The problem causing problems in the math world

·2-min read
A Japanese mathematician's proof of the abc conjecture is a subject of much debate in the world of math.

Since 2012, a Japanese mathematician named Shinichi Mochizuki has claimed to have solved one of the biggest math problems of our time, the abc conjecture. However, other world-renowned mathematicians refute his purported proof. After March 14's Pi Day and ahead of April's Mathematics and Statistics Awareness Month in the US, we take a look at one of the latest controversies gripping the enigmatic world of mathematics.

It's a story that could easily be the plot of a Netflix series. On the one hand, the eminent Japanese mathematician and Princeton alumnus Shinichi Mochizuki, claims to have solved a mathematical problem that's over 30 years old. In 2012, he published four articles outlining his proof. However, the hefty work -- with some 600 pages -- has been making waves in the math world.

On the other hand, renowned mathematicians have been stumped when trying to decipher this so-called solution to the abc conjecture. Written in an impenetrable and highly personal style, the articles seemed to be entirely built on mathematical concepts that were completely unknown to the rest of the community. "Looking at it, you feel a bit like you might be reading a paper from the future, or from outer space," wrote Jordan Ellenberg, number theorist from the University of Wisconsin-Madison, in a blog post shortly after the articles were published.

The abc conjecture (or hypothesis, in the language of mathematics) is a number theory problem. It expresses a profound link between the addition and multiplication of integer numbers.

"A serious, unfixable gap"

One of these detractors is Peter Scholze. This math world heavyweight and 2018 Fields medalist -- a kind of math Oscars -- refutes part of Shinichi Mochizuki's writings. Together with the German mathematician Jakob Stix, the pair highlighted a "serious, unfixable gap" in the proof outlined in the article in 2018.

Ten days ago, the Japanese mathematician published a report detailing the entirety of his research around the abc conjecture to defend his hypothesis. However, the editorial board of the scientific publication that served to promote the article -- Publications of the Research Institute for Mathematical Sciences -- is headed by a certain Shinichi Mochizuki, its editor-in-chief.

Shinichi Mochizuki is nevertheless supported by several Japanese researchers ... although no one is capable of correctly expressing his words to other mathematicians, which is problematic.

Solving the abc conjecture is far from a trivial affair. In fact, it would pave the way to unlocking many still unsolved theorems. If Shinichi Mochizuki's proof is confirmed to be correct, it would no doubt become one of the century's most surprising feats of mathematics. Stay tuned for the next "season" in this incredible story to find out what happens next ...

Axel Barre