A New Lower Bound in the ABC Conjecture | Hacker News Reader

A New Lower Bound in the ABC Conjecture

arxiv.org

51 pointsbmc750514 comments

In case you want an absolutely beginner-friendly and extremely hilarious intro to the ABC conjecture, I highly recommend this book - https://www.goodreads.com/book/show/28965582-trolling-euclid

Didn't Mochizuki solved ABC conjecture?

He believes so, but the proof is very difficult to follow and there's a serious problem raised about corollary 3.12 which is central to the proof. Mochizuki believes that the problem raised is due to a misunderstanding of 3.12.

Not until he can convince other mathematicians that he has solved it.

Given that your name would go down in history even for just explaining Mochizuki's stuff, if it were accurate, the fact that it has not been done is a giant red flag.

The math here is definitely out of my league; can someone ELI5 the implications of this?

absolutely none.

To be slightly more accurate, it gives a simpler proof of Fermat's last theorem, and proofs to a bunch of other way more esoteric theorems.

https://en.wikipedia.org/wiki/Abc_conjecture#Some_consequenc...

Those would be some of the implications of the ABC conjecture. However, proving the ABC conjecture, or any weaker version of it, is not what this paper is doing.

This paper is exploring a family of examples where the ABC conjecture is as close to being false as the author can manage.

The layman (like me) is probably only upvoting this because of the controversy around the ABC conjecture where there's supposedly a "proof" since 2012 but nobody in the mathematics community believes it: https://www.quantamagazine.org/titans-of-mathematics-clash-o...

It's not that no one believes it, the problem is that this particular possible proof of ABC conjecture came from 1000-1500 pages of dense, new math. As in, the proof writer invented some new math, and from that new math he claims he can prove ABC as a sort of side-project to his goal of furthering his new mathematical area. No one else can really understand his proof because it would take years to study the text behind it, but a few are trying and may have found a hole in his proof. I am not sure what the status is since the article you linked, but as with huge code bases I am pretty sure that there must be at least one error in those 1000-1500 pages of math.

That's not an entirely accurate summation of the current state of affairs, as I understand it.

At this point, several people who have tried to follow the proof have all pointed to the exact same step where their attempts came undone: Corollary 3.12. And it's become agreed by everyone that if this doesn't hold, the proof doesn't hold.

Yea, it's been a while since I followed this, at least 2 years now, so it makes sense to me that an error has been found. This proof seems very complex to me at 1000+ pages.

b-b-but my weeaboo friends tell me it has been solved and only the idiot other Fields Medal winners are standing in the way of its publication./s

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