41–50 of 82 posts
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?
[0]: https://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%2...
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.
> 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. Well, not quite. Sometimes believing in things makes them true. https://en.wikipedia.org/wiki/Culture-bound_syndrome
Spaniard here, this is nonsense, I'm pretty sure everyone in the world experienced a nervous breakdown/light panic attack.
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.
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. I think the intrigue is mainly that it's at such a high level that lay mathematicians (like me) have no hope of understanding the debate. It's a situation that lends itself to crazy s…
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...
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?
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
Earlier quoted context omitted.
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 origin…
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. I think the intrigue is mainly that it's at such a high level that lay mathematicians (like me) have no hope of understanding the debate. It's a situation that lends itself to crazy s…
> 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…
But that's fair, it's not exactly one-sided, but to my (completely inexpert) judgement the matter seems heavily weighted against mochizuki?
Earlier quoted context omitted.
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".
When I saw the headline, I really hoped the article would be about some neuro-linguistic phenomenon that made native speakers of Japanese uniquely able to understand some mathematical proof.