ABC – it’s not as easy as 1, 2, 3

An attempt to fix issues with a controversial mathematical proof has itself become the subject of controversy, marking the latest twist in a decade-long saga that involves a $1 million prize.

Background: The story centers around a proof published by Japanese mathematician Shinichi Mochizuki in 2012, which claims to solve a long-standing problem in mathematics called the ABC conjecture.

However, Mochizuki’s proof, which he spent 20 years single-handedly developing, contained 500+ pages of a brand-new and highly specialized notation that other experts struggled to decipher.

• While a handful of mathematicians have since accepted that Mochizuki’s research solves the ABC conjecture, many others say his arguments are inherently flawed and don’t prove anything. (These disagreements often involve unusually pointed insults.)

A recent proof hoped to clear the situation up – but only added more drama. Kirti Joshi, an associate math professor at Arizona University, published a proof last year that he says fixes the problems with Mochizuki’s work and proves the ABC conjecture.

But Mochizuki, as well as mathematicians who oppose his proof, remain unconvinced. In a 10-page response published last week, Mochizuki said Joshi’s work was “mathematically meaningless,” and that it reminded him of “hallucinations produced by artificial intelligence algorithms such as ChatGPT.”

👀 Looking ahead… Anyone who’s able to conclusively prove – or disprove – Mochizuki’s theory will receive a $1 million prize from Japanese businessman Nobuo Kawakami.