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An irrational number is a real number that cannot be expressed in the form $\frac{n}{m}$ where $n$ and $m$ are integers.

29 votes
5 answers
3k views

Has Apéry's proof of the irrationality of $\zeta(3)$ ever been used to prove the irrationali...

Apéry's proof of the irrationality of $\zeta(3)$ astounded contemporary mathematicians for its wealth of new ideas and techniques in proving the irrationality of a known constant. It is often the case …
7 votes
0 answers
603 views

Irrationality of the values of the prime zeta function

Preamble: I asked this question on Math.SE with a bounty of 100, but received no replies. The bounty has now ended, and it was suggested I post this here instead. Since Apéry we know that $\zeta(3) …