Software is already cracking theorems that humans have struggled to prove. Future computers could take mathematics to places too complex for our brains to follow

Our number's up: Machines will do maths we'll never understand

(Image: Roya Hamburger)

AFTER three years, Shinichi Mochizuki is still waiting. In 2012, the highly respected mathematician at Kyoto University in Japan published more than 500 pages of dense maths on his website. It was the culmination of years of work. Mochizuki’s inter-universal Teichmüller theory described previously uncharted areas of the mathematical realm and let him prove a long-standing conundrum about the true nature of numbers, known as the ABC conjecture. Other mathematicians hailed the result, but warned it would take a lot of effort to check. Months passed, then years, with no conclusion.

Ask a mathematician what a proof is and they’re likely to tell you it must be absolute – an exhaustive sequence of logical steps leading from an established starting point to an undeniable conclusion. But that’s not the whole story. You can’t just publish something you believe is true and …

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