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What do mathematicians usually do?
There are also many kinds of mathematicians. In fact, mathematics is very energy-consuming. In my P University, a professor admitted that it would be good to do research one morning a day, and the rest of the time would be reading and resting, and of course attending classes, which was also very energy-consuming. So the question is, what is the research for? In my humble opinion, the most important step is to find the problem, that is, to study the subject. This process may be reading a book, or studying an interesting question to find an accurate, meaningful and researchable question. The rest of the time is to conquer it, conquer it. In fact, China people have never been weak. How did the problem arise? This is a big problem, and it has always been a shortcoming of China people. I dare not talk nonsense. Maybe we can have a deeper understanding in the future. There are good and bad questions, and a meaningful and beautiful question is really hard to get. Of course, we can also study ready-made problems or conjectures, such as the famous Riemann conjecture. The life of a mathematician is actually so ordinary and nothing special. Sometimes ordinary life is their inspiration. I'm not trying to support myself. One day when I was playing tennis and picking up the ball, I suddenly conceived a probability problem. In other words, the inspiration of mathematics can also be vivid. Maybe it's a little off topic, just saying something I have learned so far, which is not complete.