One wonders if he will try to pursue the idea of proving the inconsistency of PA, or if the mistake spotted by Tao is too crucial to be repaired. By the way, here is a cool post on the whole issue over at Godel's lost letter and P = NP (via Ole Hjortland).
But anyway, until further notice, PA is still consistent; we can now go enjoy the weekend in peace.
(And thanks to John Baez for posting on Nelson's withdrawal at G+.)
UPDATE: Here is the message that Nelson just sent around at FOM:
Terrence Tao, at http://golem.ph.utexas.edu/category/2011/09/ and independently Daniel Tausk (private communication) have found an irreparable error in my outline. In the Kritchman-Raz proof, there is a low complexity proof of K(\bar\xi)>\ell if we assume \mu=1, but the Chaitin machine may find a shorter proof of high complexity, with no control over how high.This seems to be a good example of what J. Azzouni has described as the 'uniqueness' of mathematics as a social practice: in just a few days, a consensus has emerged as to what was wrong with Nelson's purported proof, including Nelson himself. I cannot think of any other field of inquiry where consensus on a substantive, serious issue/challenge would emerge with the same swiftness. There really is something special about mathematics...
My thanks to Tao and Tausk for spotting this. I withdraw my claim.
The consistency of P remains an open problem.