“It gives them enormous publicity”: between prestige and demonstration of the capabilities of their models, why has mathematics become the playground of AI companies?

In recent months, AI has been shaking up the world of mathematics. This scientific discipline has become the playground of companies in the sector, starting with OpenAI. The creator of ChatGPT has been making numerous announcements since last year, rejoicing in the progress of its AI models in mathematics.

An 80-year-old puzzle solved in May, a problem dating back more than a century conquered in September. The company has no plans to slow down, bringing to the attention of the world, especially mathematicians, the resolution of hundreds of previously insoluble problems by a cutting-edge model in early October. An announcement far from delighting those mainly concerned, many of whom are distraught in the face of the progress of AI in mathematics.

But beyond the sector's concerns about the future of this profession, a question arises: why are AI companies like OpenAI interested in mathematics? A question that, unsurprisingly, has not just one answer, but several. Complex problems to solve The first, and perhaps the most obvious, is purely marketing.

“It gives them enormous publicity. (...) They can say to their customers, to people who want to use these systems, 'with our language model, you have the best tools that exist at the moment,' says François Willot, mathematician and research director at the École des Mines Paris-PSL, with BFM Tech.

Because sharing the prowess of their models is also a way for these companies to show what they are capable of. Especially since they don't tackle simple math problems. “Mathematical conjectures that have not yet been demonstrated are among the most difficult problems that, until recently, humans were capable of solving and not machines,” points out the mathematician.

A position joined by François Charles, mathematician, director of the mathematics and applications department of the ENS-PSL and member of the AGMAI, the independent committee made up of nine world-renowned mathematicians, which advises the AI ​​giants, during a presentation on the impact of artificial intelligence on research in mathematics. He declared: "The development of mathematics, including pure mathematics, is very affected by the progress of general models. (...

) A year ago, the big news about LLMs (large language models, Editor's note) for mathematics was that they managed to solve competitions, certainly very difficult, but for high school students. Since the end of May, (...) we have had a very important series of cutting-edge, very visible research results, which have been resolved autonomously by LLMs.

"Large general language models have therefore become extremely powerful mathematical tools. In this scientific discipline, a conjecture corresponds to a proposition considered to be true due to observations, analogies or others, but which has not been formally proven. Last May, an OpenAI model, for example, managed to refute a conjecture concerning the problem of unit distances by Paul Erdős, which dates back to 1946.

Machine-translated from French