When I spoke with mathematician Thomas Bloom by phone, he was almost breathless describing what was happening in his field. The results were coming in so fast, he said, that things were “exponentially exploding.” Little did he know that just hours later, OpenAI would post 722 mathematical manuscripts produced by an unreleased AI model. That moment captured, in a single startling image, the strange new era mathematics has entered. AI is no longer just a tool for checking calculations or testing conjectures at the edges of research. It is now generating entire papers, sometimes by the hundreds, in a single dump. And while the sheer volume is thrilling, it also raises a deeply uncomfortable question: How is AI changing mathematical discovery, and is that change something we can actually understand and control? The answer is complicated. AI companies, locked in a race for headlines and market dominance, typically refuse to disclose their methods and training data. That secrecy, Bloom and many others fear, is beginning to erode the very thing that makes mathematics work: open, patient, human collaboration. We are being flooded with answers, but fewer and fewer people can explain why those answers are true, or what they mean for the next generation of questions.
Bloom knows this tension better than almost anyone. He runs a website that tracks progress on more than 1,000 open problems originally posed and collected by Paul Erdős, one of the most prolific mathematicians of the twentieth century. For years, the site was a quiet, collaborative space where mathematicians and enthusiasts could discuss open problems—questions whose best solutions either haven’t been found or aren’t yet known to the wider community. People would share partial ideas, ask for help, and slowly, together, push toward understanding. But lately, something had changed. Visitors were no longer just discussing. They were competing, racing to close open problems with AI-generated proofs that they often did not understand themselves. Bloom, a mathematician at the University of Manchester, found himself in an uncomfortable position: he was becoming a referee for a flood of machine-generated mathematics, trying to decide what counted as solved and what didn’t. That is not the work he signed up for. So, soon after our conversation, and before he could have known that OpenAI was about to announce its latest results, Bloom made a quiet but significant decision. He posted that he would no longer tag problems on his site as open or solved, and he closed the comments section entirely. It was a small act of resistance, a way of saying that mathematics is more than a scoreboard. It’s definitely exciting that AI can tackle so many open problems so quickly. But excitement alone is not enough. If no one can understand the answers, can we truly build on them? Can we trust them? Can we even call them discoveries?
Just two days after OpenAI’s deluge of results, a peer-reviewed study from Google DeepMind appeared, offering a very different vision of what AI-assisted mathematics could look like. The study, published in Science, described a system called AlphaProof Nexus. It had solved nine Erdős problems and made a number of other interesting mathematical advances. But what made the study remarkable was not just the results—it was the transparency. The researchers included a detailed description of how the results were obtained. Human mathematicians had vetted many of the proofs. That, Bloom said, is “quite different” from how OpenAI and Anthropic have been handling their mathematical results. The DeepMind team seemed to understand something essential: the ultimate objective of any AI for math research, as research scientist and study co-author Swarat Chaudhuri put it, should be “to advance mathematics as done by human mathematicians.” That means the machine should not be a black box that spits out incomprehensible truths. It should be a collaborator, a partner that helps human minds see further. The inside look at the system is fascinating. To tackle a collection of 353 open Erdős problems, the researchers used multiple agents powered by the Gemini language model. These agents could call on AlphaProof, an AI model specially trained to do mathematics, whenever they hit a difficult step. They also relied on Lean, mathematical software that identifies which steps remain unproven and checks the logic of their arguments. The agents shared their work with one another, circulating promising proof attempts and discarding the ones that weren’t going well. It was, in some ways, a digital version of the old collaborative ideal—machines working together, building on each other’s partial successes.
But the team also tested something simpler, and that is where the study becomes even more interesting. They took the nine problems that the full system had solved and gave them to independent Gemini agents working alone. These agents did not share attempts, did not consult AlphaProof, and had only Lean’s feedback to guide them. Remarkably, they solved all nine problems too. The simpler setup was cheaper on easy problems—it used fewer computing resources—but more expensive on the two toughest ones. The team did not establish whether the simpler setup could solve any of the problems the full system had missed. Still, the result surprised Chaudhuri. It suggests that increasingly capable language models can tackle research-level mathematics with relatively simple checking tools. You don’t always need an elaborate, multi-agent architecture. Sometimes a strong language model and a good proof checker are enough. But there is a caveat, and it’s an important one. Lean checks only the statement it is given, exactly as it is written in code. And a mathematical statement can be incorrectly translated to or from Lean code. An October 6 preprint showed why this matters. In that paper, researchers identified mismatches between parts of OpenAI’s written Navier–Stokes proof and its Lean counterpart. Those mismatches do not mean the written proof is wrong, the team was careful to note. But they do mean that a valid Lean proof does not automatically validate an AI-generated mathematics paper. There is a gap between the formal language of machines and the informal language of human mathematicians, and that gap can hide serious problems.
