The Beauty of Doing Mathematics pp 1-27 | Cite as

# What does a mathematician do and why?

## Summary

The conference started with why, for ten minutes. I do mathematics because I like it. We discussed briefly the distinction between pure mathematics and applied mathematics, which actually intermingle in such a way that it is impossible to define the boundary between one and the other precisely; and also the aesthetic side of mathematics. Then we did mathematics together. I started by defining prime numbers, and I recalled Euclid’s proof that there are infinitely many. Then I defined twin primes, (3,5), (5, 7), (11,13), (17,19), etc. which differ by 2. Is there an infinite number of those? No one knows, even though one conjectures that the answer is yes. I gave heuristic arguments describing the expected density of such primes. Why don’t you try to prove it? The question is one of the big unsolved problems of mathematics.

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### Bibliography

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