Re: [silk] This is what the Singularity looks like.

[Thaths]

On Wed, Feb 19, 2014 at 2:33 PM Thaths  wrote:

> On Wed, Feb 19, 2014 at 12:56 PM, Udhay Shankar N  wrote:
>
>>
>> http://www.newscientist.com/article/dn25068-wikipediasize-maths-proof-too-big-for-humans-to-check.html
>>
>> Wikipedia-size maths proof too big for humans to check
>>
>> 17:38 17 February 2014 by Jacob Aron
>>
>> If no human can check a proof of a theorem, does it really count as
>> mathematics? That's the intriguing question raised by the latest
>> computer-assisted proof. It is as large as the entire content of
>> Wikipedia, making it unlikely that will ever be checked by a human being.
>>
>
> Speaking of proofs that are unlikely to be checked by human beings:
>
>
> http://www.nytimes.com/2012/09/18/science/possible-breakthrough-in-maths-abc-conjecture.html
>
> On Aug. 30, with no fanfare, Shinichi Mochizuki, a mathematician at Kyoto
> University in Japan, dropped onto the Internet four papers.
>
> The papers, encompassing 500 pages and four years of effort, claim to
> solve an important problem in number theory known as the abc conjecture.
> (No, it does not involve the alphabet; it has to do with integers and prime
> numbers, and the letters represent mathematical variables used in
> equations.)
>


Two+ years later, here is a nice longform piece on the current state of
Mochizuki's proof and where Mathematicians are with respect to
understanding it :

https://www.quantamagazine.org/20151221-hope-rekindled-for-abc-proof/

Earlier this month the math world turned toward the University of Oxford,
looking for signs of progress on a mystery that has gripped the community
for three years.

Play: In new window

 | Download


Subscribe: iTunes

 | Android
 | RSS

Audio Player

The occasion was a conference on the work of Shinichi Mochizuki
, a brilliant
mathematician at Kyoto University who in August 2012 released four papers
 that were
both difficult to understand and impossible to ignore. He called the work
“inter-universal Teichmüller theory” (IUT theory) and explained that the
papers contained a proof of the *abc* conjecture, one of the most
spectacular unsolved problems in number theory
.

Within days it was clear that Mochizuki’s potential proof presented a
virtually unprecedented challenge to the mathematical community. Mochizuki
had developed IUT theory over a period of nearly 20 years, working in
isolation. As a mathematician with a track record of solving hard problems
and a reputation for careful attention to detail, he had to be taken
seriously. Yet his papers were nearly impossible to read. The papers, which
ran to more than 500 pages, were written in a novel formalism and contained
many new terms and definitions. Compounding the difficulty, Mochizuki
turned down all invitations to lecture on his work outside of Japan. Most
mathematicians who attempted to read the papers got nowhere and soon
abandoned the effort.

For three years, the theory languished. Finally, this year, during the week
of December 7, some of the most prominent mathematicians in the world gathered
at the Clay Mathematical Institute at Oxford
 in the most
significant attempt thus far to make sense of what Mochizuki had done. Minhyong
Kim
,
a mathematician at Oxford and one of the three organizers of the
conference, explains that the attention was overdue.

“People are getting impatient, including me, including [Mochizuki], and it
feels like certain people in the mathematical community have a
responsibility to do something about this,” Kim said. “We do owe it to
ourselves and, personally as a friend, I feel like I owe it to Mochizuki as
well.”

The conference featured three days of preliminary lectures and two days of
talks on IUT theory, including a culminating lecture on the fourth paper,
where the proof of *abc*is said to arise. Few entered the week expecting to
leave with a complete understanding of Mochizuki’s work or a clear verdict
on the proof.  What they did hope to achieve was a sense of the strength of
Mochizuki’s work. They wanted to be convinced that the proof contains
powerful new ideas that would reward further exploration.
[image: Shinichi Mochizuki]

Re: [silk] This is what the Singularity looks like.

