Re:How I learned to love and fear the Riemann Hypothesis
by Tade0 on Tuesday January 05, 2021 @12:00PM
(#25647576)
I understand that the real proof of the RH is the friendships we make along the way, but what would happen if we just acted with the assumption that it is true?
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Re:How I learned to love and fear the Riemann Hypothesis
by rfurmani on Tuesday January 05, 2021 @12:31PM
(#25648084)
There's been a lot of research that has assumed it to be true and built on top of it to find deeper implications.
Still, a number of people who've worked most closely with the Riemann zeta function, even the ones who led the computations and numerical verifications, have expressed doubts on whether the Riemann Hypothesis is actually true: https://arxiv.org/abs/math/0311162
Re:How I learned to love and fear the Riemann Hypothesis
by waynecochran on Tuesday January 05, 2021 @12:18PM
(#25647836)
This is the difference between a scientist and a mathematician. A scientist would consider the empirical evidence more than sufficient to consider RH to be true.
Of course there is hope that a proof of RH would reveal some deeper understanding -- not merely a conformation.
Re:How I learned to love and fear the Riemann Hypothesis
by hansvm on Tuesday January 05, 2021 @01:22PM
(#25648885)
I'm not so sure a scientist would consider RH true at this point. Math has a rich history of conjectures appearing true for the first n dimensions, the first k inputs, the first z partial/tangential proofs, etc. The evidence for RH isn't any stronger than that for a plethora of eventually-proven-false conjectures.
Do you know if anyone has tabulated stats on conjecture proofs? That could be a fun dataset to examine.