U.-educated mathematician offers proof of pivotal number theory conjecture

Shinichi Mochizuki GS ’92, a mathematics professor at Kyoto University in Japan, released a proof of what is known as the “ABC conjecture,” a problem that was first proposed in 1985 but has not been proven to this point.

According to a story in The New York Times, the conjecture is a statement about the relationship between prime numbers and their multiples. In his proof, Mochizuki shows that the product of the prime factors of two positive integers is usually not much smaller than the sum of those integers. Consequently, according to the conjecture, the sum of two integers that share no common prime factor tends to have a small number of prime factors.

In an example that Minhyong Kim of the University of Oxford explained to the Times, three divides the integer 81 four times and two divides another integer, 64, six times. However, five divides their sum, 145, only once, since dividing 145 by 5 yields 29, another prime number. According to Mochizuki’s work, this observation can be generalized to all sums of two positive integers in the form a + b = c, the equation from which the conjecture gets its name.

The discovery is the culmination of the past four years of Mochizuki’s research. He released his research online in the form of four papers totaling 500 pages.

The mathematical community has reacted with reserved excitement because Mochizuki’s research still has to stand up to criticism and challenges.

Mochizuki entered the University as an undergraduate in 1985 at the age of 16. He graduated with an A.B. in mathematics in just three years and remained at the University to do his doctoral work. After graduating in 1992, Mochizuki became a research associate at Kyoto University, where he has remained except for a two-year stint at Harvard.

Mochizuki has not spoken publicly about his discovery to major news outlets in the past week. He did not respond to repeated requests for comment from The Daily Princetonian.