[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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