Newton liked to make mechanical models and other things, such as windmills, waterwheels, sundials and so on. His elaborate water clock has won people's praise for its accurate timing. Sometimes, the way he plays ball is also very strange. One day, he made a lantern and hung it on the tail of a kite. When night falls, the lighted lanterns rise into the air with the help of the rising power of kites. Luminous lanterns flow in the air, and people are frightened and think there is a comet. Nevertheless, he is often discriminated against because of his poor academic performance.
At that time, the hierarchy of British feudal society was very serious. Students who study well in primary and secondary schools may discriminate against those who study poorly. There was a game between classes. When everyone was in high spirits, a good student kicked Newton and called him an idiot. Newton's mind was stimulated to extreme anger. He thought, we are all students. Why should I be bullied by him? I must pass him! From then on, Newton made up his mind to study hard. He gets up early and goes to bed late. Every minute counts. He studies hard and thinks hard. After studying hard, Newton's academic performance improved continuously, and he soon surpassed the classmate who bullied him and was among the best in his class.
Time treats people equally and gives people the same amount, but people use time in different ways and gain different knowledge.
When Newton was sixteen years old, his understanding of mathematics was still superficial, and he didn't even understand the advanced knowledge of mathematics. "Knowledge lies in accumulation, and cleverness comes from learning". Newton was determined to climb the peak of mathematics by his own efforts. Under the unfavorable conditions of poor foundation, Newton can correctly understand himself and make progress despite difficulties. He relearned the basic knowledge and basic formulas and made solid progress step by step. After studying Euclidean geometry, he studied Cartesian geometry. In contrast, he thought Euclidean geometry was superficial, so he studied Cartesian geometry seriously until he mastered the essentials and achieved mastery. So he invented the algebraic binomial theorem. Newton's legendary story of "calculating the wind force in a big storm" can prove Newton's body mechanics. One day, there was a big storm. The wind is howling, the dust is flying, and the mystery is long, which makes people open their eyes. Newton thought it was a good opportunity to study and calculate the wind accurately. So, he took the appliance and ran back and forth in the storm. He stumbled and measured with difficulty. Several times the dust fascinated his eyes, several times the wind blew away the paper, and several times the wind forced him to suspend his work, but none of them shook his thirst for knowledge. He finally got the correct data over and over again. He was so happy that he hurried home to continue his research.
Where there is a will, there is a way. After diligent study, Newton laid a solid foundation for his tower of science. Soon, Newton's math tower was built. He invented differential calculus at the age of 22 and integral calculus at the age of 23, which made great contributions to the cause of human science.
Newton was a very modest man and never conceited. Someone once asked Newton, "What is the secret of your success?" Newton replied, "If I have a little success, there is no other secret but diligence."
Young Newton
1643 65438+1October 4th, Newton was born in a farmer's family in Wolthorpe, Lincolnshire, England. Newton was a premature baby, weighing only three pounds at birth. The midwife and his relatives are worried about whether he will survive. No one expected that this seemingly insignificant little thing would become a giant of science and live to be 85 years old.
Three months before Newton was born, his father died. When he was two years old, his mother remarried to a priest and left Newton to his grandmother. 1 1 years old, my mother's step hubband passed away, and my mother returned to Newton with a son and two daughters born with step hubband. Newton was taciturn and stubborn since childhood, which may come from his family situation.
From about the age of five, Newton was sent to public schools. Newton was not a child prodigy when he was a teenager. He has average qualifications and average grades, but he likes reading books, reading books that introduce various simple mechanical model making methods, and being inspired by them, he makes some strange gadgets by himself, such as windmills, wooden clocks, folding lanterns and so on.
Legend has it that young Newton made a model of the mill after thoroughly understanding the mechanical principle of the windmill. He tied the mouse to a treadmill with wheels, and then put a corn in front of the wheel, just out of the mouse's reach. The mouse wants to eat corn, so it keeps running, so the wheel keeps turning; Once again, when he was flying a kite, he hung a small lamp on the rope. In the evening, the villagers were surprised to find that a comet appeared. He also made a small water clock. Every morning, the water bell will automatically drop water on his face to wake him up. He also likes painting and carving, especially carving sundials. His sundial was placed in the corner of his house and everywhere on the windowsill to observe the movement of the shadow.
Newton entered Grantham Middle School not far from home at the age of 12. Newton's mother had hoped that he would become a farmer, but Newton himself had no intention of doing so and loved reading. As he grew older, Newton became more and more fond of reading, meditating and doing small scientific experiments. When he was studying in Grantham Middle School, he lived in a pharmacist's house, which influenced him by chemical experiments.
