Japanese mathematician offers solution to important number theory


Mainichi, Sept 19, 2012
TOKYO (Kyodo) — Japanese mathematician Shinichi Mochizuki at Kyoto University has released a document on the Internet that claims to provide proof for the abc conjecture in number theory, said to be the most important unresolved problem in modern mathematics, causing a stir among peers.

The abc conjecture provides immediate proofs for other theorems including even Fermat’s famous last theorem, a vexing issue in number theory that took roughly 350 years to be demonstrated, and Mochizuki’s 500-page document, if it withstands scrutiny, will represent “one of the most astounding achievements of mathematics of the 21st Century,” Dorian Goldfeld, a mathematician at Columbia University in New York, was quoted as saying by Nature magazine in its Sept. 10 online edition.

The abc conjecture, proposed by European mathematicians in 1985, is about a simple equation of three integers — described as mathematical variables a, b and c, where a + b = c, and considers each number’s prime factors, which can be divided by 1 or themselves.

Nature said Prof. Mochizuki, 43, has devised “techniques that very few other mathematicians fully understand” in advancing his theory. The work “uses a huge number of insights that are going to take a long time to be digested by the community,” Brian Conrad, a Stanford University professor, told the magazine.

The New York Times said many are taking Mochizuki’s work seriously, even though it is hard to comprehend, because of significant proofs to his credit. “He has a long track record, and he has a long track record of being original,” the paper quoted Jordan Ellenberg, a University of Wisconsin mathematician, as saying in its Monday online edition.

Yujiro Kawamata, professor at the University of Tokyo, said, “Professor Mochizuki is an able mathematician and there is a great possibility of him having proved the abc conjecture this time.”

He is a “researcher who has built unique theories on his own and uses singular terminologies in his papers that are often voluminous.”

Mochizuki was born in 1969 in Tokyo. He moved to the United States when he was 5 years old because of his father’s work, according to sources, spending most of his life in the United States.

He entered Princeton University in the United States at age 16 and graduated in mathematics at age 19. When he took up an assistant teaching post at Kyoto University in 1992, when he was 23, he is said not to have been completely proficient in Japanese.

He became a professor in 2002 at 32. He has accumulated a diverse range of achievements in his specialty of number theories. In 2005, he was one of the first recipients of the Japan Academy’s medal to honor “young” scholars aged up to 45.

“He spent at least 10 years in writing the thesis with uninterrupted focus throughout on it,” a researcher who is acquainted with Mochizuki said.

September 19, 2012(Mainichi Japan

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