I asked a friend who is doing scientific research. What's the difference between a top mathematician and a top physicist? He thought for a moment and told me that there was almost no difference. Top physicists should have top mathematical ability, and top mathematicians can quickly accept and participate in the research of high-end physics topics. The difference is that physics is broader and mathematics is purer. I believe that with Turing's ability, even interdisciplinary research can do a lot.
When I was in the fifth grade of primary school, my classmate had a math genius who taught himself without the guidance of a teacher. The topics selected in the simulated test paper given by the teacher are all given by him, and his Chinese performance is average. His handwriting can only be read by himself, just like that written by a hospital doctor. I don't know what happened now. At that time, his family conditions were very bad.
People who are good at mathematics can see the laws of the universe that ordinary people can't see, which is always a bliss, a spiritual enjoyment that external materials can't achieve.
The crowd searched for him for thousands of Baidu, and suddenly looking back, the man was already dimly lit. That is the highest level of spiritual enjoyment. It also reminds me of the mathematician Zhang, who is the son of mathematics. Why is Yang Zhenning so awesome? What a profound theory the establishment of Young Mills equation is!
Mathematics is a formula used to replace physics. Physics is very studious, and studious is everything in the universe. Yi Xue reveals nature, pays attention to letting nature take its course and scientifically transforms nature, but it still cannot escape nature, just like people and cars, bio-machinery and metal machinery, but the theory is the same. If bones are easy to learn, then science is hyperosteogeny. If bones are easy to learn, then science is a tumor. Geniuses are lonely. There is a reason why they are called geniuses rather than talents. Hard work can make you a talent, but you can't be a genius.
Always believe that the world is led by a group of geniuses: thinkers, politicians, militarists, mathematicians, scientists and artists. They all have extraordinary abilities or thinking or technology! The times and society should give more tolerance and support, vigorously expand their space for releasing wisdom and promote the progress of human society. Go and see those real math geniuses. How much is biased? Most of them finished primary and secondary school courses early and entered universities. If you can't do this, don't call yourself a genius, but your IQ is a little higher than the average person. Genius is that IQ is several levels higher than that of ordinary people.
I did think of a popular science book, and it really felt great when I read it. Wu Jun's Beauty of Mathematics mainly introduces applied mathematics. I was poor at math when I was studying, and the biggest puzzle was what's the use of learning this? Wu Jun's Beauty of Mathematics fully solved the problem of how to use mathematics in life. The best thing is that he uses the advantage of Google background to connect the application of mathematics with the development of computer technology, which is not boring at all.
Genius is genius.
I once saw that the answer to a mathematical problem must be solved by combining auxiliary functions in a given way. I always complain about what problems can only be solved according to the questioner's ideas. In fact, I still have insufficient thinking ability and can't figure out how to construct it.
At present, modern mathematical tools are needed to prove it. The rudiment of calculus in Fermat's era has just begun to take shape. It is hard to imagine that Fermat really proved it, so it is generally believed that he is joking. It can only be said that Fermat's mathematical intuition is too strong to foresee this conjecture. Fermat proved that n=4 was true, so he took it for granted that his method could prove everything. In fact, there are many examples in the history of mathematics in which this feeling-good result proves that it is wrong. In fact, wiles spent seven years focusing on Fermat's Last Theorem. Before he started attacking Fermat's Last Theorem, he saved some small articles and distributed them every year for seven years to ensure his output. This shows that he basically worked hard on Fermat's last theorem.
In addition, wiles did say that he enjoyed his seven-year struggle with Fermat's Last Theorem, but personally, this is not contradictory to loneliness. Because my own research experience (not a big research, of course) tells me that it is lonely not to cooperate in research, and you will feel that no one cares about the problem you are doing. Although Fermat's Last Theorem has attracted great attention as a century-long problem, most mathematicians don't want to risk their academic career to solve this problem, so wiles works alone. You will have wisdom if you don't work hard. If you work hard, you will become a god. If you have this talent, then you will use it wholeheartedly. We can only call such people gods. The simplest thing is that they are also called scientists and mathematicians. However, it will take Einstein and perelman a long time to understand their achievements and papers with other mathematicians and scientists, and to have a little knowledge. This is the gap.
Mathematics is a genius, and it is almost impossible to be buried. The life experiences of great mathematicians such as Gauss, Galois, Abel, Riemann, Lamanukin and Grothendieck prove that as long as you are interested in mathematics and have enough talent, you will get results, because as long as you have a pen and a piece of paper, you will have the whole universe.
Top outstanding figures must have both ability and political integrity, and interests are not the first driving force. Only people who care about the world can be regarded as the weather vane of an era, while scientists who aim at interest can only be called the engine of the times. This kind of scientist may contribute to the development of mankind, but it is only a coincidence brought by interests. To put it bluntly, he doesn't care whether his research is beneficial or harmful to mankind. So we should pursue his contribution to mankind, not this man.
Genius can never be measured by secular standards! A genius is an independent traveler in his bones, otherwise he is not a genius! It's a pity that people in secular society require talented people to have extraordinary creative ability and live a secular life like them. That's ridiculous!