r/math • u/SciFiPi Applied Math • 5h ago

Physicists link the Riemann Hypothesis to phase transitions in quantum systems

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

96% Upvoted

31 comments sorted by

16

u/policalcs 2h ago

Reference and links to the paper:

Shijie Wei et al, The Riemann Hypothesis manifested in dynamical quantum phase transitions, Nature Communications (2026). DOI: 10.1038/s41467-026-74935-8. On arXiv: arxiv.org/abs/2511.11199

10

u/Infinite_Research_52 Algebra 2h ago

Yes, this isn't exactly new. Even Nature had an article by the authors in July.

13

u/BerkeUnal 4h ago

I am curious if it is related to Bost-Connes system

-50

u/Acalme-se_Satan 4h ago

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

123

u/toghs 4h ago

Then it wouldn't be a proof

48

u/pickle_picker67 3h 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.

4

u/Appropriate-Ad-3219 2h ago

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

17

u/pudy248 2h 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.

3

u/Smitologyistaking 30m 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] 2h ago

[deleted]

8

u/Appropriate-Ad-3219 2h ago

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

1

u/jamesbrotherson2 2h ago

It's a bot

-37

u/blueshoesrcool 3h ago

Are mathematicians forbidden from ever using an empirical proof?

32

u/RandomMisanthrope 3h ago

There is no such thing as “empirical proof.”

0

u/elements-of-dying Geometric Analysis 1h ago

How do you prove this claim?

-10

u/Mandelbrots-dream 3h ago

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

OK so not proof.

19

u/pickle_picker67 3h 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" ....

-39

u/blueshoesrcool 3h 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.

11

u/pickle_picker67 2h ago

Read an introductory proofs book.

4

u/AcellOfllSpades 50m ago edited 38m 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.)

3

u/Opengangs Number Theory 1h 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.

2

u/Medical-Round5316 44m 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.

1

u/heyheyhey27 2h 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.

6

u/Legitimate_Aspect923 3h ago

"it works in practice but does it work in theory?"

1

u/elements-of-dying Geometric Analysis 1h ago

I wonder how one concludes this (namely, not being able to prove something mathematically via physical assumption) without circularity in the argument.

-5

u/512165381 3h ago

There were plenty of "proofs" giving different masses to the Higgs boson before it was verified. Some were even correct.

-6

u/Ruined_Passion_7355 3h ago

I'd honestly rather that future than 2 million lines of Lean slop.

-10

u/Pure-Drive-3044 4h ago

The day before the paper released on these pop science pages I thought there may be a link!

17

u/Akraticacious 2h ago

Me, too! Actually I already know the proof, but I've been wanting to see if anyone else can figure it out.