I solved 6 open Erdős problems in 5 days, using OpenAI GPT-5.6 Sol

I solved 6 open Erdős problems in 5 days, using

• 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 openThe 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 candidateThe 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 anotherThe 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. SomeThe 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 substantiveI have published the materials here:github.com/ShouqiaoW/erdosThe 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, andHuge thanks to@DavideCrapis,@MarroSamuele, and@Marcello_AIfor the initial idea of using AI to work on Erdős problems; to Shurui Liu at@Stanfordand@HantaoYu_Theoryat@Columbiafor exchanging experiences and lessons from our earlier attempts; and to my PhD advisor,@ciamac - bro erdos died and somehow hes still assigning homework