The Riemann Hypothesis and other curiosities

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The Riemann Hypothesis and other curiosities

Tips: 1.00 INK Postby LawOfTheLand on Mon Feb 25, 2019 10:53 pm

At DWI's request.

Preliminary reading: https://en.wikipedia.org/wiki/Riemann_hypothesis

This statement has been shown to have the curious property that if it cannot be proven false (that is, if a counterexample cannot be found), then it has to be true. This could open up new avenues of proof along the same lines as reductio ad absurdum, instead of proving statements directly. Such new proof methods could be used to answer central questions in mathematics like P=NP and the Collatz conjecture.

P=NP in particular is important to Bitcoin, where the idea of proof of work relies on the idea that P<NP. Put simply, it's the idea that some problems are harder to find a solution for than to verify that a given solution is correct.

What's your favorite unsolved problem in mathematics, and what inroads have been taken into solving it?

This verges hard into Gödel's incompleteness theorem and Tarski's undefinability theorem: https://www.youtube.com/watch?v=O4ndIDcDSGc
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