Newton's academic performance in middle school is not outstanding, but he just loves reading and is curious about natural phenomena, such as colors, the movements of the four seasons, especially geometry, Heliocentrism of Copernicus and so on. He also takes reading notes in different categories and likes to make ingenious gadgets, tricks, inventions and experiments.
At that time, English society was permeated with new Christian ideas, and two relatives of Newton's family were priests, which may affect Newton's religious life in his later years. From these ordinary environments and activities, we can't see that Newton is a gifted child.
Later, forced by life, his mother asked Newton to drop out of school and farm at home to support his family. But Newton buried a book whenever he had the chance, so that he often forgot to work. Every time, when his mother told him to go to the market with his servant and get familiar with the trade business, he begged the servant to go shopping alone, while he hid behind a tree and read a book. Once, Newton's uncle became suspicious and followed Newton to the listed town. He found his nephew sprawled on the grass, absorbed in a math problem. Newton's studious spirit touched his uncle, so he persuaded his mother to let Newton go back to school and encouraged him to go to college. Newton went back to school and drew nutrition from books. Once, he went to play in the country and then rested under an apple tree. Suddenly, an apple fell from the tree. He wondered why the apple fell from above, not from below. He returned to China to study this problem. Later, he found that the earth was attractive and could attract objects. Then Newton's physical gravity appeared.
Years of study
16 1 year, 19-year-old Newton entered Trinity College of Cambridge University as a student with reduced tuition fees, paid for his tuition by doing chores for the college, 1664 became a scholarship winner, and 1665 received his bachelor's degree.
/kloc-In the mid-7th century, the education system of Cambridge University was still permeated with a strong flavor of medieval scholasticism. When Newton entered Cambridge, there were also some courses of scholasticism, such as logic, ancient prose, grammar, ancient history, theology and so on. Two years later, Trinity College took on a new look. Lucas created a unique lecture, which stipulated that natural science knowledge should be taught, such as geography, physics, astronomy, mathematics and so on.
The first professor of the lecture, Isaac Barrow, was a learned scientist. The scholar had a unique vision and saw that Newton had profound observation and keen understanding. So he taught Newton all his mathematical knowledge, including the method of calculating the area of curve graphics, and led Newton to the research field of modern natural science.
During this period of study, Newton mastered arithmetic and trigonometry, and read Kepler's Optics, Descartes' Principles of Geometry and Philosophy, Galileo's Dialogue between Two World Systems, Hooke's Micro Atlas, and the historical and early philosophical journals of the Royal Society.
Newton's time under Barrow's door was the key period of his research. Barrow is older than Newton 12 years old. He is good at maths and optics. He admired Newton's talent very much and thought Newton's mathematics was better than himself. Newton later recalled: "Dr. Barrow taught courses in kinematics at that time, and perhaps it was these courses that prompted me to study this problem."
Newton relied heavily on teaching himself mathematics at that time. He studied Euclid's Elements of Geometry, Descartes' Geometry, Wallis' arithmetica infinitorum, Barrow's lectures on mathematics and the works of many mathematicians. Among them, Descartes' Geometry and Wallis' arithmetica infinitorum had a decisive influence on Newton, and Newton quickly moved to the forefront of mathematics at that time-analytic geometry and calculus. 1664, Newton was elected as Barrow's assistant, and the next year, the Council of Cambridge University passed the decision to grant Newton a bachelor's degree.
1665 to 1666, a serious plague swept through London, and Cambridge was not far from London. Because of fear, the school was closed, and Newton left school and went home in June 1665.
Because Newton was influenced and influenced by mathematics and natural science in Cambridge, he had a strong interest in exploring natural phenomena, and the quiet environment in his hometown made his thoughts spread their wings and fly. The short period from 1665 to 1666 became the golden age of Newton's scientific career. He is full of thinking in the field of natural science, brilliant and productive, thinking about problems that his predecessors have never thought about, stepping into fields that his predecessors have never set foot in, and creating unprecedented amazing achievements.
At the beginning of 1665, Newton established the approximation method of series and the law that binomial with arbitrary power is transformed into series; In June of the same year 165438+ 10, the forward serial number method (differential) was established; June 5438+the following year 10, studying color theory with prism; In May, I began to study the reverse flow number method (integral). During this year, Newton began to think of studying gravity and wanted to extend the theory of gravity to the orbit of the moon. He also deduced from Kepler's law that the force that keeps planets in orbit must be inversely proportional to the square of their distance from the center of rotation. The legend that Newton didn't realize gravity until he saw the apple fall to the ground was also an anecdote that happened at this time.
