill)

In 1704, the monograph “Optics” was published (first in English), which determined the development of this science until the beginning of the 19th century. It contained an appendix “On the quadrature of curves” - the first and fairly complete presentation of Newton’s version of mathematical analysis. In fact, this is Newton's last work on the natural sciences, although he lived for more than 20 years. The catalog of the library he left behind contained books mainly on history and theology, and it was to these pursuits that Newton devoted the rest of his life. Newton remained the manager of the Mint, since this post, unlike the position of superintendent, did not require much activity from him. Twice a week he went to the Mint, once a week to a meeting of the Royal Society. Newton never traveled outside of England.

In 1705, Queen Anne knighted Newton. From now on he Sir Isaac Newton. For the first time in English history the title of knight was awarded for scientific merits; the next time it happened was more than a century later (1819, in reference to Humphry Davy). However, some biographers believe that the queen was guided not by scientific, but by political motives. Newton acquired his own coat of arms and a not very reliable pedigree.

In 1707, a collection of Newton's lectures on algebra, called “Universal Arithmetic,” was published. The numerical methods presented in it marked the birth of a new promising discipline - numerical analysis.

Newton's tomb in Westminster Abbey

In 1708, an open priority dispute with Leibniz began (see below), in which even the reigning persons were involved. This quarrel between two geniuses cost science dearly - the English mathematical school soon reduced activity for a whole century, and the European school ignored many of Newton’s outstanding ideas, rediscovering them much later. Even the death of Leibniz (1716) did not extinguish the conflict.

The first edition of Newton's Principia has long been sold out. Newton's many years of work to prepare the 2nd edition, revised and expanded, was crowned with success in 1710, when the first volume of the new edition was published (the last, third - in 1713). The initial circulation (700 copies) turned out to be clearly insufficient; there were additional printings in 1714 and 1723. When finalizing the second volume, Newton, as an exception, had to return to physics to explain the discrepancy between theory and experimental data, and he immediately made a major discovery - hydrodynamic compression of the jet. The theory now agreed well with experiment. Newton added an Instruction to the end of the book with a scathing critique of the “vortex theory” with which his Cartesian opponents tried to explain the motion of the planets. To the natural question “how is it really?” the book follows the famous and honest answer: “I still have not been able to deduce the cause... of the properties of the force of gravity from phenomena, and I do not invent hypotheses.”

In April 1714, Newton summarized his experience of financial regulation and submitted his article “Observations Concerning the Value of Gold and Silver” to the Treasury. The article contained specific proposals for adjusting the cost of precious metals. These proposals were partially accepted, and this had a beneficial effect on the British economy.

The indignant investors of the South Sea Company were satirically captured by Edward Matthew Ward

Shortly before his death, Newton became one of the victims of a financial scam by a large trading company, the South Sea Company, which was supported by the government. He purchased the company's securities for a large sum, and also insisted on their acquisition by the Royal Society. On September 24, 1720, the company bank declared itself bankrupt. Niece Catherine recalled in her notes that Newton lost more than 20,000 pounds, after which he declared that he could calculate the movement of celestial bodies, but not the degree of madness of the crowd. However, many biographers believe that Catherine did not mean a real loss, but a failure to receive the expected profit. After the company's bankruptcy, Newton offered to compensate the Royal Society for the losses from his own pocket, but his offer was rejected.

Newton devoted the last years of his life to writing the Chronology of Ancient Kingdoms, which he worked on for about 40 years, as well as preparing the third edition of the Principia, which was published in 1726. Unlike the second, the changes in the third edition were minor - mainly the results of new astronomical observations, including a fairly comprehensive guide to comets observed since the 14th century. Among others, the calculated orbit of Halley's comet was presented, the reappearance of which at the indicated time (1758) clearly confirmed the theoretical calculations of the (by then deceased) Newton and Halley. The circulation of the book for a scientific publication of those years could be considered huge: 1250 copies.

In 1725, Newton's health began to deteriorate noticeably, and he moved to Kensington near London, where he died at night, in his sleep, on March 20 (31), 1727. He did not leave a written will, but shortly before his death he transferred a significant part of his large fortune to his closest relatives. Buried in Westminster Abbey.

Personal qualities

Character traits

It is difficult to draw up a psychological portrait of Newton, since even people who sympathize with him often attribute various qualities to Newton. We also have to take into account the cult of Newton in England, which forced the authors of memoirs to endow the great scientist with all conceivable virtues, ignoring the real contradictions in his nature. In addition, by the end of his life, Newton’s character acquired such traits as good nature, condescension and sociability, which were previously not characteristic of him.

In appearance, Newton was short, strongly built, with wavy hair. He was almost never sick, and until old age he retained his thick hair (already completely gray since he was 40) and all his teeth except one. I never (according to other sources, almost never) used glasses, although I was slightly myopic. He almost never laughed or got irritated; there is no mention of his jokes or other manifestations of his sense of humor. In financial transactions he was careful and thrifty, but not stingy. Never married. He was usually in a state of deep internal concentration, which is why he often showed absent-mindedness: for example, once, having invited guests, he went to the pantry to get wine, but then some scientific idea dawned on him, he rushed to the office and never returned to the guests . He was indifferent to sports, music, art, theater, and travel, although he knew how to draw well. His assistant recalled: “He did not allow himself any rest or respite ... he considered every hour not devoted to [science] to be lost ... I think he was quite saddened by the need to waste time on eating and sleeping.” With all that has been said, Newton managed to combine everyday practicality and common sense, clearly manifested in his successful management Mint and the Royal Society.

