I want to know what the Riemann Hypothesis is good for in tangible terms.
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"what the Riemann Hypothesis is good for" - well, learning with certainty that the statement of it is true wouldn't unlock anything. Aliens telling us: "we've proven it, and it's true, but we won't tell you why" wouldn't do us any good, I think. If anybody had in mind a design of a machine that only works if Riemann Hypothesis is true and otherwise explodes catastrophically, they could just build the machine and have fun using it, or generating some kind of counter-example.
So, the usefulness could only come from the ideas in the proof being useful for something else. You'd probably need to invent a whole bunch of groundbreaking new math, and it could plausibly be useful for something: something-something algorithms? something-something encryption? something-physics? Hard to tell without seeing that proof. I'm sure it would lead to something useful given a thousand years of progress, but I suspect it would be good for nothing practical within the next 10 years.
(For comparison: did the innovations in Wileses proof of Fermat theorem or in Perelman's proof of Poincare conjecture bear any practical fruit yet? Not as far as I'm aware, would be happy to be wrong.)
Did the innovations in Wileses proof of Fermat theorem ... bear any practical fruit yet?
They did! Elliptic curves research was boosted, and now elliptic curves are used in cryptography.
@AnT And how long did that take? I don't know, perhaps it was a surprisingly short period. So yes I can accept that benefits make follow a proof in surprising ways.
However, if we haven't got a proof on 28 December 2023 how can such a benefit from the proof happen before 1 Jan 2024? Even if a proof had been submitted 14th August 2023, the day after claim creation date, mathematicians would almost certainly still be trying to work out if the proof was actually a proof rather than working out what to usefully do with it.
@Tasty_Y Thanks, have 100 mana for helping me orient better. I would still resolve this market to "yes" if someone can give me the intuitions on why people would expect the proof to bear useful insights.