Mike McCoy explores what it means for mathematics as a discipline that AI systems can now formalise century-old open conjectures. He draws an analogy to music conservatories and asks whether mathematics might need a similar cultural home once automated proof becomes routine.
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The same week that an AI system formally proved Fermat's Last Theorem in Lean, a new preprint resolved the Spherical Hadwiger Conjecture, open since 1974. McCoy uses this coincidence to probe a deeper question: if automated systems can close the outstanding problems that gave research mathematics its urgency, what role does human mathematical practice play going forward?
The conservatory analogy is apt: when recordings made musical performance economically marginal, conservatories became the institutions that maintained musical culture as an art form rather than a commercial service. McCoy asks whether mathematics might undergo a similar transition — from a knowledge-production enterprise to a cultural institution that preserves and celebrates human mathematical creativity.
Key points
AI systems are now capable of formalising major open mathematical problems, including Fermat's Last Theorem, in proof assistants.
McCoy situates this against the human-authored resolution of the Spherical Hadwiger Conjecture, noting both modes coexist.
The conservatory analogy proposes that mathematics might survive as a cultural institution even if it ceases to be primarily a knowledge-production engine.
The shift raises questions about graduate education, funding, and what mathematical creativity means when machines handle verification.
The piece is exploratory rather than prescriptive, inviting reflection rather than proposing solutions.
Why it matters
As AI theorem-provers become more capable, the mathematics community faces questions other knowledge professions encountered earlier. McCoy's conservatory frame offers a more hopeful alternative to either displacement anxiety or naive dismissal — one that takes the cultural and aesthetic value of human mathematical thought seriously.