Brought up in Puritan traditions, Newton established for himself a number of strict principles and self-restraints. And he was not inclined to forgive others what he would not forgive himself; this is the root of many of his conflicts (see below). He treated his relatives and many colleagues warmly, but had no close friends, did not seek the company of other people, and remained aloof. At the same time, Newton was not heartless and indifferent to the fate of others. When, after the death of his half-sister Anna, her children were left without a means of support, Newton assigned an allowance to the minor children, and later took Anna’s daughter, Katherine, into his care. He constantly helped other relatives. “Being economical and prudent, he was at the same time very free with money and was always ready to help a friend in need, without being intrusive. He is especially noble towards young people.” Many famous English scientists - Stirling, Maclaurin, astronomer James Pound and others - recalled with deep gratitude the help provided by Newton at the beginning of their scientific careers.

Conflicts

Newton and Hooke

Robert Hooke. Reconstruction of appearance based on verbal descriptions of contemporaries.

In 1675, Newton sent the Society his treatise with new research and speculation on the nature of light. Robert Hooke stated at the meeting that everything that is valuable in the treatise is already available in Hooke’s previously published book “Micrography”. In private conversations, he accused Newton of plagiarism: “I showed that Mr. Newton used my hypotheses about impulses and waves” (from Hooke’s diary). Hooke disputed the priority of all of Newton's discoveries in the field of optics, except those with which he did not agree. Oldenburg immediately informed Newton about these accusations, and he regarded them as insinuations. This time the conflict was resolved, and the scientists exchanged letters of conciliation (1676). However, from that moment until Hooke’s death (1703), Newton did not publish any work on optics, although he accumulated a huge amount of material, which he systematized in the classic monograph “Optics” (1704).

Another priority dispute was related to the discovery of the law of gravity. Back in 1666, Hooke came to the conclusion that the movement of planets is a superposition of falling on the Sun due to the force of attraction to the Sun, and movement by inertia tangential to the trajectory of the planet. In his opinion, this superposition of motion determines the elliptical shape of the planet’s trajectory around the Sun. However, he could not prove this mathematically and sent a letter to Newton in 1679, where he offered cooperation in solving this problem. This letter also stated the assumption that the force of attraction to the Sun decreases in inverse proportion to the square of the distance. In response, Newton noted that he had previously worked on the problem of planetary motion, but abandoned these studies. Indeed, as subsequently found documents show, Newton dealt with the problem of planetary motion back in 1665-1669, when, on the basis of Kepler’s III law, he established that “the tendency of the planets to move away from the Sun will be inversely proportional to the squares of their distances from the Sun.” However, in those years he had not yet fully developed the idea of ​​the planet’s orbit as solely the result of the equality of the forces of attraction to the Sun and centrifugal force.

Subsequently, correspondence between Hooke and Newton was interrupted. Hooke returned to attempts to construct the trajectory of the planet under the influence of a force that decreases according to the inverse square law. However, these attempts were also unsuccessful. Meanwhile, Newton returned to the study of planetary motion and solved this problem.

When Newton was preparing his Principia for publication, Hooke demanded that Newton stipulate in the preface Hooke's priority regarding the law of gravitation. Newton countered that Bulliald, Christopher Wren, and Newton himself arrived at the same formula independently and before Hooke. A conflict broke out, which greatly poisoned the lives of both scientists.

Modern authors pay tribute to both Newton and Hooke. Hooke's priority is to formulate the problem of constructing the trajectory of the planet due to the superposition of its fall on the Sun according to the inverse square law and motion by inertia. It is also possible that it was Hooke's letter that directly pushed Newton to complete the solution to this problem. However, Hooke himself did not solve the problem, and also did not guess about the universality of gravity. According to S.I. Vavilov,

If we combine into one all of Hooke’s assumptions and thoughts about the motion of planets and gravitation, expressed by him for almost 20 years, then we will encounter almost all the main conclusions of Newton’s “Principles”, only expressed in an uncertain and little evidence-based form. Without solving the problem, Hooke found the answer. At the same time, what we have before us is not at all a random thought, but undoubtedly the fruit of many years of work. Hooke had the brilliant guess of an experimental physicist who discerned the true relationships and laws of nature in the labyrinth of facts. We encounter similar rare intuition of an experimenter in the history of science in Faraday, but Hooke and Faraday were not mathematicians. Their work was completed by Newton and Maxwell. The aimless struggle with Newton for priority cast a shadow on the glorious name of Hooke, but it is time for history, after almost three centuries, to give everyone their due. Hooke could not follow the straight, impeccable path of Newton’s “Principles of Mathematics,” but with his roundabout paths, traces of which we can no longer find, he arrived there.

Subsequently, Newton's relationship with Hooke remained tense. For example, when Newton presented the Society with a new design for a sextant, Hooke immediately stated that he had invented such a device more than 30 years ago (although he had never built a sextant). Nevertheless, Newton was aware of the scientific value of Hooke’s discoveries and in his “Optics” he mentioned his now deceased opponent several times.

In addition to Newton, Hooke had priority disputes with many other English and continental scientists, including Robert Boyle, whom he accused of appropriating the improvement of the air pump, as well as with the secretary of the Royal Society Oldenburg, claiming that with Oldenburg's help Huygens stole Hooke's idea watch with a spiral spring.

The myth that Newton allegedly ordered the destruction of Hooke's only portrait is being examined.

Newton and Flamsteed

John Flamsteed.

John Flamsteed, an outstanding English astronomer, met Newton in Cambridge (1670), when Flamsteed was still a student and Newton a master. However, already in 1673, almost simultaneously with Newton, Flamsteed also became famous - he published astronomical tables of excellent quality, for which the king awarded him a personal audience and the title “Royal Astronomer”. Moreover, the king ordered the construction of an observatory in Greenwich near London and transfer it to Flamsteed. However, the king considered the money to equip the observatory to be an unnecessary expense, and almost all of Flamsteed’s income went to the construction of instruments and the economic needs of the observatory.

