GPT-5.6 Aids Advanced Math, Constructing Jacobian Conjecture Counterexamples
Recently, multiple users shared their hands-on experiences using the GPT-5.6 series models (including Pro and Sol versions) to assist with advanced mathematical research. Moving beyond simple text generation, large language models are demonstrating substantial auxiliary value in complex mathematical deduction and logical construction, attracting widespread community attention.
Key Details and Constructions
During their research, @burnytech documented the successful generalization of a mathematical construction using GPT-5.6 Pro, organizing the results into different families. Subsequently, users including @alexisgallagher pointed out that by combining Fable with GPT-5.6 Sol, they found a method to generate infinite families of counterexamples related to the Jacobian conjecture in C³. According to the descriptions, for every n ≥ 3, an example can be constructed where the generic fiber has exactly n points. @hsubyron also noted that they successfully constructed 9 counterexamples to the conjecture within just a few hours.
Reactions and Impact
These practical advancements surprised many observers. One author used the phrase "OK, this is now just being greedy" during a repost to describe the power of this technique. Users like @basedjensen believe that AI's ability to rapidly generate infinite counterexample families proves its high practical value in finding logical loopholes and assisting with complex mathematical deductions.
2026-07-20 ~ 2026-07-22 · 6 related posts
Primary sources
- AI in Math Research: Generating an Infinite Family of Counterexamples — basedjensen ·
- GPT-5.6 Pro used to generalize a math construction — burny_tech ·
- A GPT-assisted math thread surfaces an infinite family of counterexamples — alexisgallagher · 2026-07-20
- [source] GPT-5.6 Pro used to generalize a math construction — burny_tech · 2026-07-20
- [source] AI in Math Research: Generating an Infinite Family of Counterexamples — basedjensen · 2026-07-21
- A GPT 5.6 Sol workflow reportedly generates an infinite family of counterexamples — OwariDa · 2026-07-21
- Thread claims GPT-5.6 Sol helped build a new counterexample factory for the Jacobian conjecture — LucaAmb · 2026-07-21
- AI Assists Math Research: LLMs Help Construct Counterexamples to the Jacobian Conjecture — hsu_byron · 2026-07-22