GPT-5.6 Solves Decades-Old Math Problems, Boosting Proof Capabilities

Recently, OpenAI's GPT-5.6 (or GPT-5.6 Sol) has demonstrated remarkable strength in the field of advanced mathematical proofs, consecutively cracking multiple historical problems and attracting widespread attention from both the AI community and mathematicians. The model not only generates non-trivial mathematical proofs and achieves significantly higher scores on specific benchmarks but also shows potential for accelerating derivations using parallel agents.

Solving Historical Math Problems

The most striking achievement of GPT-5.6 is solving the Erdős #119 conjecture, which had been unsolved for nearly 70 years. According to users like @SebastienBubeck and @burny_tech, prompted by Korsky, the model completed the proof in just one page using standard harmonic analysis techniques, surpassing Beck's 1991 44-page paper in the *Annals*. Additionally, as noted by @Charuru, following an OpenAI announcement, GPT-5.6 advanced a convex optimization problem, filling a 30-year gap, and the proof has been verified in the Lean formal language. @cloneofsimo also remarked that the model is solving too many decade-old problems, mentioning its mathematical results on Luce permutations. Mathematician Thomas F. Bloom (via @AlexKontorovich) stated that all the new proof claims he carefully checked hold up, considering the model highly interesting and full of "math flavor."

Benchmark Performance and Capability Comparison

In a math benchmark featuring 226 problems, GPT-5.6 demonstrated more decisive reasoning and rigorous proofs compared to its predecessor, GPT-5.5. Analysis shows GPT-5.5 earned only 27 A-grades, whereas GPT-5.6's grade distribution significantly improved. Microsoft CEO Mikhail Parakhin (@MParakhin) also evaluated its math capabilities, noting that GPT-5.6 is clearly superior to Fable (especially the Pro version) in math research, but overall it still does not reach the level of the former GPT-5.2 Pro.

Reasoning Mechanisms and Prompting Techniques

The breakout performance of GPT-5.6 has sparked discussions about its underlying mechanisms. @airkatakana questioned whether its performance is due to OpenAI providing more tokens or an inherent enhancement in the model's capabilities, pointing towards reasoning pre-training. Furthermore, users shared prompting techniques for guiding the model: when it gets stuck, asking it to find the "weakest proposition that implies the conjecture" can effectively guide it to a viable argument path. A report by @新智元 also added that the model can provide Cycle-related proofs in parallel using 64 sub-agents in less than an hour.

2026-07-18 ~ 2026-07-20 · 10 related posts