AI-Assisted Math Breakthrough: Long-Context Search and Adversarial Proof Verification Shared

Developer @FinanceYF5 shared a detailed workflow for using AI to assist in solving open mathematical problems, releasing the relevant proofs and prompts. This practice demonstrates that through proper task decomposition and model orchestration, AI can play a substantial role in complex mathematical proofs.

Confirmed

The success of this workflow relies on three core components. First is **topic selection**, where the developer prioritizes problems currently focused on by mathematicians (like Terence Tao) and uses AI to filter out those that are excessively difficult or strongly tied to major unsolved conjectures. Second is **prompt construction**, which draws inspiration from OpenAI's template used for the cycle double cover conjecture. It requires the system to first precisely define "what constitutes actually solving the problem," listing out weaker invalid results and specific pitfalls. Finally, for **model selection and execution**, the developer used GPT-5.6 Sol with Ultra reasoning effort enabled, pasting the prompt directly into Codex to let it run autonomously. Some problems yielded solutions in about 6 hours, while others took up to 32 hours.

During the proof process, the system is required to execute a rigorous **adversarial review**. It maintains multiple mutually exclusive proof paths in parallel, actively searches for counterexamples, and assigns independent adversarial Agents to attack candidate arguments. If a path merely transforms the original problem into an unproven proposition of equal difficulty, it is flagged as blocked. The system continuously questions itself in this loop until no substantive flaws can be found.

Currently, the developer has released the proof PDFs, LaTeX source files, and corresponding prompts for each problem in a public repository. Some problems include Python files for computational experiments, two of which have completed Lean formalization proofs, while the remaining formalization work is still ongoing.

Why it matters

This practice showcases the potential of large language models in handling long-range, rigorous mathematical search tasks. By combining a powerful foundational model (GPT-5.6 Sol), extended operational time (up to 32 hours), and structured adversarial review prompts, AI can autonomously complete complex logical deductions and self-corrections, offering a new automation paradigm for high-difficulty academic research.

2026-07-26 ~ 2026-07-26 · 8 related posts

• [source] He used AI to filter Erdős problems by difficulty and conjecture entanglement — FinanceYF5 · 2026-07-26
• His prompt template defined exactly what counts as a real proof — FinanceYF5 · 2026-07-26
• The prompts force adversarial review of every candidate proof — FinanceYF5 · 2026-07-26
• The workflow keeps multiple proof paths alive and blocks dead ends — FinanceYF5 · 2026-07-26
• GPT-5.6 Sol with Ultra reasoning powered the long math search — FinanceYF5 · 2026-07-26
• [source] Codex ran for up to 32 hours on some of the math problems — FinanceYF5 · 2026-07-26
• The loop makes the model attack its own proof until no flaw remains — FinanceYF5 · 2026-07-26
• [source] The repo includes proofs, prompts, Python experiments, and Lean proofs — FinanceYF5 · 2026-07-26