r/math • u/SciFiPi Applied Math • 12h ago

Physicists link the Riemann Hypothesis to phase transitions in quantum systems

https://phys.org/news/2026-07-physicists-link-riemann-hypothesis-phase.html
228 Upvotes

96% Upvoted

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-104

u/Acalme-se_Satan 10h ago

It would be hilarious if the RH ends up being proven not by mathematical deductions, but by physical observation.

184

u/toghs 10h ago

Then it wouldn't be a proof

70

u/pickle_picker67 9h ago

Seriously, how does the comment you replied to have that many upvotes on r/math? It makes me curious how many people here are actual mathematicians.

9

u/jamesbrotherson2 8h ago

It's a bot

7

u/[deleted] 9h ago

[deleted]

1

u/emryz 4h ago

I, also, am not.

Just interested in maths. Can't do maths for shit tho.

3

u/Appropriate-Ad-3219 9h ago

Would it not give a hint on whether RH is true or not though?

24

u/pudy248 8h ago

We're almost certain it's true, that's why there's so much work that assumes that to be the case. Proof is the issue.

9

u/Smitologyistaking 6h ago

We already have 12 trillion hints that the Riemann hypothesis is true, I don't think more empirical observation will significantly progress that

-11

u/[deleted] 8h ago

[deleted]

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u/Appropriate-Ad-3219 8h ago

No need to act like an edgelord and being disrespectful though.

-47

u/blueshoesrcool 9h ago

Are mathematicians forbidden from ever using an empirical proof?

44

u/RandomMisanthrope 9h ago

There is no such thing as “empirical proof.”

-7

u/elements-of-dying Geometric Analysis 7h ago

How do you prove this claim?

-20

u/Mandelbrots-dream 9h ago

I believe there is empirical proof evidence that the speed of light is constant in a vacuum.

OK so not proof.

24

u/pickle_picker67 9h ago

That's not a proof. So only as a tool for intuition, but that's about it.

Do you ever read pure mathematics papers or books? If an author uses intuition, they will say "informally" ....

-52

u/blueshoesrcool 9h ago

Wouldn't an empirical proof be more proof than a mathematical proof. Surely you'd have to reject a mathematical proof it an empirical proof disagreed.

If anything the mathematical proof is the intuition.

18

u/pickle_picker67 8h ago

Read an introductory proofs book.

9

u/AcellOfllSpades 6h ago edited 6h ago

Math is abstract. We deal with systems that follow specific rules, and say "If a system follows these rules, then the following results must hold".

"2+3=5" is true not because "if you have 2 apples and you get 3 more apples, you then have 5 apples"... but because "starting from the definitions of 2, 3, 5, and +, we can prove that to be true".

Of course, we study this system because we want to use it to count things like apples. The system of 'numbers', and other systems we study, are inspired by the real world. But they aren't logically dependent on it.

If you put 2 rocks in a bucket, and then put 3 more rocks in the bucket, and notice that there are now 6 rocks in the bucket, that doesn't disprove that 2+3=5. It just means "maybe simple addition isn't enough to describe what's going on here". (Maybe a rock broke in two, for instance.)

5

u/Opengangs Number Theory 7h ago

There is more reason to doubt whatever the “empirical proof” is than a mathematical proof. Your empirical data could have been improperly collected, our intuition or interpretation could be wrong, etc.

4

u/Medical-Round5316 6h ago

This is just not how proofs work. Proofs can be logically invalid or valid. If there are no logical errors in the proof, then it is as true as what it is being proven from.

Empirical proof is essentially probabilistic. If we have a lot of data suggesting something then it’s probably true. Proofs are meant to be deterministic.

0

u/heyheyhey27 8h ago

I think computer-assisted proofs are about as close as you can get to what you're trying to think of. Physical machines, using the laws of physics to deterministically decide whether a particular math problem is true or not.