That is why the human vetting in the DeepMind study is so crucial. Chaudhuri emphasized that the human mathematician has to really think through the problem and set goals for the system. The machine is not working alone. It is being guided by human judgment, human intuition, human curiosity. And even when the system failed to finish a proof, its checked steps helped mathematicians focus on the remaining gaps. That is the kind of collaboration that makes sense. “Math is ultimately a human art,” Chaudhuri said. “The system enhances the human user’s insights, and the human user is able to guide the system with new ideas.” This is a vision of AI as a partner, not a replacement. It is also a vision of mathematics as something that remains deeply human, even when machines are doing the heavy lifting. The results themselves, Bloom noted, are “not really at the top level of importance.” But that almost doesn’t matter. What matters is the approach—the careful, transparent, responsible way the research was conducted. Google DeepMind, Bloom said, is “trying to be more responsible with the science,” while companies like OpenAI are using mathematics as a way to showcase their software. OpenAI’s papers and accompanying Lean proofs were entirely AI-generated, leaving it up to the mathematics community to figure out what was useful and what was useless. That is a heavy burden to place on a community that was not consulted in the first place.
The tension between these two visions of AI in mathematics is not just academic. It is already shaping the culture of the field. OpenAI has said it worked with an independent advisory group to develop best practices for sharing its AI math results. But that group has said their advice was to not test unreleased AI models on advanced mathematics—guidance the company clearly ignored. That kind of disregard breeds distrust. Bryna Kra, a mathematician at Northwestern University, said the company made some improvements in its efforts to cite past literature, and she is genuinely excited about AI’s potential to solve important problems in mathematics. But she also voiced a concern that many mathematicians share: AI models may have accessed people’s unpublished work. “We had a healthy, collaborative, sharing culture that is being destroyed,” she said. “Now, people are wary of sharing their ideas.” That is a devastating loss. Mathematics has always depended on openness, on the willingness to share unfinished thoughts and half-formed conjectures. If researchers begin to hoard their ideas out of fear that AI systems will absorb them and spit them out as “new” results, the entire enterprise will suffer. Not everyone sees it that way, of course. Andrew Turner, who studied math and physics and is now CTO of Plasma AI in New York City, thinks the technology is “making math more accessible.” He wonders why a small group of mathematicians should get to decide how we solve problems. He believes “math is becoming engineering,” and that doing mathematics with machines will allow people to “answer questions previously unfathomable.” There is something genuinely hopeful in that vision—a future where mathematical power is not confined to an elite few, but available to anyone with curiosity and access to the right tools.
A few days after Bloom shut down the competition on his website, Plasma AI announced a new website to track progress on Erdős problems. They will welcome AI results. That is the world we are moving toward, whether we like it or not. Bloom does not see mathematics as a Silicon Valley–style competition, a move-fast-and-break-things race to be first. And I agree. Mathematics is not a sprint. It is a slow, messy, deeply human process. It requires confusion and patience and the willingness to sit with a problem even when you have no idea how to solve it. It requires getting stuck, and then finding a way to get unstuck. It requires arguing with colleagues, laughing at your own mistakes, giving up in frustration, and then coming back after a cup of coffee to try again. At the end of his post announcing the changes to his website, Bloom wrote something that makes me tear up every time I read it. I hope everyone, even the most enthusiastic AI users, can find the time for this kind of work. “Be confused, be stuck, be inspired. Find a messy proof, then find a better one,” he wrote. “Get tired, get hungry, get into a flow state. Argue, laugh, give up, drink some coffee and attack it again. Be human. Let your brain be open.” That is the real promise of AI in mathematics, and also its greatest challenge. The machines can generate answers faster than we can ever understand them. But understanding is what mathematics is for. If we lose that, we lose everything. If AI can help us spend less time on tedious calculations and more time on the beautiful, frustrating, joyful work of being human, then it will have earned its place. But if it replaces that work entirely, we will have gained a thousand answers and lost the only question that really matters: what does it mean to discover something new?
