Fermat was born in Beaumont, near Toulouse in southern France, 160 1. His father is a businessman, and Fermat received a good family education since childhood. He studied law at university and became a lawyer after graduation. Since the age of 30, he has been obsessed with mathematics. Until his death, his spiritual world was firmly ruled by mathematics for 34 years. Fermat has produced many mathematicians and philosophers, such as Mei Sen, Robois, Mei Duo and Descartes. They meet once a week in Mei Sen apartment to discuss science and study mathematics. Besides these, Fermat often exchanges mathematical research with friends, but he is indifferent to publishing his works. Fermat did not publish a complete work when he was alive. After his death, his son Samuel Fermat, with the help of mathematicians, compiled Fermat's notes, notes and letters and published them in Toulouse.
The starting point of the development of advanced mathematics is analytic geometry and calculus. Fermat made a great contribution to this. From Fermat's correspondence with Robois and Pascal, we can see that he had quite clearly mastered some basic principles of analytic geometry at least eight years before Descartes' Geometry was published. Fermat got some important conclusions in Introduction to Plane and Three-dimensional Trajectory, and also mastered the skills of simplifying methods by shifting axes and rotating axes to some extent. The study of conic curve in analytic geometry has been preliminarily systematized. Therefore, it is well-deserved that Fermat and Descartes share the honor of creating analytic geometry.
Fermat was also a pioneer of calculus. Newton, the inventor of calculus, once said frankly, "I got the inspiration of this method from Fermat tangent method. I extended it and applied it directly to abstract equations in turn." Fermat is committed to exploring the tangent of the curve from the research of lens design and optical theory. 1692, he put forward the method of tangent in his manuscript "The Method of Finding Maximum and Minimum". However, Fermat did not have a clear concept of limit at that time, nor did he draw the conclusion that the derivative was tangent, so he missed calculus and could only go down in history as an outstanding pioneer of calculus.
Fermat also initiated the study of modern number theory. The study of logarithmic properties began with ancient Greek mathematicians Euclid, Diophantine and others, but their research lacked systematicness. Fermat noticed this problem and pointed out that the study of logarithmic properties should have its own garden-(integer) number theory. At the same time, Fermat thinks that the study of prime numbers is very important in number theory, because a large number of problems in number theory are related to prime numbers. Fermat's research achievements in this field are the most outstanding among many departments of mathematics, among which Fermat's little theorem and Fermat's great theorem are the most famous. It is worth mentioning that Fermat's Last Theorem has puzzled the mathematics field for more than 300 years, and it was not until 1993 that it was completely proved by andrew wiles, a professor of mathematics at Princeton University. In the study of "perfect number", Fermat also has two important conclusions. Although these two conclusions failed to solve the method of finding the perfect number, they took a big step forward in solving the problem.
1653, a French knight Mailer asked Pascal "the question of gambling points". 1654, Pascal told Fermat about this problem, and Fermat got the same result as Pascal after his research. Due to the in-depth study of Fermat, Pascal and Huygens, the gambling problem that cardano and others began to explore in the16th century was widely studied by mathematicians, which further theorized mathematics and formed the classical probability theory. It can be said that Fermat ignited the fire of classical probability theory.
Undoubtedly, although Fermat is an amateur mathematician, he has made pioneering contributions in the fields of calculus, analytic geometry, probability theory and number theory. His role and position in the history of mathematics cannot be underestimated.
2. Euler, a blind mathematician
Euler's amazing achievements are not accidental. He can work in any harsh environment, often holding his children on his knees to finish his papers, regardless of the noise of older children. At the age of 28, Euler was unfortunately blind in one eye. Thirty years later, his other eye was also blind. He never stopped studying mathematics after he became blind. He continued to work with amazing perseverance and perseverance. During the seventeen years from blindness to his death, he also wrote several books and published about 400 papers orally. It is very difficult to publish the complete works of Euler because there are many works. The Swiss Society of Natural Sciences began to sort out and publish them in 1909, and it has not been completed until now. The plan is 72 volumes.