Greenwich Observatory, old building

At first, Newton and Flamsteed's relationship was cordial. Newton was preparing the second edition of the Principia and was in dire need of accurate observations of the Moon to construct and (as he hoped) confirm his theory of its motion; In the first edition, the theory of the motion of the Moon and comets was unsatisfactory. This was also important for the establishment of Newton’s theory of gravitation, which was sharply criticized by the Cartesians on the continent. Flamsteed willingly gave him the requested data, and in 1694 Newton proudly informed Flamsteed that a comparison of calculated and experimental data showed their practical agreement. In some letters, Flamsteed urgently asked Newton, in the case of using observations, to stipulate his, Flamsteed's, priority; this primarily applied to Halley, whom Flamsteed did not like and suspected of scientific dishonesty, but it could also mean a lack of trust in Newton himself. Flamsteed's letters begin to show resentment:

I agree: the wire is more expensive than the gold from which it is made. However, I collected this gold, cleaned and washed it, and I do not dare to think that you value my help so little just because you received it so easily.

The open conflict began with a letter from Flamsteed, in which he apologetically reported that he had discovered a number of systematic errors in some of the data provided to Newton. This jeopardized Newton's theory of the Moon and forced the calculations to be redone, and confidence in the remaining data was also shaken. Newton, who hated dishonesty, was extremely irritated and even suspected that the errors were deliberately introduced by Flamsteed.

In 1704, Newton visited Flamsteed, who by this time had received new, extremely accurate observational data, and asked him to convey this data; in return, Newton promised to help Flamsteed in publishing his main work, the Great Star Catalog. Flamsteed, however, began to delay for two reasons: the catalog was not yet completely ready, and he no longer trusted Newton and was afraid of theft of his priceless observations. Flamsteed used the experienced calculators provided to him to complete the work to calculate the positions of the stars, while Newton was primarily interested in the Moon, planets and comets. Finally, in 1706, printing of the book began, but Flamsteed, suffering from agonizing gout and becoming increasingly suspicious, demanded that Newton not open the sealed copy until printing was completed; Newton, who urgently needed the data, ignored this prohibition and wrote down the necessary values. The tension grew. Flamsteed confronted Newton for attempting to personally correct minor errors. The printing of the book was extremely slow.

Due to financial difficulties, Flamsteed failed to pay his membership fee and was expelled from the Royal Society; a new blow was dealt by the queen, who, apparently at Newton’s request, transferred control functions over the observatory to the Society. Newton gave Flamsteed an ultimatum:

You have presented an imperfect catalog, in which much is missing, you have not given the positions of the stars that were desired, and I have heard that the printing has now stopped due to their failure to provide them. You are therefore expected to either send the end of your catalog to Dr. Arbuthnot, or at least send him the observations necessary to complete it so that printing can continue.

Newton also threatened that further delays would be considered disobedience to Her Majesty's orders. In March 1710, Flamsteed, after heated complaints about injustice and the machinations of enemies, nevertheless handed over the final pages of his catalog, and at the beginning of 1712 the first volume, entitled “Heavenly History,” was published. It contained all the data Newton needed, and a year later, a revised edition of the Principia, with a much more accurate theory of the Moon, also quickly appeared. The vindictive Newton did not include gratitude to Flamsteed in the edition and crossed out all references to him that were present in the first edition. In response, Flamsteed burned all the unsold 300 copies of the catalog in his fireplace and began preparing its second edition, this time to his own taste. He died in 1719, but through the efforts of his wife and friends this wonderful publication, the pride of English astronomy, was published in 1725.

Newton and Leibniz

Gottfried Leibniz

From surviving documents, historians of science have found out that Newton discovered differential and integral calculus back in 1665-1666, but did not publish it until 1704. Leibniz developed his version of the calculus independently (from 1675), although the initial impetus for his thought probably came from rumors that Newton already had such a calculus, as well as through scientific conversations in England and correspondence with Newton. Unlike Newton, Leibniz immediately published his version, and later, together with Jacob and Johann Bernoulli, widely propagated this epoch-making discovery throughout Europe. Most scientists on the continent had no doubt that Leibniz had discovered analysis.

Having heeded the persuasion of friends who appealed to his patriotism, Newton, in the 2nd book of his “Principles” (1687), said:

In letters which I exchanged about ten years ago with the very skilful mathematician Mr. Leibniz, I informed him that I had a method for determining maxima and minima, drawing tangents and solving similar questions, equally applicable to both rational and rational terms. for irrational ones, and I hid the method by rearranging the letters of the following sentence: “when given an equation containing any number of current quantities, find the fluxions and vice versa.” The most famous man answered me that he also attacked such a method and told me his method, which turned out to be barely different from mine, and then only in terms and outline of formulas.

Our Wallis added to his “Algebra”, which had just appeared, some of the letters that I wrote to you at one time. At the same time, he demanded that I openly state the method that I at that time hid from you by rearranging the letters; I made it as short as I could. I hope that I did not write anything that would be unpleasant for you, but if this happened, then please let me know, because friends are dearer to me than mathematical discoveries.

After the first detailed publication of Newton's analysis (mathematical appendix to Optics, 1704) appeared in Leibniz's journal Acta eruditorum, an anonymous review appeared with insulting allusions to Newton. The review clearly indicated that the author of the new calculus was Leibniz. Leibniz himself strongly denied that he had written the review, but historians were able to find a draft written in his handwriting. Newton ignored Leibniz's paper, but his students responded indignantly, after which a pan-European priority war broke out, "the most shameful squabble in the entire history of mathematics."

On January 31, 1713, the Royal Society received a letter from Leibniz containing a conciliatory formulation: he agreed that Newton arrived at the analysis independently, “on general principles similar to ours.” An angry Newton demanded the creation of an international commission to clarify priority. The commission did not need much time: after a month and a half, having studied Newton’s correspondence with Oldenburg and other documents, it unanimously recognized Newton’s priority, and in wording, this time offensive to Leibniz. The commission's decision was published in the proceedings of the Society with all supporting documents attached. In response, from the summer of 1713, Europe was flooded with anonymous pamphlets that defended Leibniz's priority and argued that "Newton arrogates to himself the honor that belongs to another." The pamphlets also accused Newton of stealing the results of Hooke and Flamsteed. Newton's friends, for their part, accused Leibniz himself of plagiarism; According to their version, during his stay in London (1676), Leibniz at the Royal Society became acquainted with Newton’s unpublished works and letters, after which Leibniz published the ideas expressed there and passed them off as his own.

