The Limits of Mathematics

Here is a great lecture given by Chaitin on incompleteness using several flavours of Berry paradox proof.

What makes it especially stand out is staying strictly in the realm of physical by computing all proofs on actual [universal] Turing machines, implemented by LISP programs. Perhaps more importantly, doing so also produces concrete upper bounds.

Interested readers may find discussion on who can name the bigger number and the essay Omega and why maths has no TOEs worth reading as well.