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World's Hardest Maths Problem 'Solved'

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If attempting long division at school still gives you nightmares, it might be safer to look away now.

Japanese mathematician Shinichi Mochizuki, of Kyoto University, has published four papers which appear to have a serious claim to be proof of one of the most difficult problems in Mathematics: the abc conjecture.

The problem exists within a strand of pure mathematics known as Number Theory and the conjecture states that where three positive numbers a, b and c, which have no common factor and satisfy a + b = c, exist, then d, the product of the distinct prime factors of abc, is rarely much smaller than c.

See, we said it was easy didn't we?

Mochizuki's work has taken four years, and runs to 500 pages; not only that, but he has created a new mathematical language to explain it, which means that peer-reviewing its accuracy may take some time. However, fellow mathematician Dorian Goldfield, has stated that, if proved, it would amount to "one of the most astounding achievements of mathematics in the 21st Century".

The problem was originally proposed in 1985 and, if Mochizuki has cracked it, it automatically leads to solutions for a great deal of related conditional proofs, including two conjectures related to Fermat (one of which is a conditional proof of his famous Last Theorem - albeit the general proof for this is already established).

Well, this is all well and good, but could he split the bill at a curry for over ten people, including a tip? That's the true test.

[View the papers at Mochizuki's website]

Image: Rex

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