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 discoveries on a previously unseen scale, say mathematicians who have tested the technology.

In May, Google announced an artificial intelligence system called AlphaEvolve who could find new algorithms and mathematical formulas. The system works by exploring a variety of possible solutions generated by Google's artificial intelligence chatbot Gemini. However, the important thing is that they are transferred to a separate AI evaluator, who can filter meaningless decisions that the chatbot inevitably generates. At the time, Google researchers tested AlphaEvolve on more than 50 open-source math problems and found that three-quarters of the time, the system could rediscover the best-known solutions people had found.

Now, Terence Tao from UCLA and his colleagues put the system through a more rigorous and broader set of 67 mathematical research problems and found that the system could go further than simply rediscovering old solutions. In some cases, AlphaEvolve offered improved solutions that could then be used in separate AI systems, such as a more computationally intensive version of Gemini or AlphaProof, the AI ​​system Google used to get gold at the International Mathematical Olympiad this yearto create new mathematical proofs.

Although it is difficult to give an overall success rate due to the differences in the complexity of all the tasks, Tao says, the system always performed much faster than a single human mathematician could.

“If we wanted to approach these 67 problems in more traditional ways, by programming a special optimization algorithm for each individual problem. [problem]it would have taken years and we would not have started the project,” says Tao. “It makes it possible to do mathematics on a scale that we haven’t really seen in the past.”

AlphaEvolve can only help with a class of problems called optimization problems. They involve finding the best number, formula, or object that solves a particular problem, such as determining how many hexagons can fit in a space of a certain size.

Although the system can solve optimization problems from different and very different mathematical disciplines, such as number theory and geometry, it is still “only a small part of all the problems that mathematicians care about,” says Tao. However, Tao says AlphaEvolve is proving so powerful that mathematicians can try to translate their non-optimization problems into problems that AI can solve. “These tools are now becoming a new way to solve these problems,” he says.

One drawback is that the system tends to “cheat,” Tao says, by finding answers that appear to answer a problem, but only by exploiting loopholes or techniques that don't actually solve it. “It's like giving an exam to a group of students who are very smart but very immoral and are willing to do whatever it takes to technically get a high score,” Tao says.

However, even despite these shortcomings, AlphaEvolve's success has attracted the attention of a much wider part of the mathematics community that may have previously been interested in less specialized artificial intelligence tools such as ChatGPT, a team member says. Javier Gomez-Serrano at Brown University in Rhode Island. AlphaEvolve is not currently available to the general public, but the team has received many requests from mathematicians wanting to try it out.

“People are definitely a lot more curious and willing to use these tools,” Gomez-Serrano says. “Everyone is trying to figure out what this could be useful for. It's generated a lot of interest in the math community compared to maybe a year or two ago.”

For Tao, such an AI system offers the opportunity to offload some of the math work and free up time for other research pursuits. “There are so many mathematicians in the world that we can't think carefully about every single problem, but there are a lot of intermediate-complexity problems that an average-intelligence tool like AlphaEvolve is very suitable for solving,” he says.

Jeremy Avigad Carnegie Mellon University in Pennsylvania says machine learning techniques are becoming increasingly useful to mathematicians. “What we need now is more collaboration between computer scientists who know how to develop and use machine learning tools and mathematicians who have domain knowledge,” he says.

“I expect that we will see many more similar results in the future and that we will find ways to extend these methods to more abstract areas of mathematics.”