BUSINESS REFLECTION: Crossed Wires: AI smashes the foundations of the global kingdom of mathematics

On the night of 6 October, OpenAI released a dump of 722 AI-generated mathematics papers, representing somewhere north of 372 proofs (or partial proofs) of unsolved and open maths problems (about 300 of them have been formally verified). The proofs wiped out decades (and more) of ongoing human enquiry in several mathematical subfields. And each proof took a mere three hours of compute time.

To say this went off like a thermonuclear weapon in the maths community would be a pallid understatement. It is much worse than that. Thousands of careers will lose their fuel and their joy, maths PhD programmes will be decimated, university students will flee to other subjects, and some maths departments might disappear in the wake of student exits. One commentator was more brutal. He said, without much emotion – maths is cooked.

AI achievement vs human tragedy

It is very difficult to celebrate this considerable AI achievement without due discomfort at the human tragedy it now represents and what it portends. We’ll get to that, but first let’s attend to some of the grief and loss.

On the night of the dump, Hugo Duminil-Copin, winner of the 2022 Fields Medal – the closest thing mathematics has to a Nobel prize – cried so hard that he woke his daughter. “They have annihilated my field of research,” he told Derek Thompson. In a note posted to the mathematics blog Proofs and Prompts, he explained why. Every major open problem he had ever mentioned in public – in a lecture, a paper, even a grant proposal – had been solved overnight. He had expected a few to fall eventually. Not all of them, not all at once, and not with such breezy nonchalance. He described himself as paralysed.

He wasn’t alone. Steven Strogatz of Cornell, perhaps the best-known translator of mathematics into plain English and the author of the only book that finally explained calculus to me (Infinite Powers: How Calculus Reveals the Secrets of the Universe), has admitted to breaking down in several interviews. Tim Gowers of Cambridge, another Fields medallist, cinematically described his community as people standing on a beach, waiting for an inevitable tsunami to roll towards them.

The Proofs and Prompts collection, now well over a hundred testimonies long, reads like a book of condolence, the sad utterings of the bereft and cast out. Matt Zaremsky had spent four years on something called the Boone-Higman conjecture, his group inching towards a solution one breakthrough a year. He likened it to an archaeological dig, slowly exposing a magnificent dinosaur skeleton, until a trillion-dollar company arrived, blasted the site with dynamite, handed over the bones and drove off.

Alain Valette from the University of Neuchâtel felt stabbed in the back – he now stands among ruins, the questions that guided 46 years of his career wiped away. Tasmin Chu, early in her career, said her grief was not for the answer to her beloved “percolation problem”, but for the years of quiet thinking she had expected to spend on it. Her grant proposal, due the following week, had to be rewritten. Tristan Humbert, in the middle of postdoc applications, spent the morning frantically redrafting a research plan that had become obsolete.

Even Terence Tao, the field’s reigning genius and a man not given to theatrics, said he was horrified at the person-years of patient work by graduate students and postdocs casually destroyed. One cannot unhear a spoiler, he noted.

Giovanni Mongardi from the University of Bologna imagined his colleagues demoted to priests of a Machine-God, interpreting its pronouncements for the laity. And the mathematician Sam Hughes put it most plainly: “How much beauty have we lost?”

The maths community was almost unanimous in its irritation (and rage) against OpenAI because of the manner in which this was done – casually, brutally, triumphantly and without warning or consultation. I have empathy, but if it had not been OpenAI, it would have been Claude or Gemini or Grok or one of the Chinese models, no matter how gently delivered. This was bound to happen. Anyone following the edge of AI closely enough over the past year or two knew that this was imminent. Vague hand-waving about AI only solving the low-hanging was always unrealistic, given AI’s continual sprinting up the knowledge curve.

The search for silver linings

Not everyone is in mourning, or at least not all the time. Strogatz, earlier tears notwithstanding, was interviewed in a 13 October episode of The New York Times podcast The Daily. He described the mood among mathematicians as “discombobulated”, with most colleagues somewhere on the conventional stages of grief – some bargaining, some accepting, some still in denial. What is being lost, he suggested, is the chance to be a hero – the first to crack something, understand it and explain it to the world. For thousands of years mathematicians could fantasise about starring in their own story. That part may be over.

And yet, putting on what he called his happy face (and insisting he was not faking it), he found genuine reasons for hope. At a recent departmental town hall a colleague compared the new models to a new telescope – the question is no longer whether you can see further, but where you choose to point the thing.

This is perhaps the biggest takeaway and reason for hope. The AI does not understand whether the problems it has solved are important, or easy or challenging, or have a history, or really anything at all. It just proves stuff. Who is going to conjure up the future puzzles for it to solve? Who is going to adjudicate whether they are worth solving? Humans will decide that. That is where the compass now points.

There is, of course, another dark cloud on the horizon (or an exciting prospect, depending on your viewpoint). AI is coming for everything else too. If maths is truly cooked, then it would be accurate to say that physics and chemistry and biology and the rest are still in the oven, and there is little chance that their kingdoms will not fall too. And so we humans need to prepare for a world where the solution to a problem is simply an easy by-product, giving way to the much more important and human matter of deciding which questions are worth asking.

What is left?

Finally, there is this – if the machines can out-reason us and out-solve us, what is left?

The answer lies in the messy, chaotic, embodied, absurd business of being alive. The capacity to feel joy and grief and boredom and lust and spite. The ability to be irrational, impulsive, self-destructive and loving. To wake up in the middle of the night with a terrible or good idea. To cry at a TV commercial. To find something funny that no one else finds funny.

AI does not choke up on a podcast because it suddenly realises that the thing it loved is gone. Those tears belong to humans. That is AI’s ultimate lacuna.

The kingdom of mathematics may be falling. But the humans who live there will go on doing surprising and inexplicable things, thinking thoughts they didn’t have yesterday and feeling the tug of curiosity. These are things that are ours and ours alone.

No AI proof, however elegant, will ever explain that. DM

Steven Boykey Sidley is a professor of practice (ex-JBS, University of Johannesburg), a partner at Bridge Capital and a columnist-at-large at Daily Maverick, where he writes the weekly Crossed Wires column. His new book, It’s Mine: How the Crypto Industry is Redefining Ownership, is published by Maverick 451 in South Africa and the Legend Times Group in the UK/EU, available now.