[FOM] Hersh on Flyspeck
Timothy Y. Chow
tchow at alum.mit.edu
Thu Jan 10 21:22:29 EST 2008
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.
This, to me, is quite an astounding claim. It is one thing to believe
that the project will never be completed, but it is quite another to say
that he *does not know anyone who believes otherwise*! (Including Hales,
even?) Just how widespread is the belief that Flyspeck will never be
completed?
Part of the issue is that Hersh misunderstands Hales's estimate of the
work required to complete Flyspeck, which is something like 20
person-years. Hersh exaggerates this to "hundreds of people working for
20 years."
The part about universal acceptance is more interesting. With a
sufficiently literal interpretation of "universal," it is not universally
accepted that angle trisection is impossible, as anyone who has dealt with
mathematical cranks knows. But presumably Hersh means to claim something
stronger---that (as I would phrase it) the Formalization Thesis is false
in this particular instance. That is, there will be substantial
disagreement as to whether the formal theorem verified by HOL Light
faithfully represents what we understand by "The Kepler Conjecture."
Do any of the opponents of the Formalization Thesis (as I stated it)
believe that, even if Flyspeck is completed as planned, there will be no
consensus among ("non-crank") mathematicians regarding whether the formal
theorem accurately expresses the Kepler Conjecture?
Tim
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