1. The answer is an emphatic NO
In order to make good contributions to mathematics, one does need to work hard. Of course, a reasonable amount of intelligence and patience is also required. But one does not need some sort of magic “genius gene” that generates supernatural abilities.
2. A romantic image of mathematics and the truth
The popular image of the lone genius—who manages by some inexplicable inspiration to come up with a breathtakingly original solution to a problem that confounded all the experts—is a romantic image, but a wildly inaccurate one in the world of modern mathematics. We do have remarkable results in this subject, of course, but they are hard-won and cumulative achievement of years, decades, or even centuries of steady work.
3. The problems of the “cult of genius”
The pressure to try to behave in this impossible manner can cause some to become overly obsessed with “big problems,” and others to become too discouraged to continue working in mathematics. Also, attributing success to innate talent, which is beyond one’s control, rather than effort and education, which are within one’s control, can lead to some other problems as well.
4. It is not denying the existence of talent
It is still the case that some mathematicians are faster, more knowledgeable, or more creative than others. However, the number of interesting mathematical research areas and problems to work on is vast. So given that even the best mathematicians take the opportunity cost into consideration, there are areas where you can make useful contributions to mathematics. It might not be the most glamorous part of mathematics, but in many cases it turns out to actually be more important than any fancy applications.
5. Professional mathematics is not a sport
The objective in mathematics is not to obtain the highest ranking, or the highest number of prizes and awards. Instead, it is to increase understanding of mathematics both for yourself and for your colleagues and students, and to contribute to its development.
References: This post is based on the article “Does one have to be a genius to do maths?” by Terence Tao (July 23, 2023). You can read the full piece here.