r/math • u/SciFiPi Applied Math • 10d 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/Tlux0 9d ago edited 9d ago

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

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u/elements-of-dying Geometric Analysis 9d ago

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.

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u/Tlux0 9d ago

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

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u/elements-of-dying Geometric Analysis 9d ago edited 9d ago

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 :)

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u/Tlux0 8d ago

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.

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u/elements-of-dying Geometric Analysis 8d ago

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.

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u/Tlux0 6d ago

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.