Among his 886 works, 530 are books and papers published before his death, many of which are textbooks. His works are fluent, simple, easy to understand and fascinating after reading, which greatly amazed readers. It is particularly worth mentioning that the plane triangle textbook he wrote used sinx, cosx, ... and so on, which is still in use today.
Euler entered university of basel in the autumn of 1720. Because of his extraordinary diligence and intelligence, johann bernoulli tasted his sweetness and gave him special guidance. Euler worked hard and became close friends with John's two sons, Nicholas Bo and daniel bernoulli.
Euler wrote a paper on masts at the age of 19, and won an award from the Paris Academy of Sciences, from which he began his creative career. I won many awards in succession. 1725, the Daniel brothers went to Russia and recommended Euler to czar Cadling I, so Euler arrived in Petersburg on 17 in May, and Daniel returned to Basel on 1733. Euler succeeded him as a professor of mathematics at the Academy of Sciences in Petersburg at the age of 26.
1735, Euler solved a difficult problem in astronomy (calculating the orbit of a comet).
It took several famous mathematicians months to solve this problem, but Euler invented it in three days. But overwork made him suffer from eye diseases, and unfortunately he was blind in his right eye. At this time, he was only 28 years old.
From1741-1766, at the invitation of Prussian frederick the great, Euler was the director of the Institute of Physics and Mathematics of the Berlin Academy of Sciences in Berlin. 1766, was hired back to Petersburg by Russian czar Cadling II. Unexpectedly, it didn't take long for his left eye vision to decline, and he could only vaguely see the object in front of him, and finally he was completely blind. At this time, Euler was nearly sixty years old.
Unfortunate things followed. 177 1 year, a fire broke out in Petersburg, which damaged Euler's house. 64-year-old Euler was blinded by illness and was trapped in the fire. In an emergency, a worker who did housework for him risked his life and rushed into the fire to rescue Euler. Euler's stacks and a lot of research results were reduced to ashes. The heavy blow still didn't knock Euler down. He vowed to recover the loss. Euler could still see vaguely in his left eye before he was completely blind. He seized the last moment, scribbled the formula he found on a big blackboard, and then dictated its contents, which were recorded by his students and his eldest son A Euler (1734- 1800, also a mathematician and physicist). After Euler was completely blind, he still fought against the darkness with amazing perseverance and studied with memory and mental arithmetic until his death.
Euler's memory and mental arithmetic are rare. He can repeat the contents of his notes when he was young, and he can recite advanced mathematics like the back of his hand. On one occasion, two students of Euler added up the 17 terms of a very complicated convergence series respectively, and when they reached the 50th place, the difference was one unit. In order to determine who made the correct calculation, Euler memorized all the calculations and finally found out the mistakes. During his seventeen years of blindness, Euler also solved the problem of moon deviation (moon movement) and many complicated analytical problems that made Newton a headache.
Euler's style is very high, and Lagrand is a great mathematician after Euler. From the age of 19, he began to communicate with Euler to discuss the general solution of isoperimetric problems, which led to the birth of variational method. The isoperimetric problem has been carefully considered by Euler for many years. The solution of Lagrand's theory won the warm praise of Euler. 1759, 10 On February 2, Euler praised Raglan's achievements in his reply, and modestly temporarily suppressed his immature works in this respect, which enabled the young Raglan's works to be published and circulated and won a great reputation. The term "variational method" was coined by Euler in 1766, and his great contribution to the popularization of variational method cannot be buried.
1783 One afternoon in September, Euler invited a friend to dinner to celebrate his successful calculation of the law of balloon rising. At that time, shortly after Uranus was discovered, Euler wrote the essentials of calculating Uranus' orbit and played a joke on his grandson. After drinking tea, he suddenly fell ill and his pipe fell out of his hand ... Euler "stopped living and calculating" like this.
