5 ms·

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

by bradleyy 4y ago

adgjlsfhk1 4y ago
absolutely none.
- adgjlsfhk1 4y ago
  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.
  - kkylin 4y ago
    https://en.wikipedia.org/wiki/Abc_conjecture#Some_consequences https://en.wikipedia.org/wiki/Abc_conjecture#Some_consequenc...
  - Sniffnoy 4y ago
    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.
gfd 4y ago
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-over-epic-proof-of-abc-conjecture-20180920/ https://www.quantamagazine.org/titans-of-mathematics-clash-o...
- ok_dad 4y ago
  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.
  - jcranmer 4y ago
    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.
    - ok_dad 4y ago
      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.

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

adgjlsfhk1 4y ago

absolutely none.

adgjlsfhk1 4y ago
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.
- kkylin 4y ago
  https://en.wikipedia.org/wiki/Abc_conjecture#Some_consequences https://en.wikipedia.org/wiki/Abc_conjecture#Some_consequenc...
- Sniffnoy 4y ago
  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.

gfd 4y ago

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-over-epic-proof-of-abc-conjecture-20180920/ https://www.quantamagazine.org/titans-of-mathematics-clash-o...

ok_dad 4y ago
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.
- jcranmer 4y ago
  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.
  - ok_dad 4y ago
    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.