Why AI is suddenly solving math problems: deep search, verifiers, negative hints

What this is about

The Latent Space essay from October 23, 2026 asks why AI models are suddenly good at mathematics and which problems they can solve. It gives these examples: in May, an internal OpenAI model reportedly found a counterexample to Erdős' unit distance conjecture (open since 1946). According to the text, a proof of the Cycle Double Cover problem followed, then solutions to ten more open problems by July and a Navier-Stokes proof in September. Anthropic is said to have published a formalization of Fermat's Last Theorem and better bounds on the Riemann hypothesis. This is the author's analysis and theory, not a peer-reviewed study.

A model of difficulty

The author describes problem solving as a sequence of insights (hints) with work in between. Mathematician W. T. Gowers measures difficulty as the shortest sequence of hints from which experts could reconstruct a proof, modeled on Kolmogorov complexity (the length of the shortest program that produces a given output). His formula is 2^k + t, where k is the number of hints and t is the work required. The formula can only be applied in hindsight. For the unit distance question, Gowers names three hints: look for a counterexample, generalize the best known construction, and try number fields of increasing degree with prime ideals of bounded norm. Order matters, because later hints only become usable after the earlier ones.

Humans go broad, models go deep

Humans explore many directions only shallowly and discard most of them, because pursuing any one can take months. Models go deep instead: one prompt leads to one solution, and parallel agents develop many approaches. Without a checker, you'd get beautiful but false proofs. With an automatic verifier that checks finished arguments, it pays to put a lot of compute into uncertain ideas. But the verifier can only judge completed proofs, not half-formed ideas.

Failed attempts serve as "negative hints". The author sketches a system made of a drafter (writes the prompts), a solver (produces solution attempts, also using subagents) and a verifier. As an example, he quotes a Cycle Double Cover prompt: it forbids partial results for special cases, demands adversarial checking agents, and includes a line telling the model not to give up as soon as gaps are reported. How OpenAI actually proceeded is the author's conjecture.

The human side

Jacob Tsimerman, now at OpenAI, reportedly worked on the counterexample, also considered increasing degrees, and then stopped. The author points to psychology studies (Metcalfe and Wiebe): with insight problems, you lack the feeling of progress. Tsimerman sees this as a possible AI advantage: models could play "longer and in trickier terrain" without becoming overwhelmed, though that isn't yet robustly demonstrated.

What changed in 2026

• Chaining of sub-steps: intermediate results from step 1 can be used in step n, which lowers t.
• Self-verification: models spot wrong steps; OpenAI reportedly trained specifically on math verification.
• Orchestration: subagents, memory and coordination collect negative hints.

According to the author, the Navier-Stokes proof completes the work of Córdoba and Martínez-Zoroa, runs to 166 pages and took 10,000 agents and 300 billion tokens over 88 hours.

Branching factor

The author adds a branching factor b: with b plausible hints per step, there are b^k paths. Humans keep b small through taste, while AI follows almost every branch. So AI works where b^k times the compute cost is small. Cybersecurity fell early, he says, because b there is around 1–2. Gowers expects humans to keep an edge in deep, highly branching search trees. So expect good results when the conceptual leaps have already been made and only laborious math remains.

Our take

The essay offers a plausible but speculative explanatory model, and the author himself admits that assessments like the "early conclusions" are tentative. The proofs are not independently checked here. As a complement, he suggests that humans prune branches while models cut the cost of checking each one. A criticism: if only final results are published, the insights from failed attempts are lost, and according to Terence Tao, those are the real point of mathematics. In a bonus section, the author speculates that a model with data up to 1901 could discover general relativity, because it needs only a few hints.