Historians list Euler, Archimedes, Newton and Gauss as the four greatest mathematicians in history. They have a remarkable similarity, that is, while creating pure theories, they also apply these mathematical tools to solve a large number of practical problems in astronomy, physics and mechanics. Their work is often interdisciplinary, and they constantly draw rich nutrition from practice, but they are not satisfied with solving specific problems, but try to explore the mysteries of the universe and reveal its internal laws.
Among the rich scientific heritages left by Euler, analysis, algebra and number theory account for 4o%, geometry for 18%, physics and mechanics for 28%, astronomy for 1 1%, and ballistics, navigation science and architecture for 3%. His Introduction to Infinitesimal Analysis was published in Lausanne, Switzerland from 65438 to 0748. It is an epoch-making masterpiece and the first complete and systematic analytical work in the world.
3. A math master with poor academic performance-Hermite.
He was the greatest algebraic geometer in the19th century, but he retaken the college entrance examination five times and failed every time because of his poor math test. He barely graduated from college, and every time he failed in the exam, it was for math subjects. After graduating from college, he couldn't get into any graduate students because the subject he didn't do well in was mathematics. Mathematics is the love of his life, but the math exam is a nightmare of his life. However, this does not change his greatness: he first put forward the "* * * yoke matrix" in textbooks, and he solved the "general solution of quintic equation" for more than 1000 years. He is the first person in the world to prove the transcendence of natural logarithm. His life has proved that "a person who fails the exam can still win?" Quot and what is even more wonderful is that failing the exam has become a blessing in his life. How did this happen? Well (expressing hesitation, etc.) ... maybe you can find the answer in this article! Open the map of Europe, there is a small map embedded in the northeast corner of France, named Lorraine.
This place has been a battleground for military strategists since ancient times, because the Rhine River estuary in the north and the Marne River in the south can go straight to Paris; The Ardennes on the verge are the military commanding heights; This stratum contains the largest iron ore in Europe. As early as the Holy Roman Empire, the Lorraine grassland was covered with the blood of knights; 187 1 After the bloody German soldiers ravaged France, the land that France was asked to cede was Lorraine.
The lineage of a revolutionary.
After a hundred years of war, Lorraine left behind a group of hardworking and philosophical French who were able to face the hardships of the environment. Charles Hermite (1822 12.24) was born in Dieg, a small village in Lorraine. His parents and grandparents both participated in the French Revolution. His grandfather was arrested by extremist political groups after the revolution and later died in prison. Some relatives died on the guillotine; His father was an outstanding metallurgical engineer. Because he was wanted by the commune, he fled to the small village of Lorraine on the French border and worked incognito as a miner in an iron mine.
The owner of the iron mine is Lallemand, a standard and tenacious Lorraine. He has a stronger daughter, Madeleine. In that conservative era, Madeleine was famous for "daring to wear pants without skirts outdoors" and her management of miners was fierce. But as soon as she met this engineer from Paris, she softened up, knew whether the other person was killed or married to him, and gave birth to seven children for him. Hermite ranks fifth among seven children. He was born with a disability in his right foot and needed to walk with crutches. Half of him has the blood of his father's excellent intelligence and ideal struggle, and the other half has the strong blood of Lorraine, whose mother dares to do things and loves and hates each other. This is the first sign of his extraordinary career.
