Problem Hunting with LLMs
This website documents attempts by advanced large language models (LLMs) to solve Erdős problems and other major open problems in mathematics, theoretical computer science, and economics.
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Acknowledgments
- Paata Ivanisvili - For the initial idea for MathOverflow problems
- Terry Tao - For the Erdos Problems database
- Thomas Bloom - For the erdosproblems.com website
- Ulam AI and the UnsolvedMath Contributors - For the UnsolvedMath database
Problem Sources
Erdos Problems
For Erdos problems, we track problems from two key resources:
- Terry Tao's Erdos Problems Database - A collaborative database of Erdos problems with formal statements and progress tracking.
-
erdosproblems.com (by Thomas Bloom) -
For detailed problem statements, historical context, and relevant comments.
For each Erdos problem number X, the full problem statement can be found at
https://www.erdosproblems.com/X.
Top Open Problems
Initially, Top Open Problems benefited from and included problems from both
MathOverflow and
ProofAtlas.
The project later broadened its sources to the much more comprehensive
UnsolvedMath collection of approximately
15,000 open and partially solved mathematical problems by
Ulam AI, available on
Hugging Face.
We now use UnsolvedMath's problem ID and category system for imported entries and add
extended mathematical statements in .tex format and LLM attempts.
Browse the Top Open Problems catalog
for mathematical statements, references, and problem statuses.
Catalog entries without a mathematical writeup are shown without an LLM attempt.
Lean contributions use a short TeX description with an external link to the complete Lean source and original generated output. They appear alongside other attempts on the relevant problem page. The description states the formalized scope, remaining gaps, model attribution, Lean/Mathlib versions, and actual checking outcome.
OpenAI Results
The OpenAI tag identifies summaries of claimed results published in OpenAI's math repository. A solved Problem Status or LLM claim attributed to OpenAI means that the paper's stated theorem was matched to the complete question on this site. It remains OpenAI's claim and has not been independently verified here. The original source catalogue status is shown separately, and Community Review records human checking.
Special cases, weaker bounds, and results that settle only part of a question are shown as partially solved, with a partial OpenAI claim. Records include the claimed mathematical hypotheses and conclusion and link to the source manuscripts and any Lean scope and Comparator files at a fixed revision. Formalization covers only the scope described by OpenAI; this site has not run those Lean files. OpenAI cautions that results without formalization may contain errors.
Economics and the Social Sciences
Unlike in mathematics and certain areas of theoretical computer science, where major open questions—such as the Millennium Prize Problems—can be precisely formulated and their solutions may fundamentally transform their fields, economics has no comparably established set of mathematically well-defined problems whose resolution would necessarily reshape the discipline. Many of the most important open questions in economics, political science, and the social sciences more broadly are conceptual, methodological, or empirical rather than purely mathematical.
The problems listed here were ranked primarily according to the estimated difficulty of solving them, as assessed by GPT-6 Astra Pro, rather than their prominence, practical significance, or potential impact on the discipline. The ranking also gives some priority to particularly difficult problems within individual subfields.
Nevertheless, certain problems in economics could have transformative implications if resolved in the affirmative, even when such a resolution appears highly unlikely. Some of these are included in the catalogue.
Community Review Labels
Here are explanations for each community review label:
- unreviewed: no community review yet.
- submitted: a contribution is recorded, with links to its submitters. Author attribution is retained separately from review acceptance.
- flagged: not reviewed; flagging for attention.
- incorrect: contains a mistake or invalid reasoning.
- technicality: formally addresses the statement but not the intended problem.
- trivial: follows immediately from known remarks or standard results.
- partial: some nontrivial progress, but far from a full solution.
- plausible: looks promising but incomplete or unverified.
- accepted: verified correct with a citation.
- known: reproduces a known result or counterexample.
Disclaimer
Important: LLM output is not fully reliable. The attempts documented on this website represent exploratory work by frontier AI models and should not be considered verified mathematical proofs.
While only the most advanced LLMs with a proven track record of making progress on open mathematical problems are featured here, their claimed solutions are not final and require rigorous verification by human mathematicians.
For Erdos problems, LLM Claim is assigned automatically from Terry Tao's collaborative database, using this rule: open, falsifiable, or decidable means unresolved; every other status means solved. The claims in individual attempts and their community reviews are preserved separately. Problem details also show the original database status and formalization links. Completion is 100% when that database records the problem as resolved. For other problems, completion remains the LLM estimate. This automatic label does not verify any particular LLM attempt. For Top Open Problems, a "solved" LLM Claim means the model claims a solution, which still requires verification. The catalog's source status and qualifications are separate from the attempt's claim and community review.
Lean code linked here is not manually reviewed for correctness or safety. Do not run untrusted submitted Lean code locally, including through an editor's automatic checking. This website displays descriptions and links; it does not download or execute the linked Lean code. An optional Lean Web reproduction link does not certify correctness or safety. A successful check of a partial formalization does not establish that the original problem is solved.
Contributing
New research attempts, reviews, and problem proposals belong on We-Solve. Its contribution guides provide current requirements and submission availability. For an existing problem, use the Contribute link on its detail page.
Licensing and Third-Party Materials
The repository's software is licensed under the Apache License 2.0. Third-party data and source material retain their respective licences.
UnsolvedMath's curation and original metadata are licensed under
Creative Commons Attribution 4.0 International (CC BY 4.0),
with attribution to the UnsolvedMath Contributors and
Ulam AI.
Our Top Open Problems catalogue retains the imported problem IDs
and categories, and adds extended .tex statements and LLM attempts.
The UnsolvedMath data has not been relicensed under Apache-2.0.
Material referenced or incorporated by UnsolvedMath may have separate terms, including CC BY-SA 4.0 for some source material. Consult the relevant records' provenance and rights notes, the upstream dataset card, and our Third-Party Notices for attribution, licence scope, and a description of our changes.