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A maths proof that is only true in Japan

newscientist.com

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Re: A maths proof that is only true in Japan

#31

Post by bananaflag »

molf wrote: post #6
bananaflag wrote: post #3

Earlier quoted context omitted.

Yeah, it's ironic how math is more or less the one "universal" truth, and we still long for somehow magically make it culturally dependent. I can definitely understand that temptation. Like the opposite one, e.g. the search for a "perfect" language (as in e.g. Umberto Eco's book). Both temptations are examples of a longing for an actual paradox or absurdity in the world.

Totally get your point, but math is still a human creation. The symbols, language, and frameworks we use are cultural, and disagreement over proofs like this one shows math depends on shared understanding, not just objective truth.

I definitely agree with that. But that is a pale cultural dependence compared to what one would wish for.

Re: A maths proof that is only true in Japan

#34

Post by pmontra »

moomin wrote: post #12

I’ve read about this a lot before. My gut tells me that if you’ve got a central genius with twelve adherents and no-one else, what you’ve got is a cult, not a proof. But also, it is frankly amazing to think that Galois’ original proof was very nearly lost. It wasn’t like he’d not tried to publish. He’d been laughed out by people like Cauchy saying it was nonsense.

Is that this controversy? https://hsm.stackexchange.com/questions/5341/did-cauchy-forg...

Re: A maths proof that is only true in Japan

#35

Post by fxwin »

stavros wrote: post #10

This title is extremely clickbaity. If a few people in Japan believe something that nobody else believes, that thing is not "only true in Japan", nobody knows if it's true anywhere.

I feel like the implication was fairly clear here (Or maybe not "extremely" clickbaity as far as headlines are concerned)

Re: A maths proof that is only true in Japan

#36

Post by simiones »

n4r9 wrote: post #13
Theofrastus wrote: post #11

Things have moved on since then, as artificial intelligence has started being used in formalisation, [...] With how AI works fundamentally, wouldn't you still need to verify the results generated by AI? Doesn't seem like an applicable field for it, at least in its current state.

I asked a very similar question a couple of weeks ago here: https://news.ycombinator.com/item?id=44028051 The top answer helped me to understand. > Presumably an AI would formalise the proof in a system such as Lean, then you only need to trust the kernel of that proof system.

I don't think trusting the Lean kernel is enough: you also need to trust that all of the Lean code is a valid translation of the informal proof. Given that the informal proof is already gigantic, and that there is no general mechanical way to verify if a formal statement corresponds 1:1 with an informal statement, it's far from trivial to trust that the Lean representation of the proof is the same thing as the original proof.

Now, if the proof works, presumably this problem goes away: Lean can show that based on this proof, the original statement holds. But if Lean says that this formal proof doesn't work, that doesn't tell you anything about the informal proof: the error may only be in the formalization.

Re: A maths proof that is only true in Japan

#37

Post by stavros »

fxwin wrote: post #35
stavros wrote: post #10

This title is extremely clickbaity. If a few people in Japan believe something that nobody else believes, that thing is not "only true in Japan", nobody knows if it's true anywhere.

I feel like the implication was fairly clear here (Or maybe not "extremely" clickbaity as far as headlines are concerned)

Really? I clicked through and was wondering what weird and interesting mathematical twist I'd read about, and it turned out to be "well only a few people believe it, and they happen to live in Japan".

Re: A maths proof that is only true in Japan

#38

Post by zkmon »

KK7NIL wrote: post #18
zkmon wrote: post #8

What can be proven depends on what is allowed be a part of mathematics and logic. Zero, negative numbers, imaginary numbers and a lot other stuff had go through the acceptance first before they can be used in proofs. A lot of foundational concepts in logic, reality, causality, boolean exclusivity, spatial locality - had to be rewritten due to advances in quantum physics etc.

We went through this over a 100 years ago, math now sits on very solid axioms (look up ZFC), they're not questioning that.

200 years passed by between Newton and Einstein. 100 years is tiny in the evolution of thought and is no basis for shutting the questions down.

Re: A maths proof that is only true in Japan

#39

Post by Barrin92 »

Qision wrote: post #32

What is so special about IUT? They say the theory is "out of this world" but in what sense exactly? Did Mochizuki found a new interesting way to look at some ideas?

It's extremely complicated. The original document he wrote up was 500 pages of maths introducing effectively an entirely new theory. I studied number theory in uni, tried to read it, and understood barely anything of it.

Which obviously leads to the epistemological problem that the article points out. You had extremely good mathematicians like Scholze look at it and thought he found a flaw, then one guy from Arizona disagreeing that it is a fatal flaw and claiming to have fixed it, which Scholze doesn't agree with.

So what do you really make of it if only a handful of mathematicians can engage with it, and they can't even agree with each other. Probably the biggest value of IUT is that it puts to the test what even counts as a proof.

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