tensorgami

The recent spectacle surrounding the machine resolution of Erdős Problem #728 is instructive less for what it reveals about artificial reasoning than for what it exposes about the sociology of the mathematical academy. To the working mathematician, the fanfare is structurally confounding; the conjecture was not a celebrated open problem, but a dormant artifact, a “corner case” inequality regarding factorial divisibility that remained unsolved not because it was impenetrable, but because it was largely invisible. As the technical autopsy of the proof suggests, the solution was effectively a latent corollary of the probabilistic machinery developed by Carl Pomerance in the mid-1990s. That an automated system could bridge this gap is a triumph of retrieval, not invention. It demonstrates that the problem was never “hard” in the architectural sense; it was merely unconnected.

This disconnect between the public perception of AI-generated genius and the technical reality of “lemma arbitrage” signals a looming correction in the economy of mathematical prestige. For decades, the incentive structures of the discipline have tolerated a certain species of epistemic rent-seeking: the production of literature that is technically novel but conceptually derivative. In fields with high template density, particularly specific corridors of discrete mathematics and asymptotic combinatorics, it has been possible to sustain careers by manually executing algorithms that search for corollaries of established frameworks. This is the “grift” to which critical observers allude: the industrial-scale publication of results that require the application of known machines to slightly permuted constraints.

The arrival of the artificial intelligence as a “Super-Librarian” threatens to collapse this market. If a neural network, operating on principles of high-dimensional vector interpolation, can swiftly identify that a conjecture is merely a specific instance of a general theorem residing in the library, then the human labor dedicated to such tasks is rendered obsolete. The machine effectively strips away the illusion of depth from these “orphan” problems. It proves empirically that solving them did not require a structural rupture or a paradigm shift, but merely a rigorous scan of the existing literature. The “easy” problems, which often masquerade as difficult due to their tediousness or obscurity, are thus exposed as computational exercises rather than creative acts.

Paradoxically, this automation of the trivial serves as a powerful vindication for the truly difficult. The silence of the machine in the face of nonlinear partial differential equations or the structural rigidity of the recent International Mathematical Olympiad’s “Problem 6” offers a new, objective metric for profundity. In a pre-AI world, it was often difficult for those outside a subfield to distinguish between a result that was hard because of its computational volume and a result that was hard because it required the invention of a bespoke invariant. The machine dissolves this ambiguity. If an AI cannot solve a problem, it is a certification that the problem resides outside the convex hull of current knowledge, that it requires the ex nihilo construction of a mechanism that does not exist in the training data.

We are therefore moving toward a bifurcated prestige economy. The “grift” papers, those that exist in the smooth interior of the mathematical map, will face an existential crisis as their production becomes zero-marginal-cost. Conversely, the “Bespoke” papers, those that require the architectural synthesis of new functional invariants, the design of novel energy estimates, or the forging of “Zeilberger-style” meta-algorithms, will appreciate in value. The failure of the machine to crack the core of hard analysis is not a sign of the field’s backwardness, but of its semantic density.

Ultimately, this is a salutary development for the intellectual health of the discipline. The machine is forcing mathematics to be honest about what constitutes a contribution. It is stripping away the credit formerly given to the cataloger of corollaries and concentrating it entirely on the architect of concepts. The mathematician of the future will not be judged by their ability to find the key that was left on the table, the machine will do that, but by their ability to forge the lock that no current key fits. The artificial intelligence is not destroying mathematics; it is merely automating the mediocrity out of it.

References

Gowers, Timothy. 2000. “The Two Cultures of Mathematics.” Mathematics: Frontiers and Perspectives, edited by V. Arnold et al., 65–78. Providence: American Mathematical Society.

Klainerman, Sergiu. 2000. “PDE as a Unified Subject.” Visions in Mathematics, GAFA 2000 Special Volume, Part I: 279–315.

Pomerance, Carl. 1996. “On the set of prime factors of .” Proceedings of the American Mathematical Society 124 (1): 87–102.

Tao, Terence. 2026. “Machine Assisted Proofs and the Future of Number Theory.” What’s New (blog). January 8, 2026.

Tensorgami. 2025. “Bespoke Craft vs. Framework Power: Why Nonlinear PDE Endures.” Tensorgami (blog). September 28, 2025.

Tensorgami. 2025. “Mathematics under AI: Why framework fields automate first while ‘chaotic’ fields endure.” Tensorgami (blog). September 27, 2025.

Zeilberger, Doron. 1993. “Closed Form (Pun Intended!).” Contemporary Mathematics 143: 579–607.¹