The Fall of the Theorem Economy: AI and the Crisis of Mathematical Understanding

The central crisis in modern mathematics is not that AI will solve unsolved problems, but that it will do so in a way that is unintelligible to humans. When the primary metric of success in mathematics is the production of a proven theorem—the "theorem economy"—AI can easily disrupt the field by generating correct but meaningless formal proofs that provide no cognitive elevation or conceptual insight.

The Distinction Between Official and Secret Mathematics

Mathematics is often perceived through two conflicting lenses: official math and secret math.

Official Math is the formal deduction system. It is a mechanical process of starting from axioms and deriving theorems. In this world, truth is binary and reasoning is either valid or invalid.
Secret Math is the human cognitive process. It involves the intuition, mental techniques, and conceptual frameworks that allow mathematicians to expand the territory of the official system.

Historically, these two have existed in a symbiotic relationship. Solving a difficult conjecture served as a "cryptographic proof" that a mathematician had developed a genuine conceptual innovation. However, the professional "honor code" of mathematics has long prioritized the theorem over the exposition, often dismissing the work of explaining or simplifying as the domain of "second-rate minds."

The Rise of "Mathslop" and the Failure of Autoformalization

As AI labs invest heavily in "AI for math," a new structural vulnerability has emerged. While AI can be trained to produce formal proofs in languages like Lean, there is a critical difference between a correct proof and a canonized proof.

The Canonization Gap

Canonization is the process of turning a one-off formalization into library mathematics—making it general, reusable, and coherent. Without canonization, a formal proof is merely a "vibe-coded blob" of logic.

For example, the autoformalization of Maryna Viazovska’s work on sphere packing produced a massive, 200,000-line formal proof. While technically correct, it lacked an intelligible interface, making it nearly useless for other mathematicians to build upon. This creates a divide between:

The Intelligible Layer (e.g., Mathlib): Human-curated formalizations that provide clean APIs and abstractions.
The Unintelligible Layer ("Mathslop"): A library of results known to be correct via proofs that no human has ever understood.

Harvesting the "Overhang"

AI possesses a unique advantage in harvesting what Bessis calls the "Overhang": the unrealized capital gains of past mathematical creativity.

Because the mathematical corpus is vast, many profound correspondences between unrelated topics exist but go unnoticed by humans, who can only read a fraction of the literature. LLMs, having processed the entire corpus, can spot these syntactic analogies and "front-run" human mathematicians by connecting existing dots to solve problems, without necessarily inventing new concepts.

The Risk of Demonetization

If theorem-proving remains the only official currency of the mathematical profession, researchers risk becoming "demonetized." When AI can one-shot technical lemmas or even major conjectures, the social reward for human effort vanishes.

This threat extends to education. If students use AI to bypass the struggle of problem-solving, they miss the neuroplastic elevation that comes from mathematical training. The result is a generation of students who can produce correct answers but lack the underlying conceptual vocabulary to think clearly about the world.

A New Path Forward: The Intelligence Scale

To survive this transition, the mathematical community must shift its narrative from problem-solving to comprehension.

Bessis proposes a "Mathematical Intelligence Scale" (similar to the levels of autonomous driving) to categorize AI achievements. Instead of claiming AI has "solved math" because it passed a benchmark of technical lemmas, the community should distinguish between different levels of capability: from simple theorem-proving to the far more difficult tasks of concept-building, reframing, and creating entirely new branches of mathematics.

Synthesis of Community Perspectives

Discussion among the technical community highlights several counterpoints and extensions to this thesis:

The Practicality Argument: Some argue that if AI produces theorems that lead to practical applications in science and technology, human intelligibility is a secondary concern. The value is in the result, not the understanding.
The Cognitive Advantage: Others suggest that humans will maintain an edge through visual and spatial reasoning—flipping between geometric and algebraic views—which current LLMs struggle to replicate.
The "Truth Mining" Future: There is a vision of a future where mathematics evolves into "truth mining," where the heavy lifting of proof verification is automated, leaving humans to focus exclusively on visualization, intuition, and high-level insight.