The war continued unabated until December 1716, when Abbé Conti informed Newton: “Leibniz is dead—the dispute is over.”

Scientific activity

A new era in physics and mathematics is associated with Newton's work. He completed the creation of theoretical physics, begun by Galileo, based, on the one hand, on experimental data, and on the other, on a quantitative and mathematical description of nature. Powerful analytical methods are emerging in mathematics. In physics, the main method of studying nature is the construction of adequate mathematical models of natural processes and intensive research of these models with the systematic use of the full power of the new mathematical apparatus. Subsequent centuries have proven the exceptional fruitfulness of this approach.

Philosophy and scientific method

Newton resolutely rejected the approach of Descartes and his Cartesian followers, popular at the end of the 17th century, which prescribed that when constructing a scientific theory, one must first use the “discernment of the mind” to find the “root causes” of the phenomenon under study. In practice, this approach often led to the formulation of far-fetched hypotheses about “substances” and “hidden properties” that were not amenable to experimental verification. Newton believed that in “natural philosophy” (that is, physics), only such assumptions (“principles”, now prefer the name “laws of nature”) are permissible that directly follow from reliable experiments and generalize their results; He called hypotheses assumptions that were not sufficiently substantiated by experiments. “Everything... that is not deduced from phenomena should be called a hypothesis; hypotheses of metaphysical, physical, mechanical, hidden properties have no place in experimental philosophy.” Examples of principles are the law of gravity and the 3 laws of mechanics in Principia; the word "principles" ( Principia Mathematica, traditionally translated as “mathematical principles”) is also contained in the title of his main book.

In a letter to Pardiz, Newton stated: Golden Rule Sciences":

The best and most safe method philosophizing, it seems to me, should first be a diligent study of the properties of things and the establishment of these properties through experiments, and then gradual progress towards hypotheses that explain these properties. Hypotheses can be useful only in explaining the properties of things, but there is no need to burden them with the responsibility of determining these properties beyond the limits revealed by experiment ... after all, many hypotheses can be invented to explain any new difficulties.

This approach not only placed speculative fantasies outside of science (for example, the Cartesians’ reasoning about the properties of “subtle matters” that allegedly explained electromagnetic phenomena), but was more flexible and fruitful because it allowed mathematical modeling of phenomena for which the root causes had not yet been discovered. This is what happened with gravity and the theory of light - their nature became clear much later, which did not interfere with the successful centuries-old use of Newtonian models.

The famous phrase “I don’t invent hypotheses” (lat. Hypotheses non fingo), of course, does not mean that Newton underestimated the importance of finding “first causes” if they are clearly confirmed by experience. Obtained from experiment general principles and the consequences from them must also undergo experimental testing, which may lead to an adjustment or even a change in principles. “The whole difficulty of physics... consists in recognizing the forces of nature from the phenomena of motion, and then using these forces to explain other phenomena.”

Newton, like Galileo, believed that mechanical motion underlies all natural processes:

It would be desirable to deduce from the principles of mechanics and other natural phenomena... for much makes me assume that all these phenomena are determined by certain forces with which the particles of bodies, due to reasons as yet unknown, either tend to each other and interlock into regular figures, or mutually repel and move away from each other. Since these forces are unknown, until now the attempts of philosophers to explain natural phenomena have remained fruitless.

Newton formulated his scientific method in his book “Optics”:

As in mathematics, so in the testing of nature, in the investigation of difficult questions, the analytical method must precede the synthetic one. This analysis consists in drawing general conclusions from experiments and observations by induction and not allowing any objections against them that do not proceed from experiments or other reliable truths. For hypotheses are not considered in experimental philosophy. Although the results obtained through induction from experiments and observations cannot yet serve as proof of universal conclusions, this is still the best way to draw conclusions, which the nature of things allows.

In the 3rd book of the Elements (starting from the 2nd edition), Newton placed a number of methodological rules directed against the Cartesians; The first of them is a variant of Occam's razor:

Rule I. One must not accept other causes in nature than those that are true and sufficient to explain phenomena... nature does nothing in vain, and it would be in vain for many to do what can be done by fewer. Nature is simple and does not luxury with superfluous causes of things...

Rule IV. In experimental physics, propositions derived from occurring phenomena by means of induction, despite the possibility of assumptions contrary to them, should be considered true either exactly or approximately, until such phenomena are discovered that they are further refined or are subject to exceptions.

Newton's mechanistic views turned out to be incorrect - not all natural phenomena follow from mechanical movement. However, his scientific method became established in science. Modern physics successfully explores and applies phenomena whose nature has not yet been clarified (for example, elementary particles). Since Newton, natural science has developed with the firm belief that the world is knowable because nature is organized according to simple mathematical principles. This confidence became the philosophical basis for the tremendous progress of science and technology.

Mathematics

Newton made his first mathematical discoveries back in student years: classification of algebraic curves of the 3rd order (curves of the 2nd order were studied by Fermat) and binomial expansion of an arbitrary (not necessarily integer) degree, from which Newton’s theory of infinite series begins - a new and powerful tool of analysis. Newton considered series expansion to be the main and general method of analyzing functions, and in this matter he reached the heights of mastery. He used series to calculate tables, solve equations (including differential ones), and study the behavior of functions. Newton was able to obtain expansions for all the functions that were standard at that time.

Newton developed differential and integral calculus simultaneously with G. Leibniz (a little earlier) and independently of him. Before Newton, actions with infinitesimals were not linked into a single theory and were in the nature of disparate ingenious techniques (see Method of Indivisibles). The creation of a systemic mathematical analysis reduces the solution of relevant problems, to a large extent, to the technical level. A complex of concepts, operations and symbols appeared, which became the starting point for the further development of mathematics. The next century, the 18th century, was a century of rapid and extremely successful development of analytical methods.

