AI Solves 80-Year Math Problems as Mathematicians Face Uncertain Future

AI's Rapid Adoption Transforms Mathematical Research

AI in mathematics has reached a tipping point that few anticipated. According to recent analysis, 25% of mathematical papers published on the arXiv preprint server in August acknowledge some use of AI1

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, up from just 1% the year before. This explosive growth signals AI's transformative impact on mathematics, fundamentally changing how mathematicians approach their work and raising questions about the future of mathematicians in a field increasingly dominated by machine intelligence.

The shift represents more than incremental progress. For nearly two decades, major mathematical breakthroughs arrived every few months at most. Now, AI's unprecedented problem-solving capabilities deliver results at an unprecedented pace, leaving the mathematical community reeling from changes that seemed impossible just years ago1

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AI Cracks Decades-Old Mathematical Barriers

AI solving problems that defeated human minds for generations has moved from theoretical possibility to documented reality. In May, an OpenAI model disproved a conjecture central to the Erdős unit-distance conjecture, a problem Hungarian mathematician Paul Erdős posed in 19462

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. The deceptively simple question—how many pairs of points on a plane can be exactly one unit apart—had stumped mathematicians for 80 years. AI demonstrated that far more such pairs were possible than previously believed.

The breakthroughs continued. By August, OpenAI announced its Astra model had resolved or made substantial progress on 10 long-standing problems in mathematics and theoretical computer science2

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. Among these achievements, AI produced the first known example of a non-sofic group, a mathematical structure too complex to be approximated by any finite system. Mathematicians had searched for one for 27 years without success2

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In theoretical computer science, AI made another breakthrough involving "the permanent," a notoriously difficult mathematical function. It proved that even the most efficient arithmetic formulas for calculating it must have a certain minimum size, setting a new lower limit that mathematicians had not previously been able to prove2

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The Truth Versus Understanding Dilemma

AI's role in advancing mathematical research introduces a troubling gap between truth and understanding. Mathematical proofs are, by definition, true forever, making it impossible to unknow a result proven by AI1

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. This remains true even for proofs written in ways humans don't understand, because their veracity can be verified via the programming language Lean, which breaks proofs down into elemental logical statements that computers can mechanically check.

Terence Tao at the University of California, Los Angeles, warned that AI solving problems resembles using up a non-renewable resource—the pool of open problems. While theoretically infinite problems exist for mathematicians to work on, identifying particular problems that lead to discovering new mathematical techniques is key to mathematical research. "The indiscriminate use of powerful solution-extraction tools can achieve the immediate short-term goal of solving problems at hand, but at the cost of sustaining the ecosystem for the next wave of progress, or in understanding the progress already obtained," Tao stated in a recent social media post1

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If AI solves problems without producing new techniques, mathematicians face an existential question about their role. The ethical dilemmas extend beyond individual careers to the nature of mathematical knowledge itself.

Can Mathematicians Remain AI-Free?

Alessandro Della Corte at the University of Camerino, Italy, has established an online declaration for mathematicians to sign, committing to eschew AI in their own work. "I don't think it's ideal if all mathematicians on the planet use the same technology as an inescapable interface between themselves and their discipline," Della Corte explains. "I think it's better if a small minority, say 5 to 10%, remains AI-free, while the bulk of the community engages with the tools, hopefully critically and within academia"1

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Yet even Della Corte acknowledges the impossibility of completely ignoring AI's presence. If he encounters a useful result obtained using AI, he won't pretend it doesn't exist, provided it's presented understandably with human authorship taking responsibility. He emphasizes caring for his personal workflow to remain "AI-clean" without promoting irrational tech asceticism1

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Terence Tao suggested ringfencing certain problem classes as deserving full analysis and understanding, not merely solving. But this approach faces practical impossibility—it takes just one person, not even a professional mathematician, to solve a problem using AI, and then it has been solved by AI forever1

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The End of Mathematical Heroes

For centuries, mathematicians occupied a heroic position in society. Newton and Leibniz became Enlightenment heroes. Later came Gauss, Riemann, and Cantor, whose discoveries drove innovation and explained natural phenomena. Physicists like Einstein and Oppenheimer joined this pantheon. Turing developed mathematical foundations for modern computers. Shannon's information theory powers today's mobile phones, internet, and satellite communications2

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Now that era appears to be ending. If machines rather than geniuses like Terence Tao, the "Mozart of Math," claim credit for the biggest breakthroughs, the place of mathematicians in society will change dramatically2

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. Computer scientist Henry Yuen noted that recent AI achievements in theoretical computer science hit home in a way earlier announcements had not, affecting problems in his own field that he never expected machines to solve2

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For now, mathematicians retain some role. Their hands remain on the steering wheel, feeding AI with prompts, setting trajectories, deciding which problems to pursue, and checking outputs. But that grip is loosening2

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. What we see represents just the tip of a very large iceberg, with implications extending far beyond current capabilities.