REALLY New Math

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"Could there be anything new to discover about the relation between addition and multiplication?"

Numbers, addition, multiplication — the basic stuff of grade-school arithmetic — are suddenly the excited talk of cutting-edge mathematicians.

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. "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."

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