In private, the mathematical Daniel is divided into three levels:
The first level is the master, creating theoretical branches or new fields;
The second level is the great god, who discovers important theorems and puts forward eternal questions and conjectures;
The third level is heroes, who solve famous problems and prove or overthrow a major conjecture.
Of course, these so-called grades are only for the convenience of classification and do not completely represent grades. People who exceed these three levels are also very powerful, but they cannot be called mathematicians. Let's call them mathematicians!
Speaking of mathematical masters, the first one is Pythagoras, an ancient Greek mathematician. He lived from about 580 BC to about 500 BC, and was an ancient Greek mathematician and philosopher of the same age as Laozi, Confucius and Buddha Sakyamuni. In that distant era, Pythagoras not only studied geometry and number theory, but also put forward Pythagoras theorem, sum of interior angles of triangle, golden section, perfect number and affinity number, irrational number operation of root number two, regular polygon and so on. Most importantly, he put forward a famous philosophical proposition: Everything is a number!
There are not many first-class masters, because there are only a few branches of mathematics.
Among the masters, Euclid systematically expounded geometry and number theory. His great achievement lies not only in the fact that geometry has benefited all walks of life for thousands of years, but also in his pioneering a method, namely "axiomatic deduction", which has benefited scientists from various disciplines in later generations.
Masters should also include Descartes who founded analytic geometry and dualism, Newton and Leibniz who founded calculus, Gauss, Lobachevsky and Riemann who founded non-Euclidean geometry (differential geometry), Arthur Kelly, an English mathematician who founded matrix theory in19th century, and von Neumann, the father of modern computer and game theory. ...
Descartes: I think I am? I think, therefore I am. )
My cognitive level is limited, and the above list is definitely incomplete. There must be, for example, Poincare, the founder of combinatorial topology, a French mathematician. In addition, the French mathematician Galois founded the group theory. If he hadn't died in a duel at the age of 2 1, he would have become a grandmaster. There are many legendary mathematical geniuses, such as Srinivasa Ramanujan, an Indian mathematical genius who died at the age of 32, and so on, so I won't go into details here!
(mathematician Galois)
The level of the second-level mathematics gods is definitely not lower than that of the masters. I only hate that they were born decades later, and many fields have been opened up by their predecessors.
For example, the German mathematician Hilbert, one of the greatest mathematicians in the 20th century, was called "Alexander in mathematics" by later generations. He made great contributions to mathematics in the fields of algebra, geometry and integral equations. What is most praised by the world is that Hilbert put forward 23 most important mathematical problems at the International Congress of Mathematicians in Paris in 1900, which inspired mathematicians to overcome difficulties and had a far-reaching impact on modern mathematical research.
The other is Euler,/kloc-one of the most outstanding figures in mathematics in the 8 th century. He not only made great contributions to mathematics, but also applied mathematics to almost the whole field of physics. His textbooks Mechanics, Analysis, Geometry and Variational Methods, Introduction to Infinitesimal Analysis, Principles of Differential Calculus and Principles of Integral Calculus are all classics in mathematics, and of course there is the famous euler theorem.
There is also a great god, Fermat, known as the "king of amateur mathematicians". He not only did a lot of pioneering work in analytic geometry, calculus, probability theory and other fields, but also put forward Fermat's Last Theorem from 1637 to 1995, which was proved by the British mathematician andrew wiles. For hundreds of years, I wonder how many top mathematicians in the field of number theory have been stumped.
There is also Goldbach, who is well known in China. His job is a German middle school teacher and, of course, a famous mathematician. Goldbach, 36, was elected as an academician of the Russian Academy of Sciences with 1725. 1742, Goldbach wrote to Euler and put forward the famous Goldbach conjecture, which has not been proved or falsified so far and is considered as one of the three major mathematical conjectures in the world.
Chen Jingrun, a mathematician in China, has made outstanding contributions to solving Goldbach's conjecture. )
Of course, mathematicians who can put forward or systematically expound famous mathematical conjectures are all great mathematicians and people with great points. Many conjectures took hundreds of years to be proved by later heroes, such as Poincare conjecture. But Rao is the height of the development of human wisdom and computer technology, and there are still many mathematical conjectures that are still mysterious and attractive.
The 23 most important mathematical problems summarized by Hilbert at the Paris 1900 International Congress of Mathematicians were all put forward by great figures.
There are also mathematical stories such as "the Millennium Prize Problem". On May 24th, 2000, the new millennium mathematics conference was held in the French Academy. At the meeting, Gavos, winner of 1997 Fields Prize, gave a speech on the topic of "The Importance of Mathematics" and put forward seven "Millennium Prize Questions". Clay Institute of Mathematics invited experts in related fields to elaborate on each issue. Clay Institute of Mathematics provided a reward of $6,543.8+0,000 for solving every "Millennium Prize problem". Of course, any solution must be published in a world-renowned mathematical magazine for two years and generally recognized by the mathematical community, before it can be examined by the scientific advisory Committee of Clay Institute of Mathematics to decide whether it is worth winning a million-dollar prize.
