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Friday, Sep. 21, 2012

Kyoto professor offers elusive proof of number theory's abc conjecture


Kyoto University mathematician Shinichi Mochizuki has caused a major stir among his peers by releasing a document online that claims to prove the abc conjecture in number theory, considered the most important unsolved problem in modern mathematics.

If Mochizuki's 500-page paper withstands scrutiny, it will provide immediate proof for a number of other theorems and represent "one of the most astounding achievements of mathematics of the 21st century," Dorian Goldfeld, a mathematician at Columbia University, was quoted as saying by Nature magazine in its Sept. 10 online edition.

The abc conjecture was first proposed by European mathematicians in the 1980s and consists of a simple equation of three integers, described as mathematical variables a, b and c and stated as a + b = c. The conjecture considers each number's prime factors.

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

The New York Times said that even though Mochizuki's document is extremely difficult to comprehend, many are still taking it seriously given his expertise in the field of number theory.

"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 online edition Monday.

At home, University of Tokyo professor Yujiro Kawamata noted that "there is a great possibility of Mochizuki having proved the abc conjecture this time," adding he is a "researcher who has built unique theories on his own and uses singular terminologies in his often voluminous papers."

A researcher acquainted with Mochizuki said he "spent at least 10 years writing the thesis with an undivided focus throughout."

Mochizuki was born in Tokyo in 1969. He moved to the United States at age 5 because of his father's work, entered Princeton University at 16 and graduated in mathematics just three years later, according to sources.

He took up an assistant teaching post at Kyoto University in 1992 at age 23, when he was reported to be completely proficient in Japanese, and was appointed professor in 2002.

Mochizuki has accumulated a diverse range of achievements in number theory, and in 2005 became one of the first recipients of the Japan Academy's award to honor young scholars up to age 45.

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