Inter-universal Teichmüller Theory

“If nobody understands a mathematical proof, does it count? Shinichi Mochizuki of Kyoto University, Japan, has tried to prove the ABC conjecture, a long-standing pure maths problem, but now says fellow mathematicians are failing to get to grips with his work.

The problem gets its name from the simple equation for adding two numbers, a + b = c, but poses deep questions about the true nature of numbers. In 2012 Mochizuki posted a 500-page paper online that claimed to solve the puzzle, but it required a dense framework of new maths dubbed “Inter-universal Teichmüller Theory” that even experienced mathematicians found difficult to follow.

Mochizuki is a highly-respected mathematician and his work is taken seriously, says Minhyong Kim of the University of Oxford, but in the years since he posted the proof no one has been able to give a definitive answer on whether it is correct. “It’s a bit disappointing that no one has come out and said it’s right or wrong,” he says.”

Mathematician’s anger over his unread 500-page proof

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