So this afternoon I got curious about what Riemann actually
said with respect to his famous hypothesis. Actually, it was
a curiously stupid statement: in all probability they (the zeroes)
are all real, but after a few weak attemps, a fully rigorous
proof was not really necessary, because superfluous to his purpose...
Well, NOT. We currently have armies of mathematicians with computers
pumping out billions of Riemann zeroes, and hoping for a way out
of the nightmare. Reimann himself, on his death, left behind cases of
computational papers that his wife had burned; man was a fire
hazard and no computational slouch.
This is not the first occurence of the phenomenon. Fermat's last theorem
( a^n + b^n = c^n has no solution for n > 2), was found in the margin of a
notebook, with the note he just didn't have room for the proof; a ridiculous
assertion, as attested by his son. Gauss - not one to miss the party - left us with
this gem: "If others would but reflect on mathematical truths as deeply and
continuously as I have, they would make my discoveries."
And as Abel said of Gauchy, (who defned the notions of limit and convergence):
"Cauchy is mad and there is nothing that can be done about him, although, right now,
he is the only one who knows how mathematics should be done."
So there we have it, running smalltalk about mathematics from its greats. Andrew
Wiles ending up developing new mathematical tools based on modularity to prove
Fermat; but that won't work here. The issue seems to be time, not space.
Je dis ça, je n'ai rien dit...
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