1. Problem Selection
The first secret: focus on problems mathematicians already care about — especially ones actively discussed by researchers like Terence Tao — and use AI to filter out extremely difficult or tightly coupled open questions.
Erdős Problem 1 — A foundational question in combinatorial number theory concerning covering systems and congruences. Actively discussed for its connections to additive combinatorics.
Problems sourced from erdosproblems.com.
2. Prompt Construction
The second secret: a prompt that precisely defines what counts as solving the problem, identifies traps, and requires independent adversarial agents to challenge every candidate.
3. Model Selection
The third secret: using GPT‑5.6 Sol with Ultra reasoning effort for sustained rigorous mathematical search, combined with Codex for long-period context retention and autonomous file management.
GPT‑5.6 Sol — Effective across a wide range of problems and much better at sustaining long, rigorous mathematical searches than earlier models.
Codex — Can work for long periods, retain full research context, and use local files with no further interaction needed. Paste the prompt as the goal and let it run.
“You need to be patient and give it enough time to explore.” — Shouqiao Wang
The Continual Research Loop
The model repeatedly abandons broken ideas, attacks its own arguments, and strengthens the proof until no substantive issues remain.