[FOM] FOM Digest, Vol 188, Issue 25

David Fernandez Breton djfernan at umich.edu
Fri Aug 31 12:58:19 EDT 2018

> Date: Thu, 30 Aug 2018 18:06:07 -0400
> From: Jos? Manuel Rodriguez Caballero <josephcmac at gmail.com>

> By the way, I meet a person in France who claimed to have a proof of the
> Riemann hypothesis. I said to him: fine, formalize your proof in a proof
> assistant. He said to me that it will be hard to learn a proof assistant. I
> reply him: if you are able to prove the Riemann hypothesis, to read the
> manual of a proof assistant is nothing for your brain.

Although correctness in mathematics is not negotiable, and it constitutes a
"sine qua non" of mathematical practice, I believe (and I'm sure others
will agree) that correctness, by itself, is worth very little, if it's not
accompanied by some aesthetic appeal and sense of understanding. A proof of
the RH of which we do not understand anything, other than the fact that it
is correct (as witnessed by some computerized proof checker) will probably
not be very valuable (cf. the proof of the four colour theorem). On the
other hand, a "proof" of RH that provides new insights, and aesthetically
pleasant new ideas, might end up being much more valuable (in the sense
that it can give rise to new questions, new lines of research, and just
generally new interesting activity within the mathematical community), even
if it is ultimately found to be incorrect. Think about Fermat's "proof" of
the FLT (which was the empty set, really, and yet it motivated 400+ years
of intense investigations) vs. Cardano's formulas for the cubic equation
(entirely correct, but ultimately irrelevant nowadays).

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