This has got to be the strangest rabbit hole I've ever stumbled into, but it is just as fascinating. Odd that all I need to focus on math is for it to be explained in a different language.
I am very grateful for the English subtitles, though it is unfortunate there are none for the questions and answers at the end. I also appreciate that the speaker addresses in a straightforward manner precisely why IUT is useful for this specific problem due to how it approaches inequalities in number theory. It is nice that the examples are digestible and straightforward. That said, I found this talk disappointing (more after the cut). Spending a few minutes reading IUT's Wikipedia page will probably teach you more than spending an hour and a half watching the talk, though it may be the case that the subtitles do not provide an accurate account of what is said. Even if so, much of this lecture is clearly aimed at children despite the subject not being appropriate for children. It takes the speaker a full half hour (one-third of the talk!) just to explain what the abc conjecture is and why it is important. He is verbose (e.g. "I'm going to explain this now" before an explanation) and uses lengthy analogies, despite their simplicity. He even takes a moment to plug his book on the tragically short life of Galois. Then, at the end of the talk, he introduces numerous unexplained definitions, objects, and processes with little or no details provided. He finally admits he does not fully understand the theory. Despite this, he is convinced IUT is nothing short of a revolution in mathematics. To say IUT is "completely different from traditional mathematics" is probably true, but I don't see that here. It is common (especially in number theory) to use relationships between groups where addition and/or multiplication work differently or even symmetries between completely different areas of mathematics (e.g. Wiles's proof of FLT) to define or reconstruct objects in order to solve difficult problems. I don't see why Hodge theaters are remarkably different from "traditional" math approaches in research apart from the implied complexity of the process he describes in very general terms. It is strange to hear him suggest that IUT has numerous applications and will revolutionize mathematics when after many years the theory has only been used in a single paper. I am not bringing up the dispute over whether IUT's lone application is mathematically sound. I'm just pointing out that even Mochizuki (the creator) who presumably understands IUT has provided no new proofs or applications for his method in the decade since he introduced it. I don't understand why the speaker believes it has wide applications unless he knows about work secretly in progress. This talk could have been given in twenty minutes without sacrificing content or comprehensibility. I am probably cynical, but perhaps the speaker takes so much time addressing the audience as though they are children because he cannot explain the theory in any greater detail than what he provided and needed a way to stretch a twenty-minute lecture into ninety minutes. If you don't fully understand a theory, is it wise to give a talk on it? Couldn't you miscommunicate concepts when you don't understand them? I'm left uncertain about whether what I learned here is correct, and if so, how this 1,000 km view of the theory is helpful in understanding how or why IUT works.
There are numerous issues with your comment. He clearly states the talk is meant for high school juniors/seniors to be able to understand. On him not fully understanding the theory, barely anyone in the world fully understands this theory (claimed even by the author himself that others have misunderstood) and that doesn't preclude him from being able to spread awareness and education. And the Wikipedia page is fairly scarce, you're not gonna get too much more information out of it. I don't see why you feel the need to be a trog and write a page dissection in the comments. If you are so concerned with these matters go put on your big boy pants and read Mochizuki's papers yourself.
The translation of the subtitle at 20:03 is likely wrong. He means "Is it possible to obtain every even number?"/"Is it possible to obtain all even numbers by adding two primes?". The subtitle says "is it possible to obtain an even number by adding two primes?" to which the answer is trivially yes.
The creation of the "other universe" in IUT is made for the express purpose of altering axioms (in this case the Peano axioms), so I think this is applicable to other axiom sets as well?
@@TrixieWolf yah, update: my Japanese nationalism kinda blinded me on how dodgy the theorem kinda is. Mr. Mochizuki needs to give a better explanation imo to really be accepted from here on
Mr. Mochizuki is perfectly baroque and we admonish, credit and thank him for his punishing treatments and the inter-personal fashion of his proper work. @@a006delta
The fact that this theory exists and is supposedly "complete" is something absolutely awesome and scary at the same time. If matemathicians can actually master it and make it useful, every other area on STEM will suffer a major revolution. I really hope that more paper come from this theory and it gets understood by more people. Excelent presentation, anyway.
Think of running an emulator inside a virtual machine on a remote computer using vnc protocol. There is something like an I.U.T. process analogous dual if you follow thru all the protocols layers and translations needed up and down the stack, with associated book keeping.
![Inter-universal Teichmüller theory via Fumiharu Kato w/English subtitles [PROPER]](/img/logo.svg){kind=logo}
