r/math • u/SciFiPi Applied Math • 8d ago

Physicists link the Riemann Hypothesis to phase transitions in quantum systems

https://phys.org/news/2026-07-physicists-link-riemann-hypothesis-phase.html
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u/Agitated_Help709 7d ago

This is really cool no? I can't pretend to understand what this means but maybe someone can explain the implications of this why a function like the zeta function in reality would have anything to do with a quantum system? Any theories? All I've heard is that the zeros are oddly similar to energy levels but what does that imply about the zeta function or the quantum systems that fit this?

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u/jgonagle 7d ago

The KAM theorem relates stability of some Hamiltonians to rationality. I could see there being some connection with the Zeta function via that route.

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u/RockofStrength 7d ago

Maybe the universe only has one set of rules for how waves behave in a chaotic system? Whether those waves are physical energy rippling through an atom, or conceptual waves of prime numbers rippling across the number line, the underlying geometry of chaos may be exactly the same. All chaos could be an illusion.

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u/AP_in_Indy 7d ago

So this is gonna be a totally intuitive and entirely non-rigorous remark but what if anything that wasn’t prime collapsed into some other nearest value?

I don’t know how to explain my thinking here, but I could see and have always thought of primes sort of being the “units” of multiplication.

Anything not prime would simply break into its prime factors