The question of how mathematicians think is closely related to the question, **“How does a musician compose?”** Similarly, this question is asked to learn how the creative process works. Those who are interested in computer science or especially artificial intelligence can give the correct answer to this question. A real mathematician is not interested in finding the answer to this question, he’s just busy doing math.

Unfortunately, there is no clear way to answer the question of how a mathematician thinks. But we can approach this question as follows; if you watched any chess tournament, the game’s analysis is shared in detail at the end of the match. When you examine the analysis, you will see a breaking point in each game. Similarly, mathematicians also experience a breaking point while working on a problem before finding a solution.

Therefore, it is helpful to analyze a few mathematical proofs to answer our question and pinpoint the breaking points. For example, as we all know, **Euclid’s theorem** states that there are infinitely many prime numbers.

## The proof of this theorem is more beautiful than the theorem itself.

So how did Euclid realize that prime numbers are infinite? Euclid’s approach to the…