Perhaps Newton came to the idea of ​​analysis through difference methods, which he studied a lot and deeply. True, in his “Principles” Newton almost did not use infinitesimals, adhering to ancient (geometric) methods of proof, but in other works he used them freely.

The starting point for differential and integral calculus were the works of Cavalieri and especially Fermat, who already knew how (for algebraic curves) to draw tangents, find extrema, inflection points and curvature of a curve, and calculate the area of ​​its segment. Among other predecessors, Newton himself named Wallis, Barrow and the Scottish scientist James Gregory. There was no concept of a function yet; he interpreted all curves kinematically as trajectories of a moving point.

Already as a student, Newton realized that differentiation and integration are mutually inverse operations. This fundamental theorem of analysis had already emerged more or less clearly in the works of Torricelli, Gregory and Barrow, but only Newton realized that on this basis it was possible to obtain not only individual discoveries, but a powerful systemic calculus, similar to algebra, with clear rules and gigantic possibilities.

For almost 30 years Newton did not bother to publish his version of the analysis, although in letters (in particular to Leibniz) he willingly shared much of what he had achieved. Meanwhile, Leibniz's version had been spreading widely and openly throughout Europe since 1676. Only in 1693 did the first presentation of Newton's version appear - in the form of an appendix to Wallis's Treatise on Algebra. We have to admit that Newton’s terminology and symbolism are rather clumsy in comparison with Leibniz’s: fluxion (derivative), fluente (antiderivative), moment of magnitude (differential), etc. Only Newton’s notation “is preserved in mathematics.” o» for infinitesimal dt(however, this letter was used earlier by Gregory in the same sense), and also the dot above the letter as a symbol of the derivative with respect to time.

Newton published a fairly complete statement of the principles of analysis only in the work “On the Quadrature of Curves” (1704), attached to his monograph “Optics”. Almost all of the material presented was ready back in the 1670-1680s, but only now Gregory and Halley persuaded Newton to publish the work, which, 40 years late, became Newton’s first printed work on analysis. Here, Newton introduced derivatives of higher orders, found the values ​​of the integrals of various rational and irrational functions, and gave examples of solving 1st order differential equations.

Newton's Universal Arithmetic, Latin edition (1707)

In 1707, the book “Universal Arithmetic” was published. It presents a variety of numerical methods. Newton always paid great attention approximate solution of equations. Newton's famous method made it possible to find the roots of equations with previously unimaginable speed and accuracy (published in Wallis' Algebra, 1685). Modern look Newton's iterative method was introduced by Joseph Raphson (1690).

In 1711, after 40 years, Analysis by Equations with an Infinite Number of Terms was finally published. In this work, Newton explores both algebraic and “mechanical” curves (cycloid, quadratrix) with equal ease. Partial derivatives appear. In the same year, the “Method of Differences” was published, where Newton proposed an interpolation formula for carrying out (n+1) data points with equally spaced or unequally spaced abscissas of the polynomial n-th order. This is a difference analogue of Taylor's formula.

In 1736, the final work, “The Method of Fluxions and Infinite Series,” was published posthumously, significantly advanced compared to “Analysis by Equations.” It provides numerous examples of finding extrema, tangents and normals, calculating radii and centers of curvature in Cartesian and polar coordinates, finding inflection points, etc. In the same work, quadratures and straightenings of various curves were performed.

It should be noted that Newton not only developed the analysis quite fully, but also made an attempt to strictly substantiate its principles. If Leibniz was inclined to the idea of ​​actual infinitesimals, then Newton proposed (in the Principia) a general theory of passage to limits, which he somewhat floridly called the “method of first and last relations.” It is used exactly modern term"limit" (lat. limes), although there is no clear description of the essence of this term, implying an intuitive understanding. The theory of limits is set out in 11 lemmas in Book I of the Elements; one lemma is also in book II. There is no arithmetic of limits, there is no proof of the uniqueness of the limit, and its connection with infinitesimals has not been revealed. However, Newton rightly points out the greater rigor of this approach compared to the “rough” method of indivisibles. Nevertheless, in Book II, by introducing “moments” (differentials), Newton again confuses the matter, in fact considering them as actual infinitesimals.

It is noteworthy that Newton was not at all interested in number theory. Apparently, physics was much closer to mathematics to him.

Mechanics

Page of Newton's Principia with the axioms of mechanics

Newton's merit lies in the solution of two fundamental problems.

• Creation of an axiomatic basis for mechanics, which actually transferred this science to the category of strict mathematical theories.
• Creation of dynamics that connects the behavior of the body with the characteristics of external influences (forces) on it.

In addition, Newton finally buried the idea, rooted since ancient times, that the laws of motion of earthly and celestial bodies are completely different. In his model of the world, the entire Universe is subject to uniform laws that can be formulated mathematically.

Newton's axiomatics consisted of three laws, which he himself formulated as follows.

The first law (the law of inertia), in a less clear form, was published by Galileo. It should be noted that Galileo allowed free movement not only in a straight line, but also in a circle (apparently for astronomical reasons). Galileo also formulated the most important principle of relativity, which Newton did not include in his axiomatics, because for mechanical processes this principle is a direct consequence of the equations of dynamics (Corollary V in the Principia). In addition, Newton considered space and time absolute concepts, uniform for the entire Universe, and clearly indicated this in his “Principles”.

Newton also gave strict definitions of such physical concepts as momentum(not quite clearly used by Descartes) and force. He introduced into physics the concept of mass as a measure of inertia and, at the same time, gravitational properties. Previously, physicists used the concept weight, however, the weight of a body depends not only on the body itself, but also on its environment (for example, on the distance to the center of the Earth), so a new, invariant characteristic was needed.

