AI Is Getting Good at Math. Here’s Why.

In recent months large language models have shown an unexpected knack for tackling open mathematical problems. In May, an internal OpenAI model produced a counterexample to Erdős’s unit‑distance conjecture, a challenge that had remained unsolved since 1946. A month later the same organization announced a proof of the double‑cycle covering problem, and in July presented solutions to ten additional questions. In September the model generated a proof related to the Navier‑Stokes equations. Other labs, such as Anthropic, have also formalized classic results like Fermat’s last theorem and pushed the boundaries of the Riemann hypothesis.

The article’s authors examine why these tasks appear “tractable” for LLMs. They suggest that a problem’s difficulty can be measured by the shortest chain of ideas or “hints” needed to reach a solution, combined with the effort required to develop each hint. Humans tend to skim many directions before committing resources, whereas AI models can devote vast amounts of compute to a single path, following a depth‑first search strategy. This difference allows AI to dramatically shorten the interval between generating a hint and fleshing it out, spending less “human time” on trial and error.

Understanding this new mode of search is important because it signals the kinds of problems where AI can outpace traditional researchers, potentially accelerating progress in fields where conceptual complexity has historically been a barrier.

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