In a word, during his two years in his hometown, Newton engaged in scientific creation with more vigorous energy than before and cared about natural philosophy. His three great achievements: calculus, gravitation and optical analysis were conceived and formed at this time. It can be said that Newton at this time has begun to describe the blueprint of most scientific creations in his life.
1667 Shortly after Easter, Newton returned to Cambridge University. 1 June1day was elected as a specialist partner of Trinity College, and he obtained his master's degree on March 16 the following year, and became a specialist partner at the same time. 1669, 10 year1October 27th, Barrow resigned as a professor to help Newton. At the age of 26, Newton was promoted to professor of mathematics and served as Professor of Lucas. Barrow paved the way for Newton's scientific career. Without the help of Uncle Newton and Barrow, Newton, a swift horse, might not have galloped on the road of science. Barrow gave way to a wise man, which was told as a story in the history of science.
Great achievement ~ establishing calculus
Among all Newton's scientific contributions, mathematical achievements occupy a prominent position. The first creative achievement in his mathematical career was the discovery of binomial theorem. According to Newton's own recollection, he discovered this theorem when he tried to modify his series of finding the area of a circle while studying Dr. Wallis' arithmetica infinitorum in the winter of 1664 and 1665.
Descartes' analytic geometry maps the functional relationship describing motion to geometric curves. Newton found a new way out under the guidance of his teacher Barrow and on the basis of studying Descartes' analytic geometry. The speed at any moment can be regarded as the average speed in a small time range, which is the ratio of a small distance to a time interval. When this small time interval is reduced to infinity, it is the exact value of this point. This is the concept of differentiation.
Derivation is equivalent to finding the tangent slope of the relationship between time and distance at a certain point. The distance traveled by a variable-speed moving object in a certain time range can be regarded as the sum of the distances traveled in a very small time interval, which is the concept of integration. Integration is equivalent to finding the area under the curve of time and speed. Newton established calculus from these basic concepts.
The establishment of calculus is Newton's most outstanding mathematical achievement. Newton founded this mathematical theory, which is directly related to physical concepts, in order to solve the problem of motion. Newton called it "flow counting". Some specific problems it deals with, such as tangent problem, quadrature problem, instantaneous velocity problem, maximum and minimum value of function, have been studied before Newton. But Newton surpassed his predecessors. From a higher angle, he integrated the scattered efforts in the past, unified all kinds of skills to solve infinitesimal problems since ancient Greece into two common algorithms-differential and integral, and established the reciprocal relationship between these two operations, thus completing the most critical step in the invention of calculus, providing the most effective tool for the development of modern science and opening up a new era of mathematics.
Newton did not publish the research results of calculus in time. He may have studied calculus earlier than Leibniz, but Leibniz adopted a more reasonable expression, and his works on calculus were published earlier than Newton.
Between Newton and Leibniz, when arguing about who is the founder of this subject, it actually caused an uproar. This quarrel lasted for a long time among their students, supporters and mathematicians, which caused the long-term opposition between European continent mathematicians and British mathematicians. British mathematics was closed to the outside world for a period of time, limited by national prejudice, and too rigidly adhered to Newton's "flow counting", so the development of mathematics fell behind for a whole hundred years.
It should be said that the establishment of a science is by no means a person's achievement. It must be completed by one person or several people through the efforts of many people and the accumulation of a large number of achievements. The same is true of calculus, which was independently established by Newton and Leibniz on the basis of predecessors.
1707, Newton's algebra lecture notes were compiled and published, named "General Arithmetic". He mainly discussed the basis of algebra and its application in solving various problems. This book states the basic concepts and operations of algebra, illustrates how to transform various problems into algebraic equations with a large number of examples, and deeply discusses the roots and properties of equations, thus achieving fruitful results in equation theory. For example, he drew the relationship between the root of the equation and its discriminant, and pointed out that the power sum of the root of the equation can be determined by the coefficient of the equation, that is, Newton's power sum formula.
Newton contributed to both analytic geometry and synthetic geometry. In Analytic Geometry published by 1736, he introduced the center of curvature, gave the concept of closed line circle (or curve circle), and put forward the curvature formula and the curvature calculation method of curve. And summed up many of my own research results into a monograph "Counting Cubic Curves", which was published in 1704. In addition, his mathematical work involves numerical analysis, probability theory, elementary number theory and many other fields.