Euler and Lagrange completed the mathematization of mechanics.

Universal gravity

Aristotle and his supporters considered gravity to be the desire of the bodies of the “sublunary world” to their natural places. Some others ancient philosophers(among them Empedocles and Plato) believed that heaviness was the desire of related bodies to unite. In the 16th century, this point of view was supported by Nicolaus Copernicus, in whose heliocentric system the Earth was considered only one of the planets. Giordano Bruno and Galileo Galilei held similar views. Johannes Kepler believed that the reason for the fall of bodies is not their internal aspirations, but the force of attraction from the Earth, and not only the Earth attracts a stone, but the stone also attracts the Earth. In his opinion, gravity extends at least to the Moon. In his later works, he expressed the opinion that the force of gravity decreases with distance and all bodies of the solar system are subject to mutual attraction. Rene Descartes, Gilles Roberval, Christian Huygens and other scientists of the 17th century tried to unravel the physical nature of gravity.

The same Kepler was the first to suggest that the movement of planets is controlled by forces emanating from the Sun. In his theory there were three such forces: one, circular, pushes the planet in its orbit, acting tangentially to the trajectory (due to this force the planet moves), the other either attracts or repels the planet from the Sun (due to it the planet’s orbit is an ellipse) and the third acts across the plane of the ecliptic (due to which the planet’s orbit lies in the same plane). He considered the circular force to decrease in inverse proportion to the distance from the Sun. None of these three forces was identified with gravity. The Keplerian theory was rejected by the leading theoretical astronomer of the mid-17th century, Ismael Bulliald, according to whom, firstly, the planets move around the Sun not under the influence of forces emanating from it, but due to internal desire, and secondly, if a circular force existed , it would decrease back to the second degree of distance, and not to the first, as Kepler believed. Descartes believed that the planets were carried around the Sun by giant vortices.

The assumption about the existence of a force emanating from the Sun that controls the movement of the planets was expressed by Jeremy Horrocks. According to Giovanni Alfonso Borelli, three forces emanate from the Sun: one propels the planet in its orbit, the other attracts the planet to the Sun, and the third (centrifugal), on the contrary, pushes the planet away. The planet's elliptical orbit is the result of the confrontation between the latter two. In 1666, Robert Hooke suggested that the force of gravity towards the Sun alone is quite sufficient to explain the movement of the planets, it is simply necessary to assume that the planetary orbit is the result of a combination (superposition) of falling on the Sun (due to the force of gravity) and movement due to inertia (due to gravity). tangent to the planet's trajectory). In his opinion, this superposition of movements determines the elliptical shape of the planet’s trajectory around the Sun. Christopher Wren also expressed similar views, but in a rather vague form. Hooke and Wren guessed that the force of gravity decreases in inverse proportion to the square of the distance to the Sun.

However, no one before Newton was able to clearly and mathematically conclusively connect the law of gravity (a force inversely proportional to the square of the distance) and the laws of planetary motion (Kepler's laws). Moreover, it was Newton who first guessed that gravity acts between any two bodies in the Universe; The movement of a falling apple and the rotation of the Moon around the Earth are controlled by the same force. Finally, Newton not only published the supposed formula of the law of universal gravitation, but actually proposed a holistic mathematical model:

• law of gravitation;
• law of motion (Newton's second law);
• system of methods for mathematical research (mathematical analysis).

Taken together, this triad is sufficient for a complete study of the most complex movements of celestial bodies, thereby creating the foundations of celestial mechanics. Thus, only with the works of Newton does the science of dynamics begin, including as applied to the movement of celestial bodies. Before the creation of the theory of relativity and quantum mechanics, no fundamental amendments to this model were needed, although the mathematical apparatus turned out to be necessary to significantly develop.

The first argument in favor of the Newtonian model was the rigorous derivation of Kepler's empirical laws on its basis. The next step was the theory of the movement of comets and the Moon, set out in the “Principles”. Later, with the help of Newtonian gravity, all observed movements of celestial bodies were explained with high accuracy; This is a great merit of Euler, Clairaut and Laplace, who developed perturbation theory for this. The foundation of this theory was laid by Newton, who analyzed the motion of the Moon using his usual method of series expansion; on this path he discovered the causes of the then known irregularities ( inequalities) in the movement of the Moon.

The law of gravity made it possible to solve not only problems of celestial mechanics, but also a number of physical and astrophysical problems. Newton indicated a method for determining the mass of the Sun and planets. He discovered the cause of tides: the gravity of the Moon (even Galileo considered tides to be a centrifugal effect). Moreover, having processed many years of data on the height of tides, he calculated the mass of the Moon with good accuracy. Another consequence of gravity was the precession of the earth's axis. Newton found out that due to the oblateness of the Earth at the poles, the earth's axis undergoes a constant slow displacement with a period of 26,000 years under the influence of the attraction of the Moon and the Sun. Thus, the ancient problem of “anticipation of the equinoxes” (first noted by Hipparchus) found a scientific explanation.

Newton's theory of gravitation caused many years of debate and criticism of the concept of long-range action adopted in it. However, the outstanding successes of celestial mechanics in the 18th century confirmed the opinion about the adequacy of the Newtonian model. The first observed deviations from Newton's theory in astronomy (a shift in the perihelion of Mercury) were discovered only 200 years later. These deviations were soon explained by the general theory of relativity (GR); Newton's theory turned out to be an approximate version of it. General relativity also filled the theory of gravitation with physical content, indicating the material carrier of the force of attraction - the metric of space-time, and made it possible to get rid of long-range action.

