Aside from the printing press and the digital computer, mathematics has been relatively free of fundamental perturbation for centuries. AI is changing that, rapidly, and more fundamentally than anything before it, for better or worse. This year, AI began to create sporadic and elemental discoveries in mathematics.
Then came a steady trickle of even more impressive progress. Now, we have reached a powerful surge, with OpenAI solving a problem related to the Navier-Stokes equations, one of the most famous in mathematics. It is unclear how far this progress will continue, but what is certain is that the role of a mathematician, their ways of working and the processes and norms of the field will all be upset.
Helen Wilson at University College London says that academics are still processing what is happening. But that is a reason to be optimistic, too. AI seems able to use existing knowledge at rapid speed to crack some of the meatiest mathematical conundrums.
Perhaps mathematicians will prosper in the future as the controllers of such powerful tools, pushing the field further than they ever thought possible. Now we’re gonna be able [to answer them],” said Sébastien Bubeck at OpenAI, speaking to New Scientist before the Navier-Stokes announcement. But other changes are more problematic, like how we train new mathematicians.
Currently, PhD students are often given a relatively low-level problem to chew over for a few years and hone their skills on, but that model falls apart with AI. And in a world where we fail to train fresh mathematicians, we soon run out of them. Within decades, the field becomes rudderless, and there are no humans left with the skills and experience needed to interpret what AI creates.
It is said that no human has understood all of mathematics since Henri Poincaré, who died in 1912, but there may soon be parts of maths that no human understands. It’s just an industry of machines producing papers that nobody reads,” says Wilson. I made a free AI chatbot solve a decade-long maths problem in 13 minutes Existing mathematicians using AI also face tricky questions, like who can claim credit for discoveries.
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