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abc conjecture

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Sep. 14th, 2012 | 01:56 pm

As reported by Nature, a purported proof of the abc conjecture has been announced:

Mathematician Shinichi Mochizuki of Kyoto University in Japan has released a 500-page proof of the abc conjecture, which proposes a relationship between whole numbers — a 'Diophantine' problem.

[...]

Like [French mathematician Lucien] Szpiro, and also like British mathematician Andrew Wiles, who proved Fermat’s Last Theorem in 1994, Mochizuki has attacked the problem using the theory of elliptic curves — the smooth curves generated by algebraic relationships of the sort y2=x3+ax+b.

There, however, the relationship of Mochizuki’s work to previous efforts stops. He has developed techniques that very few other mathematicians fully understand and that invoke new mathematical ‘objects’ — abstract entities analogous to more familiar examples such as geometric objects, sets, permutations, topologies and matrices. “At this point, he is probably the only one that knows it all,” says [Columbia University, NY mathematician Dorian] Goldfeld.

To call this exciting would be an understatement.

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Comments {11}

Eric (Pingouin!...)

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from: malver
date: Sep. 14th, 2012 08:28 pm (UTC)
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Interesting.
Hopefully, that'll be one less distributed computing project (abc@home) I'll need to participate in, then. (Joking- mostly. :) )

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Schneelocke

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from: schnee
date: Sep. 14th, 2012 08:32 pm (UTC)
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*s* Yeah — I think 17 or Bust is still going on, though, so you won't have to let your computing cycles go to waste. ;)

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Eric (Pingouin!...)

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from: malver
date: Sep. 14th, 2012 08:50 pm (UTC)
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Hadn't heard of that one (is it part of PrimeGrid actually? It rings a slight bell in that context!...) - I do have accounts through BOINC (! :) ) with several such projects, mathematical, physics-related and otherwise. Computer will probably thank me for dropping one. :)

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Schneelocke

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from: schnee
date: Sep. 14th, 2012 08:59 pm (UTC)
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No, I don't think it's part of PrimeGrid — it's one of the slightly lesser-known massively-distributed computing efforts, dedicated to attacking the Sierpinski problem, for which only 17 cases remained when the project was started. (These days, 11 of those have been solved, so there's only 6 more.)

There's a website at seventeenorbust.com, and they do have a Wikipedia article, too.

Actually, looking at their website, it seems they announced an "alliance" with PrimeGrid in 2010, too — after my own distributed computing days, which explains why I didn't know about it, but there's your bell that rang. ;)

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Moth

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from: moth_wingthane
date: Sep. 14th, 2012 09:23 pm (UTC)
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Fascinating but I can't pretend that I can understand much more than the basic concepts here.

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Schneelocke

(no subject)

from: schnee
date: Sep. 14th, 2012 09:33 pm (UTC)
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Same for me, I'll admit — but then there is a huge discrepancy between the conjecture as such (easy enough to understand) and the purported proof (completely inaccessible to just about anyone). It can be very difficult to understand any mathematical proof if you're unfamiliar with the specific field, but Mr. Mochizuki basically developed a new field completely from scratch here just for this proof, so don't feel bad about it. ;)

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tzisorey

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from: tzisorey
date: Sep. 16th, 2012 05:20 am (UTC)
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Seconded. Goes entirely over my head.

But then, so did Relativity when it first came out... now they teach it in primary school.

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Schneelocke

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from: schnee
date: Sep. 16th, 2012 09:33 am (UTC)
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Primary school? As in elementary school? o.O

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tzisorey

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from: tzisorey
date: Sep. 16th, 2012 09:46 am (UTC)
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Yup.

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tzisorey

(no subject)

from: tzisorey
date: Sep. 16th, 2012 09:48 am (UTC)
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Well.... grades Kindergarten to 7... I dunno if that crosses over with "middle" school, in some countries...

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Schneelocke

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from: schnee
date: Sep. 16th, 2012 10:08 am (UTC)
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Interesting. Well, if somebody manages to teach the subject in a manner that kids will understand, then why not?

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