AI challenges maths by solving the unsolvable / Photo: Jung Yeon-je - AFP
AI challenges maths by solving the unsolvable
Announcements over recent months that artificial intelligence models have cracked previously unsolvable problems are shaking to the core top-level mathematicians, who are now asking themselves: where do we come in?
"All the avenues of research I had are now gone; we're facing a new day," Hugo Duminil-Copin, winner of the 2022 Fields Medal, one of the highest honours in mathematics, recently told his colleagues at the French Mathematical Society.
Since April, AI firms have regularly been publishing solutions to previously unsolved mathematical problems as they seek to demonstrate the power of their latest models.
Last week OpenAI released solutions to 719 previously unsolved problems.
The advances are forcing those in the field to wonder whether this spells the end of mathematical research.
- Thinking tool -
While acknowledging the emotional shock caused by the recent publications, Stephane Mallat, 2025 Gold Medal recipient from France's national scientific research centre (CNRS), told AFP there will always be a need for mathematicians.
"Mathematics goes far beyond calculation: it's a way of thinking clearly," Mallat said.
"Beyond all the problems we face with AI, maths will remain absolutely central because it's a tool that allows us humans to think clearly and understand things," he told AFP.
An initial sign of pushback from the field has come from the Simons Foundation.
This major American patron of mathematics announced last week a $15-million programme co-funded by OpenAI and Anthropic to support mathematicians in dealing with AI.
It will fund workshops to assess the results produced by AI and establish standards for its use.
Mallat also noted mathematicians are needed for teaching, although the rapid advancement of AI will impact this area too.
"You have a lot of young people who aren't very keen on doing maths, and when you see an impact like this, they might say: 'Oh well, even researchers are going to be replaced by AI, so why should I bother?'" said Mallat.
"That question needs to be addressed, because it's completely false that we no longer need mathematicians."
- Tractors and Columbo -
For Francois Charles, mathematician and department head at the Ecole Normale Superieure in Paris, two separate issues are playing out.
"We have legitimate concerns about how the community is organised, because AI is bringing a number of changes in how people enter the profession or at the doctoral level. But on the purely scientific side, I'm not at all pessimistic," he said.
"A certain number of obstacles may be overcome. As scientists, we need to be more ambitious."
Mallat, who has recently published a book on maths and AI, makes a distinction between what is happening and the mechanisation of agriculture when tractors came on the scene.
"It was also a human tragedy for some who had to abandon the countryside, move to the cities, find jobs, retrain. Now, mathematicians are not in that situation. When you know how to do maths, you can do an enormous number of things," he argued.
Meanwhile, in the pages of French daily Le Figaro, 2010 Fields Medallist Cedric Villani, a strong critic of AI, took inspiration from the TV detective Columbo.
"In mathematics, the conclusion is less important than the path to get there."
D.Walter--FFMTZ