The proponents of the "Millennium Prize Question" are all great gods (please see the official themselves for specific names)! Because these problems are all about the basic theory of mathematics, the solution of these problems will greatly promote the development and application of mathematical theory.
(The Yang-Mills gauge field problem is also one of the Millennium Prize problems.)
Finally, list a few math heroes!
Andrew wiles, who proved Fermat's last theorem, is a mathematical hero. He is a famous British mathematician, a professor at Oxford University and a foreign academician of the American Academy of Sciences. 1986, he began to prove Fermat's last theorem. He gave up all other activities and began to study on the basis of combing the previous work and basic theory in related fields. This process is tortuous. He once endured the loneliness of no progress for more than two years and experienced the embarrassment of proving that the audit was flawed. However, just as he admitted the loophole and was ready to explain why he was wrong, he found a way to make up the loophole, thus completing the last stick of proving Fermat's last theorem.
Grigory perelman, a Russian mathematician, is the most outstanding in mathematics. He is the first mathematician to solve a "Millennium Prize problem". He shut himself in a humble apartment in St. Petersburg and solved Poincare's conjecture by himself.
After his achievements were generally recognized by the international mathematics community, he refused to receive the prize of $6,543,800+and refused to attend all the international conferences that awarded him prizes. For him, mathematics is God's greatest reward, and the pleasure of solving mathematical problems is greater than all honors and praises. Therefore, he would rather eat bread and live in a humble room, and would rather squeeze time to give lectures to middle school children than win an award: "I have to brush my clothes and go deep into anonymity." What a hero!
After grigory perelman cracked Poincare's conjecture, there are still six "Millennium Prize puzzles", which are being tackled jointly by mathematicians from many countries. Looking forward to the birth of a hero!
There is Riemann conjecture in the remaining six questions.
1859, German mathematician Riemann discovered that the mystery of prime number distribution lies in a special function, which was later called Riemann Zeta function. Riemann conjectures that all nontrivial zeros of Riemann zeta function are distributed on a special straight line called "critical line" on the complex plane.
If Riemann conjecture is established, it will have great practical significance. In fact, mathematicians have derived hundreds of theorems, involving many fields, constructed a series of theories and eagerly applied them.
In recent years, it has been claimed that Riemann conjecture has been proved. 20/kloc-in September, 2008, Michael attiya, a famous British mathematician, put forward a "simple idea" to prove Riemann's conjecture at the 6th Heidelberg International Prize Winners Forum in Mathematics and Computer Science. He said, "Riemann conjecture is a famous problem put forward by 1859, which has not been solved yet. I will give a concise proof of using the new method according to the relevant work of von Neumann (1936), Hitzbrook (1954) and Dirac (1928). "
Sir Michael Atia, who is nearly ninety years old, is the winner of Abel Prize and Fields Prize. His influence on mathematics is enormous, but his "concise proof" needs to be tested by mathematics and time.
I hope the Riemann conjecture can be proved soon. If Riemann is wrong, then many things being applied are wrong. That would be chaos!
….
Someone once asked Hilbert a question in his later years: If you could be resurrected in a few hundred years, what would you like to do most? Hilbert said: I wonder if Riemann conjecture has been proved.
Mathematics is so charming, Riemann conjecture is so magical!
There are still many math experts in the world, so I won't list them one by one.
There are also many experts in mathematics in China, such as Liu Hui (about 225-295), a famous mathematician in ancient China. His representative works "Nine Arithmetic Notes" and "Calculations on the Island" are China's most precious mathematical heritage.
Zu Chongzhi (429-500) made great contributions to mathematics, astronomical calendar and mechanical manufacturing. On the basis of exploring the accurate method of pi pioneered by Liu Hui, he calculated the "pi" to the seventh place after the decimal point for the first time, that is, between 3. 14 15926 and 3. 14 15927, which made great contributions to the research of mathematics.
Qin (1208- 126 1 year) is the author of Shu Shu Nine Chapters, among which solving the problem of linear congruence equations, the skill of triclinic quadrature and Qin algorithm (numerical solution of positive roots of higher power equations) are important contributions of world significance.
There are many famous contemporary mathematicians in China, such as:
Hua, the founder of modern mathematics in China.
Chen Shengshen, the pioneer of modern differential geometry, won the Wolff Prize for lifelong achievement in mathematics!
Sue is a world-famous differential geometer and the pioneer of the school of projective differential geometry.
Chen Jingrun, number theorist, Goldbach conjecture expert!
Qiu Chengtong won the Phil Prize for Mathematics for solving many important problems in differential geometry! Qiu Chengtong, 1949, a native of Shantou, Guangdong, moved to Hong Kong with his parents in the same year. He is a Chinese-American, an internationally renowned mathematician and the first Chinese winner of the Fields Prize.
Of course, Qian Xuesen, who proposed Yang-Mills gauge field and Qian Xuesen's trajectory ... Many people's mathematical attainments were just covered up by other light.
And so on, coupled with the emergence of young mathematical geniuses, contemporary mathematical circles should be more talented!
……
Ah, math! How amazing you are, making masters, great gods and heroes bow their heads in poverty, haunted by dreams, and even die unsatisfied!