[FOM] Hersh on Flyspeck

Joseph Shipman JoeShipman at aol.com
Sat Oct 11 22:07:35 EDT 2014

I find the situation around the classification of finite simple groups most unsatisfactory. The linked article persuades me of something its author might disagree with: that Hales's project is very important and we need more like it.

Although I am persuaded by the article that the likelihood of the classification theorem being correct is overwhelming, that's not enough. Mathematics, like science, must be reproducible.

-- JS

> On Oct 11, 2014, at 5:25 PM, "Timothy Y. Chow" <tchow at alum.mit.edu> wrote:
> Back in January 2008, I wrote:
>> In the introduction to his delightful anthology, "18 Unconventional Essays on the Nature of Mathematics," Reuben Hersh states, regarding the Flyspeck project of Thomas Hales, that he does not know anyone who either believes that the project will be completed or that, even if claimed to be complete, it will be universally accepted as definitively verifying the correctness of the proof.
> Does anybody know if Hersh has commented publicly on the announcement of the completion of Flyspeck?  Obviously, he was wrong about the completion of the project.  Hersh can trivially ensure that Flyspeck will fail to be "universally" accepted, simply by refusing to accept it himself, but does he believe that significant numbers of mathematicians will continue to resist machine-verified formal proofs?
> I'm not sure what Hersh has in mind by "definitively verifying the correctness of a proof," but I really don't believe that the mathematical community as a whole is any more skeptical about the proof of the Kepler conjecture than about, say, the proof of Fermat's Last Theorem or the Poincare Conjecture.  Does any FOM reader have anecdotal evidence to the contrary?
> Tim
> P.S. On a somewhat related note, I just learned (from Professor Joe Gallian) about the paper "A group theory of group theory" by Alma Steingart, which you can read here:
> http://alum.mit.edu/www/tchow/steingart.pdf
> Steingart takes a close look at the sociology of the proof of the classification of finite simple groups and arrives at conclusions that are somewhat similar to Hersh's philosophy of mathematics.
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