What it Means to Be a Mathematician When AI Does the Math

Artificial intelligence systems are now proving theorems and disproving conjectures at levels once reserved for elite human mathematicians, prompting a debate inside the field about what role people will play when machines can handle more of the day-to-day work of discovery [1]. The shift has accelerated rapidly. Fifty years ago, a computer settled the four-color theorem by checking 1,936 cases, a feat no human could realistically verify [1]. Today, large language models have moved beyond parroting textbook answers. In 2024, systems from Google DeepMind and OpenAI reached gold-medal status at the International Mathematical Olympiad [1]. Earlier this year, DeepMind’s Aletheia autonomously produced publishable Ph.D.-level results in arithmetic geometry, and an OpenAI system later disproved a conjecture in combinatorial geometry that top mathematicians called a milestone for independent, original reasoning [1]. A parallel advance is the pairing of LLMs with proof assistants such as Isabelle, Lean, and Rocq. These specialized languages check every logical step of a proof, but translating human-written mathematics into them—a process called formalization—has long been a bottleneck [1]. LLMs are now automating that translation. In February, the reasoning agent Gauss helped formalize Maryna Viazovska’s Fields Medal-winning solution to the 8-dimensional sphere-packing problem in days, then autonomously formalized the 24-dimensional case in two weeks [1]. Viazovska earned the medal in 2022 while at EPFL, the Swiss federal institute that enrolls over 14,000 students and has produced two Fields Medalists [6]. The capabilities have unsettled young researchers. At the 12th Heidelberg Laureate Forum in September 2025, speakers described a future of superhuman AI mathematicians that could form conjectures, search solution spaces, and verify proofs without human involvement [1]. Yang-Hui He of the London Institute for Mathematical Sciences suggested human mathematicians could become “priests to oracles” [1]. Jessica Randall, a mathematician for Google Developer Groups, said the audience felt a collective dread: “It was like a big bombshell that hit us, and we certainly started realizing AI has the potential to replace us” [1]. Not everyone shares that alarm. Carnegie Mellon mathematician Jeremy Avigad noted that some colleagues “would sell their soul for the solution to a problem” [1]. But two alternative visions are taking shape. One treats AI as a tool that serves human understanding, akin to a calculator. The other imagines human-machine teams tackling problems neither could solve alone [1]. Fields Medalist Akshay Venkatesh has urged the community to ask not just what computers can do, but what mathematics is for [1]. The debate unfolds against a backdrop of thousands of unsolved problems across disciplines from number theory to partial differential equations, some of which carry prizes such as the Millennium Prize Problems [3]. The field of AI itself was founded at a 1956 Dartmouth workshop and has cycled through periods of optimism and “AI winters” before the current boom, which was fueled by deep learning, the transformer architecture introduced in 2017, and the public release of large language models [5]. Krystal Maughan, a mathematician and computer scientist finishing her Ph.D. at the University of Vermont, recalled a pure-math camp where “we would sit with hard maths problems for half an hour and no one would say anything—everyone was just thinking” [1]. Whether that slow, communal struggle remains central to mathematics is the question the field now faces.