I. Study and research career

Hardy showed his cleverness in mathematics in his childhood, and formed the habit of asking questions and exploring freely very early. /kloc-at the age of 0/3, he got a scholarship to study at Winchester College, which was known as the cradle of mathematicians at that time.

/kloc-at the age of 0/9, Hardy entered Trinity College, Cambridge University for further study. At Professor Laffer's suggestion, Hardy read Jordan's masterpiece An Analysis Course, and said, "I will never forget the shock when I read that famous book. This is my first revelation as an algebra expert. It was when I read this book that I first realized the true meaning of mathematics. "

At the age of 2 1, Hardy obtained an honorary degree in mathematics from Cambridge University and became a first-class generalist. However, Hardy, who is very rebellious to tradition, thinks that this kind of examination is meaningless.

19 1 1 year, Hardy began a long-term cooperation with Littlewood. They mailed the letter through the college and reached a tacit understanding: when receiving the letter from the other party, they should not look at the solution first, but solve the problem independently. Hardy didn't finalize it until an agreement was reached. At that time, some uninformed foreign mathematicians thought that Littlewood was just a pseudonym invented by Hardy. In fact, Littlewood himself is an excellent mathematician. Together, they established a world-class Cambridge school of analysis in the first half of the 20th century.

Second, Hardy and Ramanukin.

Hardy called his discovery of Lamanukin a romantic episode in his life.

19 13, Ramanukin, who was born in India, wrote a letter to Hardy, in which he stated his research on the distribution of prime numbers and listed 120 formulas, involving many fields in mathematics. Most of these formulas have been proved by others, and some of them seem easy, but in fact they are difficult to prove.

Hardy was convinced that Lamanukin was a mathematical genius, so he invited him to England. Hardy spent a lot of time teaching Raman Nukin modern European mathematics. He found the limitations of Lamanukin's knowledge as surprising as its profundity. But he needs strong intuition and reasoning ability, and his work and way of thinking are challenging.

Unfortunately, Hardy's cooperation with Lamanukin did not last long. 19 19, Lamanukin died of tuberculosis. Hardy deeply regrets the untimely death of this Indian mathematical wizard. He participated in sorting out Ramanujin's prose and wrote Ramanujin. Hardy's association with Lamanukin was also passed down as a much-told story by the mathematical community.

Here is a short story that is widely circulated: Hardy once took a taxi in London to visit Lamanukin. In a chat with Lamanukin, he mentioned that he came to the hospital by taxi with license plate number 1729: "This is an annoying number, I hope it is not a bad sign."

"No," Lamanukin said, "this is a very interesting number. I can express it as the sum of two cubes in two ways: 1729=9? + 10? = 1? + 12? . (In fact, 1729 is the smallest natural number that satisfies this property. )

Later, Hardy told the end of the story with great interest: "Naturally, I asked him if he knew the answer to such a question corresponding to the fourth power. He thought about it and said that the first such number is very large, which is 6353 18657. " ?

When Littlewood heard this anecdote, he sighed: "Every positive integer is a friend of Lamanukin." Later, 1729 was called Hardy-Ramanukin constant, or the number of taxis and the number of taxis.

Third, Hardy's personality

As a famous mathematician, Hardy's character is praised as much as his knowledge. He is talkative: talking can attract many people around him; He is strict with himself, attending all kinds of meetings he should attend and performing his duties; He is full of justice, hates war, and doesn't like anything hypocritical in life.

Hardy is very modest and often emphasizes the importance of collaborators and belittles himself. He once said that it was because of equal cooperation with Littlewood and Lamanukin that he achieved unusual success. Hardy led many young people in early research and gave them help and encouragement. For example, when China mathematician Hua was studying in Cambridge, he got Hardy's guidance and help. Wiener expressed his admiration and gratitude to Hardy many times in his autobiography "I am a Mathematician".

Besides studying mathematics, Hardy's main interest is ball games. Especially in cricket, he is a player who can master the latest technology and an experienced critic. Hardy once said that he chose mathematics as his career, mainly because mathematics is the best thing he can do, not any other reason to show off. His achievements in mathematics are based on his infinite love and devotion to mathematics.

Fourthly, Hardy talks about mathematics.

Hardy expressed his views on mathematics in A Mathematician's Argument.

Regarding whether mathematics exists objectively, Hardy thinks: "I think mathematical entities exist outside of us, and our role is to find it and observe it. The theorem that is exaggerated as our' creation' is just a record of our observation. "

As for the beauty of mathematics, Hardy thinks: "It may be difficult to define the beauty of mathematics, but it is really a kind of beauty." "The best math is both beautiful and serious."

Hardy hates the application of mathematics in war. He regards pure mathematics as real mathematics and draws a clear line with applied mathematics: "On the whole, pure mathematics is obviously more useful than applied mathematics. A pure mathematician seems to have advantages not only in aesthetics but also in practice. Because useful things are mainly skills, and mathematical skills are mainly spread through pure mathematics. " "Real mathematics has no effect on war." "This is a' harmless' profession." Some of Hardy's views are still controversial. )

Hardy was recognized as the leader of pure mathematics in Britain at that time. Finally, this paper ends with his summary and evaluation of his life: "I have contributed to the field of knowledge and helped others to supplement the details;" The value of these things is only different in degree, but there is no essential difference from the value created by great mathematicians or any other artists, big or small, who left some kind of memorial behind them. "

Share another anecdote about Hardy.

Hardy likes to spend his summer vacation with mathematician Bohr (the younger brother of physicist Bohr) and discuss Riemann conjecture together. They are all involved in the discussion, and Hardy often stays until the end of holidays before returning to England. As a result, once at the dock, he unfortunately found that there was only one boat left to ride. No way, he had to bite the bullet.

It's no joke to take a boat in such a Wang Yang sea. If you do it well, it will be romantic and exciting, otherwise you will be buried in the belly of a fish. For the safety of the journey, most passengers who believe in God are busy praying for God's blessing. On the other hand, Hardy is a man who firmly does not believe in God. But Hardy has not been idle in this do or die. He sent Bohr a short postcard with only one sentence: "I have proved Riemann conjecture." ?

Did Hardy really prove Riemann conjecture? Of course not. Then why did he send such a postcard? After returning to England, he explained the reason to Bohr. He said that if his ship really sank that time, people would have to believe that he really proved Riemann's conjecture. But he knows that God will never give him such a great honor-a man who firmly does not believe in God, so God will never let his ship sink.