Understanding the beauty of mathematics from the master
Hermite was a problem student since he was a child. He always likes to argue with the teacher in class, especially some basic questions. He especially hates exams; Later, I wrote: "Learning is like the sea, and exams are like hooks. The teacher always hangs the fish on the hook, so how can the fish learn to swim freely and balance in the sea? " Seeing that he didn't do well in the exam, the teacher hit him on the foot with a wooden stick. He hates it. Later? Quot The purpose of education is to use the brain, not the feet. What's the use of kicking? Can kicking make people smart? "He did badly in the math exam, mainly because he was particularly good at math; What he said even made the math teacher mad. He said: "Math class is a pool of smelly water and a pile of rubbish. Those who do well in math are second-rate people, because they only know how to move garbage. "He pretended to be a first-class scientific madman. However, what he said is true. Most of the greatest mathematicians in history came from literature, diplomacy, engineering, military and other fields. They have nothing to do with mathematics. Hermite spent a lot of time reading the original works of mathematicians, such as Newton and Gauss. He believes that only there can we discover the beauty of mathematics, and only there can we return to the basic point of argument and get the source of mathematics excitement. " In his later years, he recalled the frivolity of his youth and wrote: "Traditional mathematics education requires students to learn step by step and cultivate them to apply mathematics to engineering or business, so it has not stimulated students' creativity. But mathematics has its own beauty of abstract logic. For example, in the program of solving multiple squares, the existence of roots is itself a kind of beauty. The value of mathematics is not only for the application in life, but also should not be reduced to a tool for engineering and commercial applications. The breakthrough of mathematics still needs to constantly break through the existing pattern. "
Filial piety genius
Hermite's performance worried his parents. They sent him to "Louis-le-Grande" in Paris, but begged him to study hard and was willing to pay more money. Because of his outstanding talent in mathematics, he can't put himself into the mold of mathematics education, but in order to comply with his parents' wishes, he has to face those subtle and complicated calculations every day, which makes him extremely painful. This filial genius seems destined to torture himself all his life. The entrance examination of Paris Institute of Technology is held twice a year. He/kloc-began to take the exam at the age of 0/8, and only passed the fifth exam with the score of Hewei. In the meantime, when he almost gave up, he met a math teacher, Richard. Teacher Richard said to Hermite, "I believe you are the second mathematical genius after Lagrange." Lagrand is known as Beethoven in the field of mathematics, and his approximate root solution is known as "the poem of mathematics". But Hermite's talent is not enough. Teacher Richard said, "You need God's grace and persistence to complete your studies, so that you won't be sacrificed by the traditional education that you think is rubbish." So, he failed again and again, but continued to take the exam.
A man riding on the back of a snail.
One year after Hermite entered the technical college, the French education authorities suddenly gave an order: people with physical disabilities were not allowed to enter the engineering department, so Hermite had to transfer to the literature department. Mathematics in the literature department has been much easier, and as a result, he still failed in mathematics. Interestingly, at the same time, he published "Reflections on the Solution of Quintic Equation" in the French Journal of Mathematical Research "Journal of Pure and Applied Mathematics", which shocked the mathematical community.
In human history, Greek mathematicians in the third century discovered the solutions of first-order equations and second-order equations. After that, many first-class mathematicians have been puzzling over the solution of the fourth-order equation to the nth power, and they have never found a solution. Unexpectedly, 300 years later, a student in the literature department, who often failed the math exam, actually put forward the correct solution. Hermite knew that he had been "deeply poisoned by the pioneering research of mathematics and deeply loved". Fortunately, his good friend Bertrand quickly helped him make up the math he was going to learn at school. For this pioneering genius, rigid mathematics education brings endless pain; Only the understanding and encouragement of friendship can support him to go on and let him graduate from college with marginal results at the age of 24. Unable to cope with the exam and continue his studies, he had to find a school to help him correct his students' homework. I have been a teaching assistant for almost twenty-five years. Although he published algebra continued fraction theory, function theory and equation theory in these twenty-five years, he was famous all over the world, and his mathematics level far exceeded that of all university professors at that time, but he could not take the exam. Without an advanced degree, Hermite can only continue to correct students' homework. Social reality is so cruel and ignorant to him.
Teachers who don't take exams
What prompted Hermite to advance cynically? There are three important factors, one is the wife's understanding and concentricity. Hermite's wife, the sister of Bertrand, his good friend in college, followed this talented husband without any regrets, year after year. Second, some people really appreciate him and will not despise him because he is physically disabled and lacks a dazzling degree. People who admired him later became famous in the field of mathematics-including Cauchy, who is famous for studying the convergence and divergence of infinite series and differential equations, Jacoby, who is famous for publishing elliptic functions and determinant theory, and joseph liouville, editor-in-chief of Journal of Pure and Applied Mathematics. These are careerists who admire each other and come from real experts. They can support a loser to go a long way more than a little vanity in getting high marks. The third is Hermite's belief. Hermite was seriously ill at the age of 43. Cauchy came to see him and spread the gospel to him. Faith gave him another kind of value and satisfaction. When Hermite was 49 years old, Paris University asked him to be a professor. In the next twenty-five years, almost all the great French mathematicians came from his door. We don't know how he attends classes, but one thing is certain-there is no exam.
