Will Mathematics Become a "Conservatory" Art?

By Mike McCoy | September 6, 2026

In a single week, two major events collided: Claude successfully formalized the proof of $\text{Fermat's Last Theorem}$ using Lean, and a new preprint titled The Spherical Hadwiger Theorem arrived in my inbox.

The Spherical Hadwiger Conjecture Spherical Hadwiger Theorem—a specialized but vital piece of integral-geometric machinery—has remained an unsolved puzzle since roughly 1974. While I won't dive into the technical weeds here, this result significantly streamlines a specific lemma I struggled with during my graduate studies.

The AI Co-Author

The preprint, authored by Wang & Wu of Hunan University, claims to have solved the conjecture with the help of artificial intelligence. The authors included a specific disclosure regarding their process:

"During the preparation of this manuscript, OpenAI Codex was used to assist with developing proof details, identifying gaps and points requiring clarification, organizing and typesetting the manuscript, and editing the English. The authors reviewed and verified all AI-assisted mathematical content and suggested changes, made all final mathematical and editorial decisions, and take full responsibility for the manuscript."

This admission is profound. It suggests that Codex may have performed tasks previously reserved for expert researchers:

• Filling in rigorous proof details.
• Spotting logical gaps.
• Structuring the final academic narrative.

The resulting paper is exceptionally polished. While I haven't performed a line-by-line verification, I reviewed it with Claude Fable, and it certainly passes the "sniff test." It is a high-quality piece of work that adheres to the ethical guidelines of the Leiden Declaration.

The AI Workflow

A Personal and Professional Milestone

This proof is personally significant. I attempted to tackle it in grad school and tried again, albeit half-heartedly, using AI earlier this year.

When GPT-4 was first released, OpenAI published a report on labor displacement. Interestingly, mathematicians were flagged as having the highest "exposure" to AI disruption of any group studied.

It might seem arrogant to suggest that the delay in AI's total dominance of math was due to the sheer difficulty of the field. In reality, it is more likely that research mathematics simply lacks the massive training datasets and immediate economic incentives found in other creative industries.

The "Conservatory" Analogy

Consider the fate of classical music. Our society no longer supports it as a primary popular medium; instead, it has been moved to the conservatory. It is treated as a preserved relic—a specialized skill that a small group of people decides is worth maintaining through limited capital and institutional training.

Perhaps mathematics is following a similar trajectory. In the era of Euclid, math was an intellectual pursuit for the few. Today, pure mathematics already exists in its own version of a conservatory: the academy. Outside of university walls, professional opportunities for pure mathematicians are scarce.

If the "hard" work of proving theorems is soon outsourced to silicon, does the human element still matter?

The Verification Checklist

• Initial read-through
• "Sniff test" with Claude
• Full rigorous verification (Pending energy/time)

The Bottom Line

We must decide if the cultural act of "doing mathematics" is worth preserving. Pure math is more than just a set of results; it is a way of storytelling that allows us to perceive the hidden architecture of existence:

$\text{Parallel lines} \implies \text{Never intersect}$ $\text{Sphere} \implies \text{Isotropic symmetry}$ $\text{Primes} \implies \text{Infinite sequence}$

However, our current incentive structures—tenure, funding, and fame—are built for a world where human intellectual labor is the sole engine of discovery. When intelligence is limited only by electricity and chips, we face a critical question:

Will we continue to value a culture that includes human mathematicians?

---

Footnotes & Reflections

• On the Conjecture: Prof. Rolf Schneider noted that the conjecture was still officially open when I wrote my previous blog post.
• On the Proof: The approach mirrors Klain and Rota's Euclidean theorem, but the "obstructions" are significant. I wonder exactly how much of the heavy lifting was done by GPT-5/6.
• Reference: See Problem 3 in Glasauer's thesis for further context.

def future_of_math(human_input, ai_capability):
    if ai_capability > human_input:
        return "Shift to Conservatory Model"
    return "Traditional Academic Model"

print(future_of_math("Intuition", "Infinite Compute"))