AI now seems to be helping mathematicians produce novel and useful research with regularity.
In a significant milestone for AI-assisted mathematics, Google DeepMind has announced that a specialized version of its Gemini model has helped prove a novel theorem in algebraic geometry, earning remarkable praise from one of the field’s most prominent figures.
Professor Ravi Vakil, a mathematician at Stanford University and president of the American Mathematical Society, described the AI’s contribution as “the kind of insight I would have been proud to produce myself.” The research, detailed in a paper titled “The motivic class of the space of genus 0 maps to the flag variety,” represents a collaboration between Google DeepMind researchers and Professors Jim Bryan, Balazs Elek, and Vakil.
According to Adam Brown, a scientist at Google DeepMind who announced the breakthrough, the team integrated Gemini into various stages of the mathematical project to test its effectiveness. While the AI proved useful for routine tasks like identifying connections to cross-disciplinary papers and writing data-generation code, Vakil noted that “the most striking experience was how it propelled the project forward intellectually.”
The pivotal moment came when the team asked Gemini to verify a result they expected to be true. “While its outputs generally required substantial human oversight to distinguish valid insights from errors, this specific proof was rigorous, correct, and elegant,” Vakil explained. The AI’s exposition revealed a latent structure the mathematicians hadn’t previously foreseen, suggesting the result held in a much more general setting and ultimately leading to the team’s final result.
Crucially, Vakil emphasized that Gemini’s contribution wasn’t simply repackaging existing proofs. “As someone familiar with the literature, I found that Gemini’s argument was no mere repackaging of existing proofs: it was the kind of insight I would have been proud to produce myself,” he wrote. “While I might have eventually reached this conclusion on my own, I cannot say so with certainty.”
The breakthrough adds to a growing body of evidence that AI systems are making meaningful contributions to mathematical research. Earlier instances include Robinhood CEO Vlad Tenev’s math AI startup claiming to solve a 30-year-old Erdős problem, and reports that GPT-5.2 and Harmonic autonomously solved another previously unsolved Erdős problem.
These developments align with predictions from tech leaders about AI’s mathematical capabilities. Former Google CEO Eric Schmidt suggested in late 2024 that AI could create superhuman mathematicians and coders within one to two years.
Vakil’s reflection on the collaboration captures both the promise and the nature of human-AI partnership in advanced mathematics: “My primary takeaway is how meaningful mathematical progress emerged from this genuine synergy between human ingenuity and Gemini’s contributions.” The work was conducted by DeepMind’s Professor Freddie Manners and researcher G. Salafatinos, hosted by the company’s Blueshift team. And as AI systems continue to demonstrate their ability to contribute original insights to cutting-edge mathematical research, the field appears to be entering a new era where the boundaries between human and machine creativity in mathematics are becoming increasingly blurred—not through replacement, but through collaboration.