Understanding another world in trigonometric geometry
Failure to pass the exam brought him a lot of troubles: his work was not smooth, he retaken the exam many times, others looked down on him and he felt inferior. But it brought him many blessings: knowing his wife, friends, beliefs and the maturity of his whole life. Later, Bell, a professor of mathematics at California Institute of Technology, described Hermite in a passage in "Review of Great Mathematicians in History": The more talented mathematicians in history, the more cynical they are, and the more ironic they speak. There is only one exception, that is, Hermite, who has a truly perfect personality. Hermite died on190165438+1October 4th. In his later years, he wrote: "Trigonometric geometry is immortal. Nothing in nature is an absolute triangle, but there is a perfect absolute triangle in human mind to measure the external shape. Nobody knows why the sum of triangles is 180, and nobody knows why the longest hypotenuse of a triangle corresponds to the largest angle. These basic features of trigonometric geometry were not invented or imagined by people, but existed when people were ignorant, and will not change no matter how time and space change. I'm just a person who stumbled across these features. The existence of triangular geometry proves that there is a world that will never change. "
4. A mathematical wizard-Galois
1832 On the morning of May 30, a young man was unconscious near Lake Glazer in Paris. Passing farmers judged that he was seriously shot after a duel, so they sent the unknown young man to the hospital. He died at ten o'clock the next morning. The youngest and most creative mind in the history of mathematics stopped thinking. People say that his death has delayed the development of mathematics for decades. This young man is Galois, who died before 2 1 year old.
Galois was born in a town not far from Paris. His father is the headmaster of the school and has served as mayor for many years. The influence of family makes Galois always brave and fearless. 1823, 12-year-old galois left his parents to study in Paris. Not content with boring classroom indoctrination, he went to find the most difficult mathematics original research by himself. Some teachers also helped him a lot. Teachers' evaluation of him is "only suitable for working in the frontier field of mathematics".
1828, 17-year-old Galois began to study the theory of equations, and founded the concept and method of "permutation group", which solved the problem of solving equations that had been a headache for hundreds of years. Galois's most important achievement is that he put forward the concept of "group" and changed the whole face of mathematics with group theory. 1829 In May, Galois wrote down his own achievements and submitted them to the French Academy of Sciences, but this masterpiece was accompanied by a series of blows and misfortunes. First, my father committed suicide because he couldn't bear the priest's slander, and then he failed to enter the famous Paris Polytechnic because his defense was simple and abstruse, which made the examiner dissatisfied. As for his paper, he thinks that there are too many new concepts, which are too brief and need to be rewritten; The second draft with detailed derivation was missing because the reviewer died of illness; The third paper 183 1 submitted in June was rejected because the reviewers could not fully understand it.
On the one hand, young Galois pursues the true knowledge of mathematics, on the other hand, he devotes himself to the cause of social justice. 183 1 In the "July Revolution" in France, Galois, as a freshman in a normal university, led the masses to protest against the autocratic rule of the king and was unfortunately arrested. In prison, he contracted cholera. Even under such harsh conditions, Galois continued his mathematical research after he was released from prison and wrote a paper for publication. Shortly after he was released from prison, he died in a duel because he was involved in a boring "love" entanglement.
After Galois died in 16, his 60-page manuscript was published and his name spread all over the scientific community.
