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World's most complex mathematical theory 'cracked'

September 19, 2012 18:04 IST

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 Telegraph' reported.

Confirming the breakthrough, however, may take many more year as Mochizuki has created an entirely new mathematical language to explain the steps that he took -- and others in the field will have to learn to read it first.

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.

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."

Mochizuki describes himself not as a mathematician but as a "inter-universal geometer" and - as long as his theory stands up to the scrutiny - there are hopes that his findings will settle a number of knotty problems in number theory and other branches of maths.
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