zlacker

>>jeremy+(OP)
Mathematician Edward Nelson has a very interesting take on "big" numbers. He claims that the exponential function is not necessarily total, and a number like 2^1000000000000 might not actually exist. The reason he singles out exponentiation is that the reasoning that exponential numbers are "real" numbers, is circular (impredicative). According to Nelson, speaking about such numbers might lead to condradictions, just like speaking about "the set of all sets that don't contain themselves" leads to a contradiction.

He also relates these issues to Christian philosophy, which I find very interesting. In particular, he claims that the a priori belief in the objects defined by Peano Arithmetic, is equivalent to worshipping numbers, as the Pythagoreans did.

I think this is the best starting point if you're interested in reading about his ideas: https://web.math.princeton.edu/~nelson/papers/warn.pdf

>>swatow+im
Nelson withdrew the claim in this paper based on a blog interaction with Terry Tao.

http://m-phi.blogspot.com/2011/10/nelson-withdraws-his-claim...

The whole episode: - Reputed Princeton mathematician publishes paper questioning the foundations of math - Terry Tao 'disproves' him in a series of blog comments is one of the more interesting recent happenings in the world of math