Weird Things Happen When Math Gets Too Expressive

https://www.youtube.com/watch?v=EVwQsvof7Hw

Peano arithmetic is sufficiently expressive enough to be equivalent to any possible future theory of mathematics.

Even before I started the video, I had a feeling it was going to lead to a kind of "introspective" mathematics that can reason about its own reasoning. I was not disappointed, thank you.

Physics, Topology, Logic and Computation: A Rosetta Stone - https://arxiv.org/abs/0903.0340