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Possible Proof of ABC Conjecture 102

Posted by Unknown Lamer
from the lord-of-the-proof dept.
submeta writes "Shinichi Mochizuki of Kyoto University has released a paper which claims to prove the decades-old ABC conjecture, which involves the relationship between prime numbers, addition, and multiplication. His solution involves thinking of numbers not as members of sets (the standard interpretation), but instead as objects which exist in 'new, conceptual universes.' As one would expect, the proof is extremely dense and difficult to understand, even for experts in the field, so it may take a while to verify. However, Mochizuki has a strong reputation, so this is likely to get attention. Proof of the conjecture could potentially lead to a revolution in number theory, including a greatly simplified proof of Fermat's Last Theorem."
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Possible Proof of ABC Conjecture

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  • Assuming the paper is correct and as impenetrable as the summary claims, this won't simplify the proof of FLT. It'd be a massive rug that the hard parts of of FLT would be swept under.

  • by Anonymous Coward on Monday September 10, 2012 @07:21PM (#41294329)

    ...and solved. I think it was the early (19)70's. A researcher named Jackson
    (with the help of his brothers) came to the conclusion that it was simple as 1-2-3.
    Additional verification shown that do-re-mi fit the bill as well. At the time, people
    were sing all about it - I'm surprised this has come up again.

    • by game kid (805301)

      Jackson's prior graduate studies were never too much for him to jam into his schedule. Furthermore, his fellow grads were kind enough to leave him alone, so he could learn enough to heal the world and still have time to rock Robin (Billie Jean was not his lover) and make her want to scream.

    • A researcher named Jackson (with the help of his brothers) came to the conclusion that it was simple as 1-2-3.

      This cannot be truth because spreadsheet software wasn't available until the 80's.

  • by insecuritiez (606865) on Monday September 10, 2012 @07:36PM (#41294437)

    Peter had a pretty good first glance reaction to the paper: http://www.math.columbia.edu/~woit/wordpress/?p=5104 [columbia.edu]

    I haven't seen any good discussions of the actual math content of the paper yet though.

    • by Anonymous Coward on Monday September 10, 2012 @09:14PM (#41295207)

      See http://mathoverflow.net/questions/106560/philosophy-behind-mochizukis-work-on-the-abc-conjecture for a discussion on the mathematical content by experts.

    • by fatphil (181876)
      The thing that most worries me about the paper is that 60% of the references in the paper are to his own work, and many of the rest are to general texts not specific to the question at hand.

      Sounds like he's working in a bit of a vacuum. That's always high-risk. At least it's out now, so critique can begin. I won't be convinced until Tao, Mazur, Elkies, etc. are convinced.
  • NBC , CBS, and FOX say about this conjecture?

  • thinking of numbers not as members of sets (the standard interpretation), but instead as objects which exist

    Of course he was able to solve the problem; he used an Object Oriented framework!

  • I find these titbits about number theory absolutely fascinating... I followed a few courses at undergraduate level that touched on this material - without giving me a solid grounding. What I'd like to know is this: Is there a good textbook that would bring me up to speed with this material? I like Wikipedia articles - but I find them disjointed.. what I'd like from a textbook is something that leads me through the subject from undergraduate level onwards. Can anyone make any recommendations?

    • by WhiteDragon (4556)

      I find these titbits about number theory absolutely fascinating... I followed a few courses at undergraduate level that touched on this material - without giving me a solid grounding. What I'd like to know is this: Is there a good textbook that would bring me up to speed with this material? I like Wikipedia articles - but I find them disjointed.. what I'd like from a textbook is something that leads me through the subject from undergraduate level onwards. Can anyone make any recommendations?

      I've had pretty good success with Wolfram MathWorld [wolfram.com].

  • Nice article to spur a bit of recreational math. They even have a nice little "quality" formula to use for rating your finds. It's obvious that the place to look is powers of small numbers, especially primes.

    I used a few command line tools, bc and factor, and some bash shell scripting to check a few combinations. Skimmed through the results of commands like this:

    for ((i=1;i < 25;i++));do echo -n "$i "; echo "13^15-5^$i"|bc|factor;done

    With that, I found a few decent quality combinations:

    5 + 2^1

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