In the history of mankind, a few super-class mathematicians have promoted the development of mathematics for decades or even hundreds of years by their own efforts, leaving a rich legacy to mankind, such as the following.
Euler
Euler, a mathematical hero, has made many contributions in the field of mathematics. His inspiration and manipulation skills in mathematics made the whole world admire him. What made Euler famous at one fell swoop was a series-the Basel series.
Before Euler, the problem of Basel series puzzled the mathematics field for more than a century. Leibniz is one of the inventors of calculus, and his mathematical skills have reached the peak. With the help of calculus, he can use mathematical series freely. Leibniz even said to his friend Huygens: As long as all convergent infinite series follow certain laws, I can find the sum.
Then in 1673, the British mathematician Pell took out the Basel series and stunned Leibniz at once. No matter how hard Leibniz racked his brains, he couldn't find the sum of Basel series.
Then at 1734, 27-year-old Euler suddenly solved this problem. Why all of a sudden? Let's look at Euler's solution to Basel series:
Only two simple mathematical knowledge were used in the whole process, but the skills used by Euler were so ingenious. I believe that anyone who can understand the proof process will admire Euler's extraordinary wisdom.
Riemann
German mathematician Riemann is a student of the great mathematician Gauss. It is said that a good teacher makes a good teacher. This student of Gauss is really not simple. He created new fields, such as Riemannian geometry and analytic number theory.
1859, Riemann was elected as an academician of the Berlin Academy of Sciences. In order to express his gratitude, Riemann submitted a paper entitled "On the number of prime numbers less than a given value" to the Berlin Academy of Sciences. It was this paper that kept later mathematicians busy for more than a hundred years, and some conclusions that Riemann seemed to take for granted have not been answered yet.
In this paper, there are six conjectures in just a few pages, but Riemann doesn't seem to regard them as conjectures, but put them forward in terms of "obvious" or use them directly without any explanation; In the following decades, five conjectures were independently proved by other mathematicians, some of whom won the Fields Prize. But the last conjecture has not been proved, which is the famous Riemann conjecture.
It is enough to see that Riemann was a mathematician far beyond that era, and his Riemann geometry became the mathematical basis of later general relativity.
Poincare
Poincare was a famous French mathematician and physicist, and was recognized as a generalist and mathematical leader at the end of 19 and the beginning of the 20th century. Poincare was a genius since childhood, and his ability to learn knowledge shocked the world.
Poincare mastered seven languages at the age of six, and his extraordinary memory enabled him to recite a certain knowledge point clearly in a few lines and pages. 1870, the Franco-Prussian War broke out. In order to understand the present situation, Poincare only spent a week learning German. Some people say poincare: he exists to prove the existence of genius. Others work hard all their lives, he just needs to work hard at once.
Terence Tao
Tao Zhexuan is a mathematician who is still alive today. He has a high IQ. At the age of 4, he finished all the primary school courses in kindergarten. At the age of seven, he taught himself calculus. /kloc-at the age of 0/2, he won the gold medal in the International Mathematical Olympiad. 15 years old received a master's degree, 2/kloc-0 years old received a doctorate, and 3/kloc-0 years old won the Fields Prize.
At present, the field of mathematics has been highly detailed, and it is almost impossible for mathematicians to master all the knowledge in the field of mathematics. However, Tao Zhexuan is an exception. He has made breakthroughs in many fields of mathematics and is known as "Mozart in mathematics".