The answer to this question is a capital letter: no! In order to make a good and meaningful contribution to mathematics, we must work hard; Learn your own field well and master some knowledge and tools in other fields; Ask more questions; Communicate with other mathematicians; We should have a macro understanding of mathematics. Of course, a certain degree of intelligence, patience and mental maturity is necessary. However, mathematicians never need any magical "genius" genes or natural insight; You don't need any supernatural ability to be inspired to solve unexpected problems all the time.

The public has a wrong understanding of the image of mathematicians: these people seem to have created lonely (even a little crazy) geniuses. They don't pay attention to the work of their peers, don't think in a conventional way, and always get unexplained inspiration (or suddenly get it after a painful struggle), and then make a breakthrough on a major issue when all experts are helpless. Such a romantic image is really attractive, but at least in modern mathematics, there is basically no such person or thing. In mathematics, we do have many amazing conclusions and profound theorems, but they have been accumulated for several years, decades, or even centuries, and gained bit by bit with the efforts of many excellent and great mathematicians. Every time we deepen our understanding from one level to another, it is really extraordinary, and some of them are even very unexpected. Nevertheless, these achievements are all based on the work of predecessors, and they are not brand-new. (For example, wiles solved Fermat's last theorem, or perelman solved Poincare's conjecture. )

Today's mathematics is like this: some intuition, a lot of literature, plus a little luck, slowly accumulate progress in a lot of continuous efforts. In fact, I even think the real situation is more satisfactory than the romantic hypothesis mentioned above, although I used to think that the development of mathematics mainly depends on a few geniuses and some mysterious inspirations when I was a student. In fact, this "myth of genius" is flawed, because no one can generate inspiration regularly, or even guarantee that these inspirations are correct every time (if someone claims to be able to do this, I suggest being skeptical). I believe that inspiration can also cause some problems: some people will devote themselves too much to big problems; People should have reasonable doubts about their work and the tools they use, but the above attitude has gradually lost some people's doubts; There are also some people who are extremely insecure about mathematics and have many problems.