Today I stumbled across two lovely bits of math(s) I’d like to share.
The first is a fun topological proof that there are infinitely many prime numbers.
The second is a proof that the set of prime numbers is bounded…
[Wait for it…]
…in certain models of weak arithmetic. (I paused for Hotovy to say ‘What?!’ and shake his head in that goofy way. You know the one.) Have a look for yourself: MO21367. (Also, is rational in the model given in that answer.)