I’m very interested in the connection between advanced maths and physics etc but I have no background in mathematics so a lot of the explanations of the deep stuff are really difficult to parse. I can’t get my head around the importance of prime numbers or why their discovery could unlock new advances in other disciplines.
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The biggest reason why people are interested in the Riemann hypothesis is because mathematicians have developed many “conditional” proofs which show that if RH is true then some other conjecture must be true too.
I seriously doubt there would be any immediate practical applications in science or engineering though. RH is from number theory, an area of maths which isn’t really known for its practical applications. In general it takes a long time for new mathematical results to filter through into scientific applications. The main applications of number theory are in modern cryptography, which often makes use of results developed centuries ago by people who would never have guessed that what they were doing had anything to do with cryptography.
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