Faster-than-light neutrinos? Boring... let's see something really revolutionary. Edward Nelson, a math professor at Princeton, is writing a book called Elements in which he claims to prove the inconsistency of arithmetic. He writes:

"I am writing up a proof that Peano arithmetic (P), and even a small fragment of primitive-recursive arithmetic (PRA), are inconsistent. This is posted as a Work in Progress at http://www.math.princeton.edu/~nelson/books.html

A short outline of the book is at:

http://www.math.princeton.edu/~nelson/papers/outline.pdf

The outline begins with a formalist critique of finitism, making the case that there are tacit infinitary assumptions underlying finitism. Then the outline describes how inconsistency will be proved. It concludes with remarks on how to do modern mathematics within a consistent theory."

Thanks to +David Roberts and +Andres Caicedo for pointing this out.

I have no idea if Nelson's proof is correct! He has, however, done good mathematics in the past: in his PhD thesis he was the first to rigorously construct an interacting quantum field theory.
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