May 22, 2019 | Updated: 08:18 AM EDT

Japanese Mathematician Claims To Solve Problem By Introducing New Branch Of Mathematics

Dec 24, 2015 02:13 AM EST

ABC Conjecture
(Photo : Wikimedia) The ABC conjecture is easy to understand but is hard to prove.

A mathematician from Japan has claimed that he manages to solve a notorious mathematical problem in years. Shinichi Mochizuki of Kyoto University in Japan has published a 500-page document a math problem "ABC Conjecture."

According to Shinichi Mochizuki of the Research Institute for Mathematical Sciences, the ABC conjecture is an important problem in number theory. The ABC conjecture should be similarly opaque as Wile's proof of Fermat's Last Theorem.  A group of mathematicians met at Oxford earlier this month and another is currently meeting at Utrecht in the Netherlands to discuss the conjecture.

The conjecture is not complex to state. For example, there are three positive integers a, b, c satisfying a + b = c and having no prime factors in common. Let d denote the product of the distinct prime factors of the product abc. There are only finitely many triples with c > d as the Mochizouki's conjecture asserts. Simply put, if a and b are built up from small prime factors then c is divisible only by large primes most of the times.

A more concrete example would be,

a = 16, b = 21, c =37

d = 2x3x7x37 = 1554 > c


The above is an example that supports the ABC conjecture; however, this does not happen "all of the time" but almost all the time. There are several numerical evidence that support this conjecture. Most mathematicians do actually believe that it is true; however, there are no mathematical proof of conjecture until Mochizuki's.

Nevertheless, the papers written by Mochizuki is hard to decipher because of new definitions and new terminology invented by the mathematician. Anyone in the mathematical community is having a hard time understanding reading it. He even made a new branch of mathematics called "inter-universal Teichmuller theory." His methods are considered by other mathematicians as impenetrable.

"The exciting aspect is not just that the conjecture may have now been solved, but that the techniques and insights he (Mochizuki) must have had to introduce should be very powerful tools for solving future problems in number theory," Brian Conrad of Stanford University said.

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