A maths proof that is only true in Japan

> When the likes of Peter Scholze (fields medal!) and other very high profile mathematicians find (serious) flaws in every posted manuscript about this... I mean, it's pretty clear to me what's going on. The proof just doesn't go through.

On the other hand, Ivan Fesenko (also a heavyweight; he is for example the PhD advisor of the Fields medalist Caucher Birkar) insists that Mochizuki's proof is correct.

* Here is a popular scientific article from 2016 where Ivan Fesenko presents his perspective on this topic: https://inference-review.com/article/fukugen

* A popular scientific article by David Michael Roberts (also a renowned mathematician) from 2019 about where he believes an important contentious point in the different viewpoints of Scholze/Stix vs Mochizuki lies: https://inference-review.com/article/a-crisis-of-identificat...

It's interesting how the debate is transferable to other topics. In theory maths should be able to be broken down to its basic components and be proven to be all true, or if something is false, then the whole thing collapses. But in practice things like this become so complex that it becomes a matter of conviction, influenced by things like ego.

Now imagine taking something like biology and vaccines. What happens if you rely on your experts and other rely on theirs, and they disagree?

The most damning part to me is that Mochizuki dismissed Joshi's work and insulted it. That's a crazy response to someone trying to improve on his theory, and shows more of a religious belief that a mathematical conclusion.

Yeah, I was wondering how can debates like these exist nowadays when formal methods appear to my layman's eyes as the ultimate arbitrer of proof. Is that not how the math community looks at it?

    They've surrounded me. Cameras in every corner.
    Every move dissected in blogs, forums, peer-reviewed takedowns.
    "Cult leader". "Crank". "Outcast".
    Good. Let them watch.
    
    I'll solve equations with my right hand... and write names with my left.
    I'll take a potato chip... and eat it. [CRUNCH echoing like thunder]
    
    If I praise Joshi, he's tainted—marked as one of mine. Dismissed by association.
    But if I drag him... if I bury him in scorn... then they listen.
    Then they think, "Maybe he's different. Maybe he's not one of them.""
    I'll throw him under the bus... and save him!
    
    And the witness to my alibi... is the mathematical community itself.
    [A flicker of Scholze's blog. Stix's preprint. Joshi's strained silence.]
    They're all watching.
    
    They won't get it now.
    But when the theorems land... when every insult has aged into irony...
    
    ...they'll see it was all part of the proof.

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

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.

They use LLMs to help write formal proofs (in languages like Coq) that are then checked by traditional programs; they're not using AI as the checker.

https://youtu.be/e049IoFBnLA

Reads like the Obama giving himself an award meme

I'm not a mathematician (but I've seen exact sequences and commutative diagrams) and to me the stuff out of his IUT papers[0] looks borderline LLM-generated. I can only imagine what the LaTeX source looks like.

[0]: https://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%2...

It reminds me of Lambda calculus

You can express `a + b` or `a * b` in their regular algebraic notation or you can express them as a lambda expressions

ADD = λab.(a S)n

MUL = λxyz.x(yz)

Manipulating these expressions instead of algebra, you can suddenly compute things such as "+ * +" (Plus times plus). That will yield you another expression for sure, but we don't even know what that means.

So maybe an analogy would be, it's like you developed a field where, from that mess, you could derive important insights and even turn them back into proofs

And there's debate on whether all invariants truly are maintained throughout the entire process

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.

Is this the Japanese equivalent of The Onion?

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.