[thom]

I’m both a layman and a simpleton, but seeing Guth’s comments, surely it can’t be a new idea that the fundamental interpretation of primes is something to do with waves and harmonics?

[impendia]

Analytic number theorist here --

"Fundamental interpretation of primes" is a bit much, but this has been understood for a long time. The short version of the story is

- The primes are closely related to the Riemann zeta function, which is more-or-less cobbled out of them;

- The Riemann zeta function has a lot more symmetry than one might initially expect, and harmonic analysis is how you prove this;

- The (still unproved) Riemann Hypothesis is that the zeta function has still more symmetry beyond what we've been able to prove.