5. Thales, the father of mathematics
Born in 624 BC, Ju Lushi was the first famous mathematician in ancient Greece. He used to be a shrewd businessman. After he accumulated considerable wealth by selling olive oil, Cyrus devoted himself to scientific research and travel. He is diligent and studious, at the same time, he is not superstitious about the ancients, and he is brave in exploration, creation and positive thinking. His hometown is not too far from Egypt, so he often travels to Egypt. There, Ju Lushi learned about the rich mathematical knowledge accumulated by ancient Egyptians for thousands of years. When he traveled in Egypt, he calculated the height of the pyramids in a clever way, which made the ancient Egyptian king Amerasis admire him very much.
Cyrus's method is ingenious and simple: choose a sunny day, erect a small stick at the edge of the pyramid, and then observe the change of the shadow length of the stick. When the length of the shadow is exactly equal to the length of the stick, quickly measure the length of the pyramid shadow, because at this time, the height of the pyramid is exactly equal to the length of the tower shadow. It is also said that Ju Lushi calculated the height of the pyramid with the ratio of the length of the stick shadow to the tower shadow equal to the ratio of the stick height to the tower height. If this is the case, it is necessary to use the mathematical theorem that the corresponding sides of a triangle are proportional. Ju Lushi boasted that he taught this method to the ancient Egyptians, but the fact may be just the opposite. It should be that the Egyptians knew a similar method a long time ago, but they were only satisfied with knowing how to calculate, without thinking about why they could get the correct answer.
Before Ju Lushi, when people knew nature, they were only satisfied with how to explain all kinds of things. Ju Lushi's greatness lies in that he can not only explain it, but also add a scientific question mark to why. The mathematical knowledge accumulated by ancient orientals is mainly some calculation formulas summarized from experience. Cyrus believes that the formula thus obtained may be correct in one problem, but it may not be correct in another. Only when they are proved to be universally correct in theory can they be widely used to solve practical problems. In the early stage of the development of human culture, it is commendable that Ju Lushi consciously put forward such a view. It endows mathematics with special scientific significance and is a great leap in the history of mathematics development. This is why Cyrus is called the father of mathematics. Cyrus first proved the following theorem:
1. The circle is divided into two by any diameter.
2. The two base angles of an isosceles triangle are equal.
3. Two straight lines intersect and the vertex angles are equal.
4. The inscribed triangle of a semicircle must be a right triangle.
5. If two triangles have one side and the two angles on this side are equal, then the two triangles are congruent.
This theorem was first discovered and proved by Cyrus, and later generations usually call it Cyrus theorem. According to legend, Ju Lushi was very happy when he proved this theorem. He slaughtered a bull to worship the gods. Later, he also used this theorem to calculate the distance between the ship at sea and the land.
Ju Lushi also made pioneering contributions to ancient Greek philosophy and astronomy. Historians affirm that Cyrus should be considered as the first astronomer. He often lies on his back to observe the constellations in the sky and explore the mysteries of the universe. His maid often joked that Cyrus wanted to know the distant sky, but ignored the beautiful scenery in front of him. According to the research of Herodotus, a historian of mathematics, it is known that the day suddenly turned into night (actually a solar eclipse) after hals War, and Ju Lushi had predicted this before the war.
There is an inscription on Ju Lushi's tombstone: "The tomb of the king of astronomers is a little small, but his glory in the field of stars is quite great."
6. The father of geometry-Euclid
The geometry we are studying now was founded by the ancient Greek mathematician Euclid (330 BC-275 BC). The Elements of Geometry, written by him in 300 BC, has been regarded as the standard textbook for studying geometry for more than 2,000 years, so Euclid is called the father of geometry.
Born in Athens, Euclid accepted Greek classical mathematics and various scientific cultures and became a famous scholar at the age of 30. At the invitation of the king of Egypt, he stayed in Alexandria to teach and do research.
Mathematics research in ancient Greece has a very long history, and there have been some works on geometry, but all of them discuss a certain aspect and the content is not systematic enough. Euclid collected predecessors' achievements and adopted an unprecedented and unique writing method. First, he put forward definitions, axioms and postulates, then proved a series of theorems from simple to complex, and discussed plane figures and three-dimensional figures, as well as integers, fractions and proportions. , finally completed the masterpiece "Geometry".
