[HN Gopher] A New Lower Bound in the ABC Conjecture
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A New Lower Bound in the ABC Conjecture
Author : bmc7505
Score : 47 points
Date : 2023-01-31 15:30 UTC (7 hours ago)
(HTM) web link (arxiv.org)
(TXT) w3m dump (arxiv.org)
| garbagecoder wrote:
| 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
| bradleyy wrote:
| The math here is definitely out of my league; can someone ELI5
| the implications of this?
| adgjlsfhk1 wrote:
| absolutely none.
| adgjlsfhk1 wrote:
| 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 wrote:
| https://en.wikipedia.org/wiki/Abc_conjecture#Some_consequen
| c...
| Sniffnoy wrote:
| 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 wrote:
| 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...
| ok_dad wrote:
| 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 wrote:
| 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 wrote:
| 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.
| dvh wrote:
| Didn't Mochizuki solved ABC conjecture?
| ndsipa_pomu wrote:
| 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.
| bsder wrote:
| 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.
| yewenjie wrote:
| 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
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