What an AI maths breakthrough means for human discovery

Albert Einstein described the harmony of pure mathematics as “in its way, the poetry of logical ideas”. Yet the field that underpins science and all it describes is now in uproar, after OpenAI produced a proof of a high-profile maths problem.

The turmoil over the AI lab’s intervention and its wider impact shows how maths is on the frontline of the possibilities and perils of the technology. While headlines focus on the risks that AI will cause mass unemployment, accelerate global heating or even destroy humanity, its impact on scientific discovery is also fundamental.

OpenAI, the maker of ChatGPT, announced this month that it had developed a solution for the Navier-Stokes maths problem set 26 years ago as a Millennium Prize challenge with a $1mn reward (which the company has said it won’t take). The news sparked dismay from many leading mathematicians over how OpenAI obtained its result and what it means for maths’ future. Some fear it will open an era of computational brute-force shortcuts to solutions, shunning crucial insights that humans would have gained along the way.

On one level, the story highlights familiar concerns about AI exploiting human intellectual property. OpenAI’s announcement prompted a New York University mathematician, Tristan Buckmaster, who had been working on related research with Levent Alpöge, a mathematician at OpenAI’s rival Anthropic, to raise questions about possible foul play. OpenAI chief executive Sam Altman rejected what he called “unfounded accusations of plagiarism”.

The incident caused a deeper unease in the global community of mathematicians. In an open letter, 27 winners of the prestigious Fields Medal argued that the goals of AI companies and the maths community were “severely misaligned”. Solving problems should be “only a tool and proxy for achieving the primary goal of conceptual understanding and insight”, driving the formulation of new questions and ideas, they wrote.

The stakes are much higher than esoteric discussions about theories very few people on Earth understand. Maths is the foundation of our understanding of the natural world and human civilisation. The patterns it reveals are crucial to billions of years of evolution and to the latest technologies, including AI.

The idea that humans should be central to mathematical discovery is not a misplaced argument against digital progress. AI has a potentially exciting and constructive role in mathematics, just as in the physical sciences in areas from medical imaging to understanding the origins of disease, which could transform healthcare.

There is, though, a long history of mathematical understanding gained from being a person moving through the material world. From the (embellished) stories of Archimedes leaping from his bath to Newton being hit on the head by a falling apple, physical observations have long been linked with sparking transformative chains of thought. The Navier-Stokes problem itself relates to the flow of fluids such as water and air.

There are powerful arguments that skipping to the solution of a maths problem in an opaque way could deprive us of essential knowledge that humans might have discovered. For example, Fermat’s Little Theorem, along with Euler’s generalisation of it, underpins modern cryptographic methods that protect data across the globe. More broadly, maths and its pursuit by thinkers over millennia have had a profound role in grappling with great philosophical questions relating to the human condition and the world around us.

The maths dispute is a powerful reminder that in the pursuit of progress, human-led processes matter as well as outcomes — for hard-nosed practical reasons as well as romantic ones.