AI models are improving at mathematical reasoning, diverging from human problem-solving patterns

In May 2024, an internal OpenAI model found a counterexample to the Erdős unit-distance conjecture, a problem open since 1946 that had eluded many experts. OpenAI followed with a proof of the Cycle Double Cover conjecture in June, then solutions to ten more open problems by July, and a proof of the Navier–Stokes existence problem in September. Anthropic separately formalized a proof of Fermat’s Last Theorem and advanced bounds on the Riemann hypothesis.

A Latent Space analysis argues that AI models solve problems using a depth-first search strategy enabled by automated verification, contrasting with human breadth-first exploration. Humans typically explore multiple promising directions shallowly and abandon most after early discouragement, constrained by months-long validation cycles. Models, by contrast, can pursue a single trajectory aggressively using test-time compute and tokens, then verify outcomes rapidly with automated checkers.

The analysis frames problem-solving as a sequence of hints or insights separated by work. Human difficulty scales with the length of the shortest hint sequence and the effort required to develop each hint. Models reduce the effective cost of exploring each hint, enabling more exhaustive depth-first traversal of the hint tree.

Automated verifiers allow models to prune completed trajectories quickly, making it rational to spend large compute on uncertain ideas. However, verifiers can only judge finished arguments, not half-developed ones, mirroring a key limitation in current systems.

The divergence in search strategy suggests a predictable pattern in which problems are tractable for models: those amenable to compute-intensive, verifier-guided exploration rather than human-like insight sequencing.