What is up with people saying you cannot prove a negative? Of course you can! (At least in formal settings)

For example it's extremely easy to prove there is no square with diagonals of different lengths. I'm the hard end, Andrew Wiles proved Fermat's Last Theorem which expresses a negative.

That's just a nit though, you're right about the infinite regress problem.

It's pretty easy to prove lots of negatives outside of mathematics, too. It's easy to prove there's no elephant in my living room at the moment.