[FOM] Unreasonable effectiveness

Tom Dunion tom.dunion at gmail.com
Tue Nov 5 14:27:52 EST 2013

Whatever the specification of a mathematical model of reasonable
effectiveness might be, it seems likely it would often "under predict" the
usefulness of something like a lemma.  Here is why.

Often conjectures become proven, and may become lemmas in the proof of a
grander theorem, which then connects up with something else, and so on...

Superb example: Who would ever have thought the Taniyama-Shimura conjecture
would be of use (or even interest) to more than a handful of specialists?
But then someone else's conjecture (the epsilon conjecture) becomes proven
(Ribet's theorem) and wow! -- the connection is revealed toward a possible
proof of FLT, successfully luring Andrew Wiles into the attempt.

Somehow one gets the feeling that there was something "out there" and that
earlier mathematics was unreasonably effective in providing large bricks of
the edifice to be stumbled upon.

-- TD
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