[Pranesh Prakash]

On Tue, Feb 18, 2014 at 8:56 PM, Udhay Shankar N ud...@pobox.com wrote:
 http://www.newscientist.com/article/dn25068-wikipediasize-maths-proof-too-big-for-humans-to-check.html

I present an anti-thesis:
http://www.dilbert.com/blog/entry/how_the_robots_will_take_over/

Re: [silk] This is what the Singularity looks like.

[Thaths]

On Wed, Feb 19, 2014 at 12:56 PM, Udhay Shankar N ud...@pobox.com wrote:


 http://www.newscientist.com/article/dn25068-wikipediasize-maths-proof-too-big-for-humans-to-check.html

 Wikipedia-size maths proof too big for humans to check

 17:38 17 February 2014 by Jacob Aron

 If no human can check a proof of a theorem, does it really count as
 mathematics? That's the intriguing question raised by the latest
 computer-assisted proof. It is as large as the entire content of
 Wikipedia, making it unlikely that will ever be checked by a human being.


Speaking of proofs that are unlikely to be checked by human beings:

http://www.nytimes.com/2012/09/18/science/possible-breakthrough-in-maths-abc-conjecture.html

On Aug. 30, with no fanfare, Shinichi Mochizuki, a mathematician at Kyoto
University in Japan, dropped onto the Internet four papers.

The papers, encompassing 500 pages and four years of effort, claim to solve
an important problem in number theory known as the abc conjecture. (No, it
does not involve the alphabet; it has to do with integers and prime
numbers, and the letters represent mathematical variables used in
equations.)

He has remained quiet since then. Others have not.

I hope it's right, said Minhyong Kim, a mathematician at the University
of Oxford in England and the Pohang University of Science and Technology in
South Korea. It would be a fantastic breakthrough.

What is even more fascinating is that Dr. Mochizuki has devised new
mathematics machinery that he employs for the proof.

The abstract ideas and notations that mathematicians manipulate are
unfathomable to most people. Dr. Mochizuki's new mathematical language -- on
his Web page, he describes himself as an inter-universal geometer -- is at
present incomprehensible even to other top mathematicians.

He's taking what we know about numbers and addition and multiplication and
really taking them apart, Dr. Kim said. He creates a whole new language --
you could say a whole new universe of mathematical objects -- in order to
say something about the usual universe.

Jordan Ellenberg, a University of Wisconsin mathematician who writes a
mathematics blog, Quomodocumque, said, At first glance, it feels like
you're reading something from outer space.


-- 
Homer: Hey, what does this job pay?
Carl:  Nuthin'.
Homer: D'oh!
Carl:  Unless you're crooked.
Homer: Woo-hoo!

Re: [silk] This is what the Singularity looks like.

[Shenoy N]

On 19 February 2014 09:03, Thaths tha...@gmail.com wrote:

 On Wed, Feb 19, 2014 at 12:56 PM, Udhay Shankar N ud...@pobox.com wrote:

 
 
 http://www.newscientist.com/article/dn25068-wikipediasize-maths-proof-too-big-for-humans-to-check.html
 
  Wikipedia-size maths proof too big for humans to check
 
  17:38 17 February 2014 by Jacob Aron
 
  If no human can check a proof of a theorem, does it really count as
  mathematics? That's the intriguing question raised by the latest
  computer-assisted proof. It is as large as the entire content of
  Wikipedia, making it unlikely that will ever be checked by a human being.
 



 The abstract ideas and notations that mathematicians manipulate are
 unfathomable to most people. Dr. Mochizuki's new mathematical language --
 on
 his Web page, he describes himself as an inter-universal geometer -- is
 at
 present incomprehensible even to other top mathematicians.


 Just as I was drawing solace from the Israeli mathematicians observation
that we didn't have to wade through the 10GB proof word by word as long as
we could come up with another way of computer-proving the same result, here
comes this guy whose methods are apparently fathomable to none save
himself, and to him only on his own word! Reminded of the Queen in Alice
who believed in six impossible things before breakfast. I've gotten to two
(three, if you count Kejriwal's assertion that his party is business
friendly).

It's been a lovely morning!



-- 
Narendra Shenoy
http://narendrashenoy.blogspot.com