# World’s most complex mathematical theory cracked

#### by saravana 2012-09-26 18:58:53 World’s most complex mathematical theory cracked

A Japanese mathematician may have finally cracked ‘the ABC Conjecture’ — one of the world’s most complex mathematical theories.

Shinichi Mochizuki, a scholar at Kyoto University, has released four papers on the Internet describing his proof of what is known as ‘ABC Conjecture’

Experts said he took four years to calculate the theory and if confirmed it would be one of the greatest mathematical achievements of this century.

The ABC Conjecture was first proposed by British mathematician David Masser, working with France’s Joseph Oesterle, in 1985. It was, however, never proven.

It refers to equations of the form a+b=c. It involves the concept of a square-free number, meaning a number that cannot be divided by the square of any number.
For example: 15 and 17 are square-free numbers, but 16 is not because it is divisible.

From that, the ABC Conjecture concerns a property of the product of the three integers ABC. The conjecture states that for integers a+b=c, the square free part always has a minimum value greater than zero and nearly always greater than 1.

The paper, which is 500 pages long, can be viewed on his website in a series of PDFs labelled "Teichmuller Theory".

Dorian Goldfeld, a mathematician at Columbia University in New York, told Nature magazine that Mochizuki's discovery is "one of the most astounding achievements of mathematics in the 21st century."