After the publication of the original, its manuscript has been circulated for 1800 years. After 1482 was printed and published, it was reprinted about 1000 times, and it was also translated into major languages in the world. /kloc-was introduced to China in the 3rd century and soon lost. The first six volumes were retranslated in 1607, and the last nine volumes were retranslated in 1857.
Euclid was good at solving complex problems with simple methods. He measured the length of the shadow of the pyramid at the moment when the figure of a person was just equal to the height, and solved the big problem of the height of the pyramid that no one could solve at that time. He said: "At this time, the length of the tower shadow is the height of the pyramid."
Euclid was a gentle and honest educator. Euclid was also a rigorous scholar. He opposes opportunism and the pursuit of fame and fortune in his studies, and the style of opportunism and quick success. Although Euclid simplified his geometry, the king (Ptolemy) still didn't understand and wanted to find a shortcut to learn geometry. Euclid said: "In geometry, everyone can only take one road, and there is no paved road for the king." This sentence has become an eternal learning motto. Once, one of his students asked him, what are the benefits of studying geometry? He said humorously to his servant, "Give him three coins because he wants to get real benefits from his study."
Euclid also wrote the known number and division of numbers.
7. Hilbert
Hilbert (David, 1862 ~ 1943), a German mathematician, was born in Lao Wei near Konigsberg in East Prussia (Kaliningrad, former Soviet Union). In middle school, Hilbert was a studious student, who showed strong interest in science, especially mathematics, and was good at mastering and applying the contents of the teacher's lectures flexibly and profoundly. 1880, although his father wanted him to study law, he entered the university of konigsberg to study mathematics. 1884 received his doctorate, later obtained the qualification of lecturer, and was promoted to associate professor in this university. 1893 was appointed as a full professor, 1895 was transferred to the University of G? ttingen as a professor, and has been living and working in G? ttingen since then, so 1930 retired. During this period, he became a member of the School of Communication of the Berlin Academy of Sciences, and won the Steiner Prize, the Lobachevsky Prize and the Boyle Prize. 1930 won the science prize of Swedish Academy in Mittag-Leffler, and 1942 became an honorary academician of Berlin Academy of Sciences. Hilbert is an upright scientist. On the eve of the First World War, he refused to sign the book To the Civilized World published in Germany for deceptive propaganda. During the war, he dared to publish an article in memory of "enemy mathematician" Dabu. After Hitler came to power, he resisted and wrote books against the Nazi policy of excluding and persecuting Jewish scientists. Due to the intensification of Nazi reactionary policies, many scientists were forced to emigrate, the once prosperous Gottingen School declined, and Hilbert died alone in 1943.
Hilbert is one of the mathematicians who had a profound influence on mathematics in the 20th century. He led the famous Gottingen School, made the University of Gottingen an important mathematical research center in the world at that time, trained a group of outstanding mathematicians and made great contributions to the development of modern mathematics. Hilbert's mathematical work can be divided into several different periods, and in each period he almost devoted himself to one kind of problems. In chronological order, his main research contents include: invariant theory, algebraic number field theory, geometric foundation, integral equation, physics and general mathematics foundation, among which research topics include: Dirichlet principle and variational method, Welling problem, eigenvalue problem, "Hilbert space" and so on. In these fields, he has made great or pioneering contributions. Hilbert believes that science has its own problems in every era, and the solution of these problems is of far-reaching significance to the development of science. He pointed out: "As long as a branch of science can raise a large number of questions, it is full of vitality, and the lack of questions indicates the decline and termination of independent development." In Paris 1900 International Congress of Mathematicians, Hilbert delivered a famous speech entitled "Mathematical Problems". According to the achievements and development trend of mathematical research in the past, especially in the 19th century, he put forward 23 most important mathematical problems. These 23 problems, collectively called Hilbert problems, later became the difficulties that many mathematicians tried to overcome, which had a far-reaching impact on the research and development of modern mathematics and played a positive role in promoting it.