Poincare: The last mathematical generalist

We often use the term "intelligence quotient" to measure how smart a person is, but I'm afraid few of us can say exactly what it means. And because of the complexity of the person's intelligence, accurately and objectively measuring IQ is not an easy thing, so psychologists used the common method of measuring intelligence quotient (IQ), which is widely accepted and approved by the questionnaire test, we design a questionnaire test, design of the problem, of course, is the use of intelligence to answer.

French famous psychology expert Binet and educator Simon in 1905 designed a popular worldwide measurement of IQ scale, but by this table test, was judged to be "stupid", there is a world-class master of mathematics - known as the "encyclopedia of mathematics" Poincare.

Born in France in April 1854, Poincare had a very unhappy childhood, and his skilled father did not give him good health. Since childhood, he has suffered from a strange motor nervous system disorder that makes it difficult to write or paint. At the age of five, he developed a severe case of diphtheria, which slowed the development of his speech and severely impaired his vision. Fortunately, he had a talented and educated mother, so he received a good home education, so Poincare's talent through family education and self-training began to show. The class can not see the teacher's blackboard, unable to record, he listened with rapt attention, heart in mind. The following short story can fully reflect the legendary character's learning characteristics:

In the fall of 1864, in a classroom of a French high school, a famous local astronomer was lecturing the students on the motions of the planets. The students who showed little interest in astronomy were mostly absent, expressionless, or yawning, to the obvious annoyance of the thankless teacher. Then he noticed again that a small boy in the back row was looking down at the blackboard, not looking at it, and he strode over.

"Classmate, what are you doing? Why don't you look at the blackboard? Do you understand everything?" "Asked the teacher angrily.

"I'm used to hearing, and I understand, thank you!" The little boy stood up and answered respectfully.

"Really? Then please tell them!" The teacher who didn't believe it made it difficult.

"The motions of the planets..." The little boy repeated exactly what the teacher had just said.

"Good heavens! Amazingly, you can never forget!" The teacher gaped, feeling incredible: "That you why don't read the content on the blackboard, so understand more convenient ah!" The teacher was still puzzled.

"Teacher, he is too short-sighted to see the words on the blackboard." Next, the classmate hurriedly explained the way.

"Oh, that's right. It seems that God is fair, your concentration has made up for the lack of sight, and you have the best 'inner eye'!"

The boy with an extraordinary memory was the later master of mathematics, Poincare. Due to his visual impairment, Poincare could only listen to lectures and memorize them, which meant that he had to pay more effort and hardships than ordinary people. But what he gained at the same time was that his brain was surprisingly developed, especially his ability of understanding and memory. His memory of things has the characteristics of rapid, accurate, and lasting, and his thinking is highly concentrated, especially in mathematics, he can complete complex operations and reasoning in his head. That high concentration of attention, no matter how much external interference, can not interrupt his thinking, and these are the characteristics a mathematician must have. At that time, he was often tested on math problems by senior students, and Poincare gave answers almost instantaneously, while his examiners took so long to verify his answers that he earned the nickname "the Math Monster."

In 1873, at the age of 19, Poincare took the entrance exam for the Ecole Polytechnique in Paris, a school known around the world for its rigid examinations. Poincare's mathematical ability has its debut at this moment, the examiners to test his ability, to defer the test time for 45 minutes, they use this time carefully designed specifically for him for a few difficult math problems, the obscure young man didn't write, in the head is easily completed the operation, when he announced the answer, the short of time, methods of clever, The examiners were stunned and ecstatic. Although Poincare's drawing ability was poor, and he got zero points in the geometric drawing problem, the very talented examiners finally broke the convention and gave him first place.

During his college years, Poincare became even more obsessed with mathematics, and in his frail health, he devoted himself to the wonderful and magical ocean of mathematics. In 1878, he was awarded a Doctor's degree in mathematics by the French Academy of Sciences after an "extraordinary" paper on the general solution of differential equations amazed the professors. Soon he was hired as a lecturer in mathematical analysis at Kahn University, and two years later he was offered a professorship at the University of Paris, where he taught mechanics and experimental physics, thus beginning his scientific career as a professional mathematician.

