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!
