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On 8 September, OpenAI claimed that its AI agents had solved the Navier-Stokes problem, one of the most famous and difficult challenges in mathematics. Had a human solved it, they would have collected both prize money and plaudits from their fellows. The announcement instead ignited what some mathematicians have called an “existential crisis” in their field over the power of AI, and accusations that OpenAI misused human work.
The maths behind Navier-Stokes is difficult to understand, but the critiques levelled by mathematicians will be familiar to artists, office workers, or anyone else concerned about AI. OpenAI’s results, like any arising from a large language model, depend on digesting work by human mathematicians. The OpenAI paper cites sources, but many believe the company didn’t give sufficient credit, especially to several mathematicians believed to be very close to a solution – bad form that erases human ingenuity and hogs all the glory. The mathematician Tristan Buckmaster also has concerns that work he was doing on Navier-Stokes using OpenAI’s Codex model was seen by the OpenAI team. OpenAI has denied directly accessing this material, but could not rule out that data from Buckmaster’s use of their products “helped improve our model”.
This lack of attribution and compensation for the human labour that AI is built on has turned many against the companies that develop these systems. It has yet to be adequately addressed. This is a particular misstep in the case of mathematics. As many mathematicians have pointed out, AI firms are keen to use their models’ maths prowess as an advertisement. But they rely on mathematicians to check their – often sloppy and baffling – work, and to tell them if it is useful and how it might be applied. An AI-produced movie or vaccine would have a clear and obvious use, whatever its merits, but it will take time and human intellectual labour to tell whether OpenAI’s purported solution contains any novel mathematical tools or insights. This should be an opportunity for collaboration. It has instead become yet another source of alienation and resentment.
Despite this, mathematicians are remarkably open to the use of AI, even as they commit their names to open letters denouncing tech firms. Most recognise that the technology is undeniably powerful and particularly good at maths. There has been a nuanced discussion of how maths might change and integrate AI, with humans guiding and interpreting its work. There has also been some soul-searching as to whether celebrating the person – or machine – that achieved a flashy final result in the form of a mathematical proof is the best way to value contributions. As Bill Thurston, the Fields Medal-winning mathematician, put it in 2010, well before the age of AI: “The product of mathematics is clarity and understanding. Not theorems, by themselves.” These are still uniquely human qualities.
Some critics of AI are still stuck dismissing its outputs as uniformly useless “slop”. AI will not become good at everything. But more people may find themselves in the current position of mathematicians, confronted with the undeniable effectiveness of AI, while deeply concerned about how it is being used. This anxiety might not exist, the mathematician Nestor Guillen wrote recently, if we could separate the tech from the tech companies, and democratise its use. It is increasingly urgent that we find ways to do so.