Optics and theory of light

Newton made fundamental discoveries in optics. He built the first mirror telescope (reflector), in which, unlike purely lens telescopes, there was no chromatic aberration. He also studied the dispersion of light in detail, showing that when white light passes through a transparent prism, it decomposes into a continuous series of rays of different colors due to the different refraction of rays of different colors, thereby Newton laid the foundations of the correct theory of colors. Newton created the mathematical theory of interference rings discovered by Hooke, which have since been called “Newton’s rings.” In a letter to Flamsteed, he outlined a detailed theory of astronomical refraction. But his main achievement was the creation of the foundations of physical (not only geometric) optics as a science and the development of its mathematical basis, the transformation of the theory of light from an unsystematic set of facts into a science with rich qualitative and quantitative content, experimentally well substantiated. Newton's optical experiments became a model of deep physical research for decades.

During this period there were many speculative theories of light and color; mainly fought the point of view of Aristotle (“different colors are a mixture of light and darkness in different proportions”) and Descartes (“different colors are created when light particles rotate with at different speeds"). Hooke, in his Micrographia (1665), proposed a variant of Aristotelian views. Many believed that color is an attribute not of light, but of an illuminated object. The general discord was aggravated by a cascade of discoveries in the 17th century: diffraction (1665, Grimaldi), interference (1665, Hooke), double refraction (1670, Erasmus Bartholin, studied by Huygens), estimation of the speed of light (1675, Roemer). There was no theory of light compatible with all these facts.

Light dispersion
(Newton's experiment)

In his speech to the Royal Society, Newton refuted both Aristotle and Descartes, and convincingly proved that white light is not primary, but consists of colored components with different “degrees of refraction.” These components are primary - Newton could not change their color with any tricks. Thus, the subjective sensation of color received a solid objective basis - in modern terminology, the wavelength of light, which could be judged by the degree of refraction.

Title page of Newton's Optics

In 1689, Newton stopped publishing in the field of optics (although he continued research) - according to a widespread legend, he vowed not to publish anything in this field during Hooke's lifetime. In any case, in 1704, the next year after Hooke’s death, the monograph “Optics” was published (in English). The preface to it contains a clear hint of a conflict with Hooke: “Not wanting to be drawn into disputes on various issues, I delayed this publication and would have delayed it further if not for the persistence of my friends.” During the author's lifetime, Optics, like Principia, went through three editions (1704, 1717, 1721) and many translations, including three in Latin.

• Book one: principles of geometric optics, the study of light dispersion and the composition of white color with various applications, including the theory of the rainbow.
• Book two: interference of light in thin plates.
• Book three: diffraction and polarization of light.

Historians distinguish two groups of then-current hypotheses about the nature of light.

• Emissive (corpuscular): light consists of small particles (corpuscles) emitted by a luminous body. This opinion was supported by the straightness of light propagation, on which geometric optics is based, but diffraction and interference did not fit well into this theory.
• Wave: light is a wave in the invisible world ether. Newton's opponents (Hooke, Huygens) are often called supporters of the wave theory, but it must be borne in mind that by wave they did not mean a periodic oscillation, as in modern theory, but a single impulse; for this reason, their explanations of light phenomena were hardly plausible and could not compete with Newton’s (Huygens even tried to refute diffraction). Developed wave optics appeared only in early XIX century.

Newton is often considered a proponent of the corpuscular theory of light; in fact, as usual, he “did not invent hypotheses” and readily admitted that light could also be associated with waves in the ether. In a treatise presented to the Royal Society in 1675, he writes that light cannot be simply vibrations of the ether, since then it could, for example, travel through a curved pipe, as sound does. But, on the other hand, he suggests that the propagation of light excites vibrations in the ether, which gives rise to diffraction and other wave effects. Essentially, Newton, clearly aware of the advantages and disadvantages of both approaches, puts forward a compromise, particle-wave theory of light. In his works, Newton described in detail the mathematical model of light phenomena, leaving aside the question of the physical carrier of light: “My teaching about the refraction of light and colors consists solely in establishing certain properties of light without any hypotheses about its origin.” Wave optics, when it appeared, did not reject Newton's models, but absorbed them and expanded them on a new basis.

Despite his dislike of hypotheses, Newton included at the end of Optics a list of unsolved problems and possible answers to them. However, in these years he could already afford this - Newton’s authority after “Principia” became indisputable, and few people dared to bother him with objections. A number of hypotheses turned out to be prophetic. Specifically, Newton predicted:

• deflection of light in a gravitational field;
• the phenomenon of polarization of light;
• interconversion of light and matter.

Other works in physics

Newton was the first to derive the speed of sound in a gas, based on the Boyle-Mariotte law. He suggested the existence of the law of viscous friction and described the hydrodynamic compression of the jet. He proposed a formula for the law of drag of a body in a rarefied medium (Newton’s formula) and, on its basis, considered one of the first problems about the most favorable shape of a streamlined body (Newton’s aerodynamic problem). In “Principles” he expressed and argued the correct assumption that a comet has a solid core, the evaporation of which under the influence of solar heat forms an extensive tail, always directed in the direction opposite to the Sun. Newton also worked on heat transfer issues, one of the results is called the Newton-Richmann law.

Newton predicted the oblateness of the Earth at the poles, estimating it to be approximately 1:230. At the same time, Newton used a homogeneous fluid model to describe the Earth, applied the law of universal gravitation and took into account centrifugal force. At the same time, similar calculations were performed by Huygens, who did not believe in long-range gravitational force and approached the problem purely kinematically. Accordingly, Huygens predicted a compression less than half that of Newton, 1:576. Moreover, Cassini and other Cartesians argued that the Earth is not compressed, but elongated at the poles like a lemon. Subsequently, although not immediately (the first measurements were inaccurate), direct measurements (Clerot, 1743) confirmed Newton’s correctness; actual compression is 1:298. The reason this value differs from that proposed by Newton in favor of Huygens’s is that the model of a homogeneous liquid is still not entirely accurate (density increases noticeably with depth). A more accurate theory, explicitly taking into account the dependence of density on depth, was developed only in the 19th century.

