[FOM] Hersh on Flyspeck
Timothy Y. Chow
tchow at alum.mit.edu
Sat Oct 11 17:25:48 EDT 2014
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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