Can mathematicians still refuse to use AI at this point?

I have been writing about mathematics for almost 20 years, and in that period, I don’t think there has ever been a time quite like today. For the majority of my career, landing a big maths story was something that happened perhaps every few months at most – the Venn diagram of maths results that are both interesting and explainable to a general audience has a pretty narrow overlap. That all changed as artificial intelligence became shockingly capable at mathematics, a story we have been covering in detail for the past year or so. According to one analysis, 25 per cent of mathematical papers published on the arXiv preprint server in August acknowledge some use of AI, up from just 1 per cent the year before. Mathematicians are still reeling from the changes we’re seeing, and it has left me – and them – wondering whether it will even be possible to do mathematics without AI in the near future. One analogy that springs to mind is chess, for which we have had superhuman AI players for decades. But that doesn’t mean that people stopped playing chess – instead, chess AIs can inspire and train new players. Where the analogy falls down, of course, is that one game of chess doesn’t build on every other game of chess that comes before it. In a way, mathematics is more like one big multiplayer puzzle, and once AI has joined the game, it is impossible to ignore. Advertisement Mathematical proofs are, by definition, true forever, which makes it impossible to unknow a result proven by AI. That is even the case for a proof written in such a way that humans don’t understand it, because its veracity can be verified via the programming language Lean, which breaks a proof down into elemental logical statements that can be mechanically checked by a computer. The potential for a gap to open up between truth and understanding is concerning. Mathematician Terence Tao at the University of California, Los Angeles, has warned that solving problems with AI is akin to using up a non-renewable resource, meaning the pool of open problems. He argues that, while there are theoretically an infinite number of problems for mathematicians to work on, identifying particular problems that will lead to the discovery of new mathematical techniques is a key part of mathematical research. If AI hoovers up these problems and solves them without producing new techniques, where does that leave mathematicians? “The indiscriminate use of powerful solution-extraction tools can achieve the immediate short-term goal of solving problems at hand, but at the cost of sustaining the ecosystem for the next wave of progress, or in understanding the progress already obtained,” said Tao in a recent social media post. One solution he suggests is that classes of problems should be ringfenced as deserving full analysis and understanding, not merely solving. I think this is probably impossible, as Tao essentially admits himself. It just takes one person – and it doesn’t even have to be a professional mathematician – to solve a problem using AI, and then it has been solved by AI forever. The suggestion also reminds me of the 2008 novel Anathem by Neal Stephenson, which imagines a world in which the infosphere has been so polluted by “artificial inanity” that truth becomes impossible to discern. Researchers now occupy monastery-like institutions that are intentionally cut off from the rest of the world in order to rely only on their own reasoning systems. Ironically, the problem mathematicians face today is almost the exact opposite – thanks to Lean verification, truth is almost too easy to come by. Could a similar idea – AI-free mathematicians, rather than AI-free maths problems – work? “I don’t think it’s ideal if all mathematicians on the planet use the same technology as an inescapable interface between themselves and their discipline,” says Alessandro Della Corte at the University of Camerino, Italy. “I think it’s better if a small minority, say 5 to 10 per cent, remains AI-free, while the bulk of the community engages with the tools, hopefully critically and within academia.” Della Corte has set up an online declaration for other mathematicians to sign and join him in eschewing AI in their own work, but he agrees that it won’t be possible to ignore the spectre of AI completely. He says that if he encounters a result that would be useful for his work that was obtained using AI, he wouldn’t pretend it doesn’t exist. “As long as it is presented in an understandable way, preferably in a paper where a human author takes responsibility. I care for my personal workflow and like it to be ‘AI-clean’, but for sure I don’t want to promote irrational forms of tech asceticism.” Some mathematicians are more positive about the impact of AI. Daniel Litt at the University of Toronto has written that the profession is entering a new era. “I think we are at the beginning of an incredible, wonderful explosion of mathematics, and if we value human understanding, there will be more need for human mathematicians than ever before,” he writes – but what mathematicians do will have to change, with less of a focus on creating mere proofs and more on understanding and communication. This feels like the most realistic scenario to me. Putting aside the fact that AI is still pretty bad at generating text you want to read, you can simply ignore AI-generated novels if you wish. I don’t see how mathematicians can ignore AI-generated mathematics once it enters the literature. As Litt puts it, it is now “impossible to stop people, amateur or professional, from pushing a button to produce mathematics”. As an outside observer, it is fascinating to watch mathematicians as they try to adapt to this new reality. I’m also very glad that I don’t have to be the one to develop new rules for the great mathematical puzzle, now that AI looks set to dominate the game. [Image text:] nJl p(n) nJt COS n anJt e Sin 90= COSO= sin