Students

Strictly speaking, Newton had no direct students. However, a whole generation of English scientists grew up reading his books and communicating with him, so they themselves considered themselves Newton’s students. Among them the most famous are:

• Edmund Halley
• Roger Cotes
• Colin Maclaurin
• Abraham de Moivre
• James Stirling
• Brooke Taylor
• William Whiston

Other areas of activity

Chemistry and alchemy

In parallel with the research that laid the foundation of the current scientific (physical and mathematical) tradition, Newton (like many of his colleagues) devoted a lot of time to alchemy, as well as theology. Books on alchemy made up a tenth of his library. He did not publish any works on chemistry or alchemy, and the only known result of this long-term hobby was the serious poisoning of Newton in 1691. When Newton's body was exhumed, dangerous levels of mercury were found in his body.

Stukeley recalls that Newton wrote a treatise on chemistry, “explaining the principles of this mysterious art from experimental and mathematical proofs,” but the manuscript, unfortunately, was destroyed by fire, and Newton made no attempt to restore it. Surviving letters and notes suggest that Newton was pondering the possibility of some kind of unification of the laws of physics and chemistry into a single system of the world; He placed several hypotheses on this topic at the end of Optics.

B. G. Kuznetsov believes that Newton’s alchemical studies were attempts to reveal the atomic structure of matter and other types of matter (for example, light, heat, magnetism):

Was Newton an alchemist? He believed in the possibility of transforming one metal into another and for three decades he was engaged in alchemical research and studied the alchemical works of the Middle Ages and antiquity... The very fact of the predominance of theoretical interest and the complete lack of interest in obtaining gold takes Newton beyond alchemy as an element of the medieval cultural tradition... At the core His atomism is based on the idea of ​​a hierarchy of corpuscles formed by increasingly less intense forces of mutual attraction of parts. This idea of ​​an infinite hierarchy of discrete particles of matter is related to the idea of ​​the unity of matter. Newton did not believe in the existence of elements that were not capable of transforming into each other. On the contrary, he assumed that the idea of ​​​​the indecomposability of particles and, accordingly, of qualitative differences between elements is associated with the historically limited capabilities of experimental technology.

This assumption is confirmed by Newton’s own statement: “Alchemy does not deal with metals, as the ignorant believe. This philosophy is not one of those that serves vanity and deception; it rather serves benefit and edification, and the main thing here is the knowledge of God.”

Theology

"Refined chronology of ancient kingdoms"

Being a deeply religious man, Newton viewed the Bible (like everything in the world) from a rationalistic position. Newton's rejection of the Trinity of God is apparently connected with this approach. Most historians believe that Newton, who worked for many years at Trinity College, did not believe in the Trinity himself. Scholars of his theological works have found that religious views Newton were close to heretical Arianism (see Newton’s article “ Historical Tracing of Two Notable Corruptions of Scripture»).

The degree of closeness of Newton's views to various heresies condemned by the church is assessed differently. The German historian Fisenmayer suggested that Newton accepted the Trinity, but closer to the Eastern, Orthodox understanding of it. American historian Stephen Snobelen, citing a number of documentary evidence, decisively rejected this point of view and classified Newton as a Socinian.

Outwardly, however, Newton remained loyal to the state Anglican Church. There was a good reason for this: the 1698 legislation for the suppression of blasphemy and impiety. The Act for the Suppression of Blasphemy and Profaneness ) for denying any of the persons of the Trinity provided for loss of civil rights, and if this crime was repeated - imprisonment. For example, Newton's friend William Whiston was stripped of his professorship and expelled from Cambridge University in 1710 for his claims that the creed of the early Church was Arian. However, in letters to like-minded people (Locke, Halley, etc.) Newton was quite frank.

In addition to anti-trinitarianism, elements of deism are seen in Newton’s religious worldview. Newton believed in the material presence of God at every point in the Universe and called space “the sense of God” (lat. sensorium Dei). This pantheistic idea unites Newton’s scientific, philosophical and theological views into a single whole; “all areas of Newton’s interests, from natural philosophy to alchemy, represent different projections and at the same time different contexts of this central idea that reigned supreme over him.”

Newton published (partially) the results of his theological research late in his life, but it began much earlier, no later than 1673. Newton proposed his own version of biblical chronology, left work on biblical hermeneutics, and wrote a commentary on the Apocalypse. He studied the Hebrew language, studied the Bible using scientific methods, using astronomical calculations related to solar eclipses, linguistic analysis, etc. to substantiate his point of view. According to his calculations, the end of the world will come no earlier than 2060.

Newton's theological manuscripts are now kept in Jerusalem, in the National Library.

Ratings

Newton statue at Trinity College

The inscription on Newton's grave reads:

Here lies Sir Isaac Newton, who, with an almost divine power of reason, was the first to explain with his mathematical method the movements and shapes of the planets, the paths of comets and the tides of the oceans.

He was the one who explored the differences in light rays and the resulting different properties of colors, which no one had previously suspected. A diligent, cunning and faithful interpreter of nature, antiquity and Holy Scripture, he affirmed with his philosophy the greatness of the almighty creator, and in his disposition he instilled the simplicity required by the Gospel.

Let mortals rejoice that such an adornment of the human race lived among them.

Original text(lat.)

H. S. E. ISAACUS NEWTON Eques Auratus,
Qui, animi vi prope divinâ,
Planetarum Motus, Figuras,
Cometarum semitas, Oceanique Aestus. Suâ Mathesi facem praeferente
Primus demonstravit:
Radiorum Lucis dissimilitudines,
Colorumque inde nascentium proprietates,
Quas nemo antea vel suspicatus erat, pervestigavit.
Naturae, Antiquitatis, S. Scripturae,
Sedulus, sagax, fidus Interpres
Dei O. M. Majestatem Philosophiâ asseruit,
Evangelij Simplicitatem Moribus expressit.
Sibi gratulentur Mortales,
Tale tantumque exstitisse
HUMANI GENERIS DECUS.
NAT XXV DEC. A.D. MDCXLII. OBIIT. XX. MAR. MDCCXXVI.