When AI Can Do It All, What Will Be Left for Human Mathematicians and Scientists?

George Musser

Among all the fields of research, mathematics is the one that one can most clearly foresee being automated. Artificial intelligence systems are already able to suggest new mathematical conjectures. They can translate them into a rigorous form. They can prove them. So, once you combine all three capabilities into one system, what will be left for humans to do? “Mathematicians become priests to oracles,” predicted Yang-Hui He, a mathematical physicist at the London Institute and University of Oxford, during the Hot Topic session at this year’s Heidelberg Laureate Forum.

A.I. was the dominant theme all week at the HLF, and the two Hot Topic panels – the first on mathematics, the second on physics – gave attendees a chance to share their delight as well as dread. All the panelists said they felt both poles of emotion. “We can be excited about the possibilities while also being aware of the potential downsides,” said Maia Fraser, a mathematician at the University of Ottawa. “We can do both at the same time.”

No one doubted that computer tools – including but not limited to large language models – are revolutionizing mathematics research. “In the math community that I come from, progress was measured in years, sometimes even in decades, and now we start to measure things in months,” said Javier Gómez-Serrano, a mathematician at Brown University. As A.I. takes over the chore of formulating and checking rigorous proofs, humans will be freed to concentrate on achieving and conveying intuitive understanding. “They’ll do even less formal proof, and the machines will convert it into some formal form,” said Sanjeev Arora, a computer scientist at Princeton University and recipient of the 2011 ACM Prize in Computing. “So, writing a paper will be much easier.”

The quickening pace makes it even harder than it already was to keep up with the literature, but Arora described how LLMs help him with that, too. He feeds a paper into a model and then engages in dialogue with it, which – he finds – gives much better results than simply asking for a summary. “You do a question-answer with a good model, and you understand the paper very well in 5, 10 minutes,” he said.

So far, A.I. has yet to make any nontrivial discoveries on its own, a threshold that Yang calls the “Birch test,” after his Oxford colleague Bryan Birch. But Yang cited instances in knot theory, number theory, and group theory where it has come close. So, a fully automated advance is probably just a matter of time. He’s fine with that, if it means seeing the solutions to longstanding puzzles:“I really want to see the proof of the Riemann hypothesis, whether it’s given to me by God or by an oracle or by the mind of Terence Tao.”

But Fraser cautioned that we should be careful what we wish for. The willingness of society to support mathematics research, already tenuous, may not survive automation. “I don’t want to speculate on how to maintain the public’s awareness of the importance of mathematicians when they’ve already been cut out of the loop,” she said.

Cognitive de-skilling is another worry. In a poll, audience members expressed concern that A.I.-reliant students are failing to acquire core skills. Gómez-Serrano said this prospect worries him, too. “If we don’t think carefully about this, then this is going to arrive and we will not really know how to react.”

Physics Is Hard Even for A.I.

The physics panelists expressed no such ambivalence; for them, A.I. has been unequivocally good. It has sped up data analysis without threatening to usurp the human role anytime soon. The difference from mathematics is that the main bottleneck is not brainpower but the cost – in time, energy, and money – of experiments.

“We do experiments that take 10, 20 years to plan and pull off and require convincing a large fraction of the world to pitch in to be able to do it,” said Kyle Cranmer, a particle physicist at the University of Wisconsin–Madison. Furthermore, experiments entail tradeoffs. Thea Klaeboe Åarrestad, a particle physicist at ETH Zurich, said the detectors at the Large Hadron Collider throw away 99.98 percent of the data they collect. That may seem wasteful, but strikes a balance. To save more would require more power cables and readout circuitry, which would get in the way of the very particles they are trying to measure. “We physically can’t read out all of the data,” she said.

In general, whenever A.I. interfaces with the physical world, it faces the same constraints we humans do. “There’s going to be this natural brake on the progress of A.I.,” said David Silver, a computer scientist at Google DeepMind and University College London and recipient of the 2019 ACM Prize in Computing. Silver has argued that A.I. has entered an “era of experience” in which it learns more from its own exploration than from ingesting human knowledge. But exploring means tolerating failure, and we can’t always do that. “If it’s too unsafe to explore, well, OK, maybe it’s not something [on which] we’re ready to go beyond human knowledge,” he said.

The panelists enthused over how A.I. helps them, for example, to decide which 99.98 percent of data the LHC detectors should throw away. “We know there has to be physics beyond the Standard Model somewhere,” Åarrestad said. “Could it be there? That’s what keeps me up at night.” A.I. also creates surrogate models – models of models that are trained on full-up simulations and can mimic their output much faster. Not only physicists but also cosmologists, neuroscientists, economists, and climate scientists are making use of these surrogates. They pick up on patterns in the underlying dynamics and, in a sense, express higher-order laws of nature. “It does seem to me to be reasonably fair to describe these neural networks as encapsulating a new model of science,” Silver said.

As for hiring and promotion, the physics panelists also painted a positive picture. “We’re not yet seeing the job displacement,” Cranmer said. If anything, he said, A.I. has brought new investment into his field.

For all its risks, the emerging human-machine partnership is making progress on the great mathematics and science questions of our time. “Anyone who is a mathematician or a scientist should be just so excited to be alive now, of all times,” Silver said. “We are alive now when the greatest changes are going to happen and biggest discoveries, the most advances, are going to happen.”

The post When AI Can Do It All, What Will Be Left for Human Mathematicians and Scientists? originally appeared on the HLFF SciLogs blog.