[FOM] Question about theoretical physics
Timothy Y. Chow
tchow at alum.mit.edu
Sat Mar 2 15:37:34 EST 2013
On Sat, 2 Mar 2013, Joe Shipman wrote:
> Tim's analogies to mathematics are on the right track but there are
> distinctions his examples need to reflect. The Appel-Haken-Koch proof
> was objectionable only because the calculations were too large to be
> verified by hand, but the documentation was always excellent so that it
> was easy both to verify the proof that the algorithm was correct, and to
> reproduce the calculation.
This is not quite accurate. Though the use of a computer was what got all
the tongues wagging, the most tedious part of the job for any potential
verifier was checking all the little hand-drawn diagrams on the 400-page
microfiche supplement to the paper. I have heard that someone did make a
heroic effort to try to verify everything, and in the process discovered
lots of little bugs in the diagrams. I believe that that verification
effort was never carried out to completion. When Robertson, Sanders,
Seymour, and Thomas decided to take a crack at it, they eventually decided
that it was easier to re-prove the result using the same general strategy,
because checking the original proof (and fixing all the bugs) was just too
painful. The RSST proof *is* satisfactorily documented, and today we even
have a Coq proof of the four-color theorem, thanks to Gonthier. But I
hesitate to say that the documentation of the original proof was
"excellent."
Tim
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