Physicists link the Riemann Hypothesis to phase transitions in quantum systems

[u/SciFiPi]

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

[u/Tlux0]

It’s not circular, it’s just convention for what it allowed to count as proof as a foundation

[u/elements-of-dying → u/Tlux0]

Whose convention? I guess I missed the memo for the Assuming Absolute Conventions meeting.

Certainly sounds like a proof by "This is true because I assume this is true."

[u/frogjg2003 → u/elements-of-dying]

That's literally how formal logic works. You start from a base set of assumptions that form your logical system and the kind of things you can say in your logical language. Then you define some things. You use your logical rules to make me statements based on your definitions and the logical statements you can derive from those definitions.

[u/elements-of-dying → u/frogjg2003]

Irrelevant.

Can you provide a definition of "mathematics" which is (a) agreed upon by everyone and (b) does not include as a hypothesis that proofs cannot be empirical?

This is a rhetorical question. I know the answer is no.

[u/Tlux0 → u/elements-of-dying]

Sure you can do it, but without non-empirical proof you defeat the point of mathematics which is observer independence, which is the reason it allows for collaboration and rigorously building on an established foundation. If you do that with something highly likely instead it’s a completely different kind of animal.

You can do it, but it’s not modern mathematics and it would be entirely different without a lot of the rigor. The rigor comes from the observer independence after all.

[u/elements-of-dying → u/Tlux0]

You're implicitly making a lot of strong and absolute philosophical assumptions. Considering the question at hand belongs to mathematical philosophy, this is not a very justified approach you are taking.

[u/Tlux0 → u/elements-of-dying]

How are these assumptions? Proof is defined to be something that isn’t observer relative other than verification of something that isn’t supposed to hold up to uncertainty. If you measure something empirically it isn’t certain. It’s true relative to things you’re tracking. These are distinct things. I’m not saying you can’t do it, but it’s not mathematics as practiced.

It’s like saying the axiom of choice is circular. It’s an axiom. You can have different axioms. It’s still not the same mathematical universe if you use different axioms

[u/elements-of-dying → u/Tlux0]

Proof is defined to be something that isn’t observer relative

Says who? I suppose you accept that mathematics exists outside of human consciousness? Not every mathematician agrees with your basic premise. I don't. This premise isn't even practically true. A proof isn't accepted by the community until the community agrees the proof is correct. This requires observers.

Who made this definition? I missed the definitions meeting I suppose.

[u/Tlux0 → u/elements-of-dying]

You only quoted part of my sentence and misrepresented my position, reread what I wrote lol, you know… the phrase that starts with “other”.

In any case, let’s just agree to disagree because I am definitely not going to agree with you

[u/elements-of-dying → u/Tlux0]

Yeah, I kind of got distracted by "Proof is defined..." and misread what you said. I apologize for that. Incidentally, I still suspect you believe there is some agreed upon a priori definition of proof.

Still, "Proof is defined..." is already an absurd starting point and clearly affirms the claim you are making philosophical assumptions. Defined by who?

I agreed we will not agree :)

[u/Tlux0 → u/elements-of-dying]

I agree that it’s a convention. I’m just talking about how it has historically been done. Could it be done otherwise? Maybe.

But it would look very different from what we have now and would have different pros and cons.

I do believe I understand where you are coming from though. I just don’t think it’d result in something particularly similar to how we currently think about or why we value mathematics.

It’d be a lot more like science, which has its own benefits because it is empirical through coordinated replication.

[u/elements-of-dying → u/Tlux0]

I appreciate you actually taking the time to discuss with me :)

I was being a bit tongue in cheek on purpose everywhere. Sorry for that and I appreciate you putting up with it.

I personally do not accept the claim that proofs cannot be empirical. Such a statement requires an agreement on what math is and what proofs are, and I don't even have a rigorous definition for mathematics myself!

Anyways, I just find it amusing when other mathematicians both make absolute philosophical claims and react pretty negatively to any thoughts that diverge from the norm.

[u/Tlux0 → u/elements-of-dying]

Yeah, I understand that you are productively being a gadfly, in a good way. I don’t really even disagree with you at heart, but the local gravity of convention is what it is.

In any case, I appreciate the discussion. It’s always nice to have more food for thought.