s*****V
发帖数: 21731 | 1 http://www.math.columbia.edu/~woit/wordpress/?p=6514#comments
In case you haven’t been following this story, “abc” refers to a famous
conjecture in number theory, for which Shin Mochizuki claimed last year (see
here) to have found a proof. His argument for abc involves a new set of
ideas he has developed that he calls “Inter-Universal Teichmuller Theory”
(IUTeich). These are explained in a set of four papers with a total length
over 500 pages. The papers are available here, and he has written a 45 page
overview here. One can characterize the reaction to date of most experts to
these papers as bafflement: what Mochizuki is doing is just so far removed
from what is known and understood by the experts that they have no way of
evaluating whether or not he has a new idea that solves the abc problem.
In principle one should just be able to go line by line through the four
papers and check the arguments, but if one tries this, one runs into the
problem that they depend on a long list of “preparatory papers”, which run
to yet another set of more than 500 pages. So, one is faced with an
intricate argument of over 1000 pages, involving all sorts of unfamiliar
material. That people have thrown up their hands after struggling with this
for a while, deciding that it would take years to figure out, is not
surprising.
Mochizuki has just released a new document “concerning activities devoted
to the verification of IUTeich”. It explains the state of his efforts to
get other mathematicians to check his work, a project that has been going on
since last year, leading to many ongoing updates to the papers making up
the proof. He explains that he submitted the four IUTeich papers to a
journal last August, but will not have anything to say about the journal or
the state of the submission process. This is the way mathematics is supposed
to work: the papers should be refereed by experts who have agreed to go
through and check them carefully (and confidentially). Given the unusual
character of the series of papers, finding willing and able referees may be
very difficult. It would of course be most satisfying if such referees can
be found and can either identify holes in his argument, or vouch for
correctness of the whole thing.
In the meantime, he has been working since October 2012 with Go Yamashita,
who has carefully gone through the papers and is now writing a 200-300 page
survey of what is in them. Yamashita may also give a course on the topic at
Kyushu University sometime after next April. As part of this process, three
other mathematicians participated in a seminar in which Yamashita lectured
on the papers.
Another mathematician working on this is Mohamed Saïdi, who devoted
about six months to studying the papers, then spent three months visiting
Kyoto and discussing them with Mochizuki. According to Mochizuki, he has
said that he believes the theory to be correct. Mochizuki summarizes the
current situation as
the issue of whether or not one should regard the verification of
IUTeich as being, for all practical purposes, complete, i.e., as a result of
the activities of Yamashita and Saïdi, is by no means clear, and any
sort of “final conclusion” on this topic must be regarded as a matter that
lies beyond the scope of the present report.
Mochizuki goes on to claim that, based on what he has heard from Yamashita
and Saïdi, researchers trying to read his papers should find it
possible to understand the theory if they work on it for roughly half a year
. He warns that they do need to be aware though that an attempt to make
sense of what he is doing by expecting “a similar pattern of argument to
existing mathematical theories is likely to end in failure.” They also need
to keep in mind that he’s not particularly focused on proving abc, that
for him it is the IUTeich theory itself that is the object of interest.
This is a remarkable story, with little precedent. After more than a year, I
haven’t heard anyone willing to bet either way on how it will turn out.
Mochizuki is a talented mathematician and maybe he has a proof. Or maybe he
has a complicated set of ideas which don’t do what he hopes. Perhaps
someday one of these alternatives will start to emerge, but it doesn’t now
look like this will be anytime soon. | w**k
发帖数: 320 | 2 苏联已经不存在了
话说这厮不能出来讲讲吗
see
”
page
to
【在 s*****V 的大作中提到】
: http://www.math.columbia.edu/~woit/wordpress/?p=6514#comments
: In case you haven’t been following this story, “abc” refers to a famous
: conjecture in number theory, for which Shin Mochizuki claimed last year (see
: here) to have found a proof. His argument for abc involves a new set of
: ideas he has developed that he calls “Inter-Universal Teichmuller Theory”
: (IUTeich). These are explained in a set of four papers with a total length
: over 500 pages. The papers are available here, and he has written a 45 page
: overview here. One can characterize the reaction to date of most experts to
: these papers as bafflement: what Mochizuki is doing is just so far removed
: from what is known and understood by the experts that they have no way of
| r*g
发帖数: 3159 | 3 写个好莱坞剧本，望月新一ABC证明50年后被证实；而那时他已经靠比特币成世界首富
了。 | s*****V
发帖数: 21731 | 4 某种意义上，望月新衣的境遇和民科很像，做出来东西都没有人愿意验证，虽然他过往
还是有很好的CREDIT. | Y**********n
发帖数: 1930 | 5 怎麼「新一」的「一」被砍掉了？
【在 s*****V 的大作中提到】
: 某种意义上，望月新衣的境遇和民科很像，做出来东西都没有人愿意验证，虽然他过往
: 还是有很好的CREDIT.
| y******1
发帖数: 913 | 6 I read it but couldn't get a clear picture of how it works.
see
”
page
to
【在 s*****V 的大作中提到】
: http://www.math.columbia.edu/~woit/wordpress/?p=6514#comments
: In case you haven’t been following this story, “abc” refers to a famous
: conjecture in number theory, for which Shin Mochizuki claimed last year (see
: here) to have found a proof. His argument for abc involves a new set of
: ideas he has developed that he calls “Inter-Universal Teichmuller Theory”
: (IUTeich). These are explained in a set of four papers with a total length
: over 500 pages. The papers are available here, and he has written a 45 page
: overview here. One can characterize the reaction to date of most experts to
: these papers as bafflement: what Mochizuki is doing is just so far removed
: from what is known and understood by the experts that they have no way of
| s*****V
发帖数: 21731 | | s**********n
发帖数: 1485 | 8 文不对题啊。这不好几个人看了，还在组织讨论班还要开课嘛。很多人也许在偷偷看，
但还没懂，要面子不说。
see
”
page
to
【在 s*****V 的大作中提到】
: http://www.math.columbia.edu/~woit/wordpress/?p=6514#comments
: In case you haven’t been following this story, “abc” refers to a famous
: conjecture in number theory, for which Shin Mochizuki claimed last year (see
: here) to have found a proof. His argument for abc involves a new set of
: ideas he has developed that he calls “Inter-Universal Teichmuller Theory”
: (IUTeich). These are explained in a set of four papers with a total length
: over 500 pages. The papers are available here, and he has written a 45 page
: overview here. One can characterize the reaction to date of most experts to
: these papers as bafflement: what Mochizuki is doing is just so far removed
: from what is known and understood by the experts that they have no way of
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