Chinese mathematician uses large language model to refute central conjecture in algebraic geometry

Jihao Liu, an algebraic geometer at Peking University, posted a preprint on arXiv (identifier 2608.19301) reporting that a large language model succeeded in refuting the Yau-Tian-Donaldson conjecture. The conjecture, which lies at the core of K-stability theory and is linked to the existence of Calabi-Einstein metrics on Fano manifolds, has been regarded as one of the field’s most important open problems. The paper has not yet undergone peer review.

According to the report, the contribution is not a recombination of existing results or a “low-hanging fruit” that could be harvested easily. The claim is that the model generated novel mathematical methods, constructing arguments and structures that had not previously appeared in the literature. If true, this would represent a significant leap in the ability of language models to contribute original mathematical research, rather than merely assisting with phrasing or literature search.

Leroy Li highlighted a critical point on X: reproducibility. The issue is not whether a single run produced a correct outcome, but whether the same setup repeatedly yields new and valid constructions, or whether the success was a one-off event. The provenance of each step in the proof is as important as the headline result; without a complete trace of the logical chain produced by the model, the proof cannot be incorporated into the mathematical canon.

The manuscript is a preprint; comparative performance metrics were not released, the specific model used was not identified, and details of the execution protocol (prompts, temperature, number of samples) were omitted. The community will need to examine the proof step by step, replicate the process, and determine whether the model can generate further original mathematics in the same or adjacent domains. Until then, the result remains an interesting claim, not an established fact.