============================ WHOLE numbers, addition and multiplication are among the first things schoolchildren learn, but a new mathematical proof shows that even the world's best minds have plenty more to learn about these seemingly simple concepts.

Shinichi Mochizuki of Kyoto University in Japan has torn up these most fundamental of mathematical ideas and reconstructed them as never before. The result is a fiendishly complicated proof for the 27-year-old "ABC conjecture" - and an alternative mathematical universe that should prise open many other outstanding enigmas.

Not only that, Mochizuki's work also offers an alternative way to prove Fermat's last theorem, a long-standing problem that became one of the most famous results in the history of mathematics when it was proved in 1993

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The above extract is from a 15 September 2012 New Scientist cover story titled, Super Imaginary Numbers.

While I read the full article, I neither understand Shinichi Mochizuki's work nor the magnitude of his breakthroughs.

Would someone please explain this all to me in a way that makes some sense to a naïve mathematician?

Thank you

Jonathan Crabtree

Here are the original papers currently being studied...