I solved 6 open Erdős problems in 5 days, using GPT-5.6 Sol.
I have a math background, but the Codex workflow I used does not require deep mathematical knowledge.
Here’s exactly how I approached it, including my prompts 
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The six problems were:
• 390: erdosproblems.com/forum/thread/3
• 486: erdosproblems.com/forum/thread/4
• 536: erdosproblems.com/forum/thread/5
• 788: erdosproblems.com/forum/thread/7
• 1002: erdosproblems.com/forum/thread/1
• 1038: erdosproblems.com/forum/thread/1
I attempted around 13 problems in total, for a roughly 46%
The first secret is in problem selection.
I focused on problems mathematicians already cared about, especially ones actively discussed by people like Terence Tao.
I then used AI to filter out problems that seemed extremely difficult or were closely tied to major open
The second secret is in prompt construction.
I used a prompt inspired by the one OpenAI used to solve the cycle double cover conjecture: cdn.openai.com/pdf/04d1d1e4-b
The key was to make the prompt define exactly what counts as solving the problem.
Each prompt:
• restates the problem precisely,
• specifies what a complete proof or disproof must establish,
• lists weaker results that do not count,
• identifies problem-specific traps and edge cases,
• requires independent adversarial agents to challenge every candidate
The prompt also tells the system how to manage the search:
• start with many independent approaches,
• keep several incompatible routes alive,
• search aggressively for counterexamples to proposed lemmas,
• mark a route as blocked if it only reduces the problem to another
The third secret is model selection.
I used GPT-5.6 Sol with Ultra reasoning effort. Compared with earlier models, it was effective across a much wider range of problems and much better at sustaining long, rigorous mathematical searches.
I then pasted the prompt into Codex, set it as the goal, and let it run. The reason is that Codex can work for long periods, retain the full research context, and use local files with no further interaction needed.
You need to be patient and give it enough time to explore.
Some
The process was a continual research loop:
attempt → failure → diagnosis → new approach → proof draft → adversarial audit → repair
The model repeatedly abandoned broken ideas, attacked its own arguments, and strengthened the proof until it could no longer find substantive
I have published the materials here: github.com/ShouqiaoW/erdos
The repository includes the proof PDFs, LaTeX source files, and prompts used for each problem.
Some problems also include Python files for computational experiments. Two already have Lean formalizations, and
Huge thanks to , , and for the initial idea of using AI to work on Erdős problems; to Shurui Liu at and at for exchanging experiences and lessons from our earlier attempts; and to my PhD advisor,
Two problems already have complete Lean formalizations, posted and verified correct. Key lemmas for the other four are also formalized in Lean and pass AI verification. I can’t claim full rigor on the remaining proofs yet, but I’ll finish all Lean proofs soon.
Great, maybe solving physics next?
Fable is already testing in simulations various candidates for deeper Lagrangian - effectively described close to Standard Model + gravity, e.g. to reduce from ~30 to ~3 parameters:
github.com/openwave-labs/
Consider creating a Codex skill for this based on what you've learned, I think it would be useful to others.
Mathematicians spent 40 years on these. Bro needed 5 days and a good prompt 
I would guess that there are more than enough papers written as puzzles to solve these but nobody had the capacity to go through them all.
Which makes the AI very valuable
6 erdős claims need independent proof checking before the codex workflow means much
Maybe solving physics now?
Just needs finding a compact deeper Lagrangian, which would be effectively described close to this huge of Standard Model + gravity.
Reducing number of parameters from ~30 to a few.
Fable-based environment already in search: github.com/openwave-labs/
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