He even chose an historical name for his book: "Elements", invoking Euclid's set of books which included sections on number theory. This is much like Whitehead and Russell's title "Principia Mathematica" which would have made many think of Newton's "Philosophiæ Naturalis Principia Mathematica". Regardless of Russell and Frege, I think of Russell being more famous because of "Principia Mathematica" being struck down by Gödel. In other words, Nelson would be the new Russell and Tao the new Gödel. On Wed, Oct 5, 2011 at 14:55, Dan Asimov <dasimov@earthlink.net> wrote:

Apparently, Prof. Ed. Nelson of the Princeton U. math dept. has been about to publish a book in which he supposedly proves the inconsistency of Peano arithmetic.

But his outline of his proof, made public, led to Terence Tao's pointing out a problem in the reasoning, and apparently Nelson has withdrawn his claim.

Discussion here:

< http://golem.ph.utexas.edu/category/2011/09/the_inconsistency_of_arithmeti.html>

(Which sounds a bit like a reenactment of Bertrand Russell's pointing out a problem with the fundamentals of Gottlob Frege's about-to-be-published magnum opus on set theory, a little over a century ago.)

--Dan

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