Poincare was quick to react, good at discussion, agile thinking like a spring of water, writing papers like a stream of water, tens of thousands of words of academic papers can be quickly conceived in the mind to complete, write out without revising a word. What is more, his research and contributions involve various branches of mathematics, such as function theory, algebraic topology, Abelian function, algebraic geometry, number theory, differential equations, mathematical foundation, etc. Many topics of contemporary mathematical research can be traced back to his work. Since the 20th century, mathematics has developed rapidly and entered the modern stage of multi-discipline and high difficulty. Remarkably, an outstanding mathematician can master one or several branches of mathematics, but mathematicians can rarely understand almost all mathematical fields. It is not possible for mathematicians today to do the first-class work of Poincare in all four basic areas of mathematics: arithmetic, algebra, geometry, and analysis. From the beginning of the 20th century, for the only admitted that "two and a half" in the true sense of universal mathematician, the first is the Poincare, another is the von Neumann, the half is the Hilbert, visible Poincare in maths lofty position, so that he is a can and 19th-century mathematics Wang Gaosi master of mathematics. Poincare not only made extraordinary contributions in the field of mathematics but also made outstanding achievements in the fields of aeromechanics, physics, and philosophy of science, so he was evaluated by the authority of the history of mathematics as "the last mathematical generalist who had a comprehensive knowledge of mathematics and its applications".

Poincare's pioneering work in the field of physics is comparable to Madame Curie's discovery of radium and Einstein's discovery of the theory of relativity. He successfully solved three-body problems such as the motion of the sun, the earth, and the moon. He was an intellectual pioneer in relativity and quantum mechanics, two pillars of modern physics. In his study of the philosophy of science, he put forward the basic law of "agreement emphasizes the analysis of human rational knowledge", which has been paid more and more attention by contemporary philosophers. In his 34 years of scientific research, he published 500 papers and more than 30 books, not including a series of natural philosophy classics published as a philosopher of natural science. Because of his outstanding contribution, he won all the honors that the French government could give him, won awards from countries such as Britain, Russia, Sweden, Hungary, and so on, and was successively appointed as an academician in more than 30 countries.

In 1904, Poincare formulated one of the most famous conjectures in mathematics -- the Poincare conjecture, one of the seven-century puzzles of mathematics, which is a central problem in topology. If all the closed curves in any closed, flexible three-dimensional space can be shrunk to a point, then the space must be blown up into a three-dimensional sphere. Colloquially, a curve is a one-dimensional manifold, a surface is a two-dimensional manifold, and a connected piece of geometry is called connected (connected can also be subdivided). Poincare conjecture: A smooth, compact N-1 connected N-dimensional manifold in an N + 1-dimensional space must be homomorphic to an n-dimensional sphere. The so-called two graphs homeomorphism means that a graph can be transformed into another graph one to one continuously. For n = 1, n = 2 we already know that. For everything n≥5, Smale proved it to be true in 1960. In 1981 Friedman's proof also worked for n = 4, but it has not been solved for n = 3.

Poincare was not only brilliant but also hard-working. In 1911, at the age of 57, he was feeling unwell and his energy was waning. Poincare, who had been ill all his life, sensed that his days were numbered and did not want to let the many new ideas that had grown in his mind go with him. In his last public speech before his death on June 26, 1912, Poincare spoke from the bottom of his heart: "Life is a constant struggle. If we occasionally enjoy relative tranquility, it is because of the tenacious struggles of our forebears. If our energies, if our vigilance, were slack for a moment, we would lose the fruits of the struggles for which our forebears labored." Poincare said and did so. On July 17, 1912, Poincare's constantly thinking brain suddenly stopped working due to cerebrovascular disease, but he is remembered as a master of mathematics who made achievements in all fields of mathematics.

Poincare, as the master of mathematics, the leading figure in the world of mathematics, his IQ is not "stupid" in the conclusion of the test, even the opposite. Thus it can be seen that human intelligence can not be determined by a table, tables and data can not accurately predict the future development of people. Poincare used his life of unrelenting progress to tell us a fact: intelligence quotient alone is a partial measure of a person's intelligence or ability. A person's lack in one aspect, but can greatly stimulate the potential of other aspects. Poincare is such an example!