I solved 6 open Erdős problems in 5 days, using @OpenAI 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 🧵
@Qiaoqiao2001 claims GPT-5.6 solved six open Erdős math problems
The Codex-style prompting workflow requires no deep mathematical expertise
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Prompts replace deep expertise
The workflow spells out problem boundaries, weaker results to avoid, and trap cases up front, then runs multi-hour searches that hunt counterexamples before drafting proofs.
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Independent checks still pending
The researcher lists prior success on one Erdős problem and shares Lean files plus LaTeX sources, yet no formal verifications or database updates have appeared so far.
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Positive users praise GPT-5.6 for solving six open Erdős problems in five days as an impressive breakthrough toward the singularity, while negative users dismiss the claims as unverified or not genuine solutions.
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You know what's cooler than solving 1 Erdos problem?
I solved 6 open Erdős problems in 5 days, using @OpenAI 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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Math is over dawg
I solved 6 open Erdős problems in 5 days, using @OpenAI 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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I solved 6 open Erdős problems in 5 days, using @OpenAI 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 🧵
the floodgates opened today we will be drowning in proofs once we have GPT-6
I solved 6 open Erdős problems in 5 days, using @OpenAI 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 🧵
A single researcher solved 6 open Erdős problems in 5 days using GPT-5.6 Sol. He attempted 13 problems in total, so the success rate sits near 46%. He wrote the prompt almost as a contract, not a question. It restated the problem, then spelled out what a finished proof must actually establish. listed the weaker results that would not count, so near-misses could not sneak through. Known traps and edge cases went in before the model ever started thinking. Then he told it how to search, which is where most people stop. Chase many approaches at once, keep incompatible ones alive, and never commit early. Hunt for counterexamples to your own lemmas, and kill a route that only leads to another open problem. Separate adversarial agents then tried to break every draft that survived. None of this works without the right target, so he picked problems mathematicians already argue about, avoiding anything welded to a famous conjecture. Codex held the whole search in memory for hours while that loop ran itself.
I solved 6 open Erdős problems in 5 days, using @OpenAI 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 🧵
The models are increasingly good at Erdos problems, but some experts like @Qiaoqiao2001 seem to have exceptional skill at prompting We sponsored him to see how far he could go He solved six this week, including one that had been studied by Terence Tao Here’s how he did it:
I solved 6 open Erdős problems in 5 days, using @OpenAI 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 🧵
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 argument.
I have published the materials here: https://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 formalization of the others is ongoing.
takeoff eh
Huge thanks to @DavideCrapis, @MarroSamuele, and @Marcello_AI for the initial idea of using AI to work on Erdős problems; to Shurui Liu at @Stanford and @HantaoYu_Theory at @Columbia for exchanging experiences and lessons from our earlier attempts; and to my PhD advisor, @ciamac at @Columbia_Biz for many helpful discussions. And huge thanks to @paradigm and @danrobinson for sponsoring the project and making these long compute runs possible.
The six problems were: • 390: https://www.erdosproblems.com/forum/thread/390/proof-claims • 486: https://www.erdosproblems.com/forum/thread/486/proof-claims • 536: https://www.erdosproblems.com/forum/thread/536/proof-claims • 788: https://www.erdosproblems.com/forum/thread/788/proof-claims • 1002: https://www.erdosproblems.com/forum/thread/1002/proof-claims • 1038: https://www.erdosproblems.com/forum/thread/1038/proof-claims I attempted around 13 problems in total, for a roughly 46% success rate.
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 gaps.
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 conjectures.
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.
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 unproved statement of comparable strength. The prompts I used for each problem are in the GitHub repository linked below. To try this yourself, give GPT the problem together with a few of my successful prompts, and ask it to generate a new problem-specific prompt in the same style. Then verify that it preserves the original statement exactly.
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 problems produced a solution in around 6 hours. Others ran for roughly 32 hours before reaching a final answer.
@thedrchronos @Qiaoqiao2001 @OpenAI why are you so bitter you poughkeepsie ass nigga?
@Qiaoqiao2001 @suekuer1 @OpenAI "Pass AI verification"? Sorry but Lean is the tool to verify. I think your AI has just gaslighted you.
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The second secret is in prompt construction. I used a prompt inspired by the one OpenAI used to solve the cycle double cover conjecture: https://cdn.openai.com/pdf/04d1d1e4-bc75-476a-97cf-49055cd98d31/cdc_prompt.pdf The key was to make the prompt define exactly what counts as solving the problem.