• Kyodo, Jiji

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A proof by mathematician Shinichi Mochizuki of a major conundrum in number theory that went unresolved for over 30 years has finally been validated, Kyoto University said Friday following a controversy over his method, which was often labeled too novel or complicated to understand.

Accepted for publication by the university’s Research Institute for Mathematical Sciences was Mochizuki’s 600-page proof of the abc conjecture, which provides immediate proofs for many other famous mathematical problems, including Fermat’s last theorem, which took almost 350 years to be demonstrated.

The abc conjecture, proposed by European mathematicians in 1985, is an equation of three integers a, b, and c composed of different prime numbers, where a + b = c, and describing the relationship between the product of the prime numbers and c.

“There are a number of new notions and it was hard to understand them,” Masaki Kashiwara, head of the team that examined the professor’s theory, said at a news conference.

He proved the abc conjecture with a “totally new, innovative theory,” said fellow professor Akio Tamagawa. “His achievement creates a huge impact in the field of number theory.”

In the four papers, Mochizuki expounds on what he calls “Inter-universal Teichmuller Theory.” He says the solution of the abc conjecture is one of the consequences of the theory.

Mochizuki, 51, released his study in 2012 on his website. It was published in the institute’s journal after nearly 20 years of research.

His proof, however, courted controversy with its denseness and length, which baffled peers who tried to confirm it. Additionally, two respected mathematicians, Peter Scholze and Jakob Stix, said in 2018 there was a flaw with the proof. Stix reportedly found a “serious, unfixable gap.”

Scholze told Kyodo News after the announcement that his position remains “unchanged” and that the news came “as a surprise” to him.

Mochizuki, who has declined requests for interviews over the years, did not show up at the news conference but released a statement through the university in which he said he completed the proof through trials of numerous prototype theories.

Mochizuki was born in Tokyo in 1969. He grew up in the United States, where he moved to when he was 5 years old.

A wunderkind, he was accepted at Princeton University in New Jersey at age 16 and graduated three years later.

After receiving his doctorate, he accepted an assistant teaching post at Kyoto University in 1992, when he was 23, and became a full professor when he was 32.

In 2005, he was one of the first recipients of the Japan Academy’s medal honoring “young” scholars up to 45 years old.

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