Mathematicians say Google’s AI tools are supercharging their research

AI tools developed by Google DeepMind are surprisingly effective at assisting mathematical research and could usher in a wave of AI-powered mathematical discovery at a previously unseen scale, say mathematicians who have tested the technology.

In May, Google announced an AI system called AlphaEvolve that could find new algorithms and mathematical formulae. The system works by exploring many possible solutions, produced by Google’s AI chatbot Gemini. Crucially, though, these are fed to a separate AI evaluator that can filter out the nonsensical solutions that a chatbot inevitably generates. At the time, Google researchers tested AlphaEvolve on more than 50 open mathematical problems and found that, in three-quarters of cases, the system could rediscover the best-known solutions found by humans.

Now, Terence Tao at the University of California, Los Angeles, and his colleagues have put the system through a more rigorous and wider set of 67 mathematical research problems, and found that the system can go further than rediscovering old solutions. In some cases, AlphaEvolve came up with improved solutions that could then be fed into separate AI systems, such as a more computationally intensive version of Gemini, or AlphaProof, an AI system that Google used to score gold on this year’s International Mathematical Olympiad, to produce new mathematical proofs.

While it is hard to give an overall metric of success due to the variations of difficulty in all the problems, says Tao, the system was consistently much faster than a single human mathematician would have been.

“If we wanted to approach these 67 problems by more conventional means, programming a dedicated optimisation algorithm for each single [problem], that would have taken years and we would not have started the project,” says Tao. “It offers the opportunity to do mathematics at a scale that we really have not seen in the past.”

AlphaEvolve can only help with a class of problems called optimisation problems. These involve finding the best possible number, formula or object that solves a particular problem, such as working out how many hexagons it is possible to fit in a space of a certain size.

While the system can tackle optimisation problems from distinct and very different mathematical disciplines, such as number theory and geometry, these are still “only a small fraction of all the problems that mathematicians care about”, says Tao. However, Tao says that AlphaEvolve is proving so powerful that mathematicians might try to translate their non-optimisation problems into ones that the AI can solve. “These tools now become a new way to actually attack these problems,” he says.

One downside is that the system has a tendency to “cheat”, says Tao, by finding answers that appear to answer a problem, but only by using a loophole or technicality that doesn’t truly solve it. “It’s like giving an exam to a bunch of students who are very bright, but very amoral, and willing to do whatever it takes to technically achieve a high score,” says Tao.

Even with these deficits, however, AlphaEvolve’s success has attracted attention from a much-wider part of the mathematical community that may previously have been interested in less specialised AI tools like ChatGPT, says team member Javier Gómez-Serrano at Brown University in Rhode Island. AlphaEvolve isn’t currently available to the public, but the team has had many requests from mathematicians who want to try it out.

”People are definitely a lot more curious and willing to use these tools,” says Gómez-Serrano. “Everybody’s trying to figure out what it can be useful for. This has sparked a lot of interest in the mathematical community versus a situation maybe a year or two ago.”

For Tao, this kind of AI system offers a chance to offload some mathematical work and free up time for other research pursuits. “There’s only so many mathematicians in the world, we can’t think very hard about every single problem, but there’s a lot of medium difficulty problems for which a medium intelligence tool like AlphaEvolve would be very suited for,” he says.

Jeremy Avigad at Carnegie Mellon University in Pennsylvania says machine-learning techniques are increasingly useful for mathematicians. “What we need now are more collaborations between computer scientists, who know how to develop and use machine-learning tools, and mathematicians, who have domain-specific expertise,” he says.

“I expect we’ll see many more results like these in the future and that we’ll find ways to extend the methods to more abstract branches of mathematics.”