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.
What’s next for mathematics now that AI is upending the field? 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. 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? 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.
Extract — continue reading at the source.
