What is this?
A public catalogue of 719 mathematical manuscripts grouped into 372 families, written by an internal OpenAI model during evaluations on open research problems. About 42% of top-line results already have Lean formalizations.
A public catalogue of 719 mathematical manuscripts grouped into 372 families, written by an internal OpenAI model during evaluations on open research problems. About 42% of top-line results already have Lean formalizations.Is this a tool I install, or a set of documents?Documents rather than a software product: the preprints/ directory holds PDFs and source files with per-paper citation and build instructions, alongside a Lean library of formal proofs linked to the manuscripts.
Documents rather than a software product: the preprints/ directory holds PDFs and source files with per-paper citation and build instructions, alongside a Lean library of formal proofs linked to the manuscripts.How do I find my way around the collection?Open the overview for descriptions of the families, then use the manuscript map to find individual papers; the formalization catalogue lists the available Lean proofs and their verification configurations.
Open the overview for descriptions of the families, then use the manuscript map to find individual papers; the formalization catalogue lists the available Lean proofs and their verification configurations.Can I trust every proof in here?No — results sit at different stages of verification and not all have Lean formalizations yet; the authors warn that some unformalized results could have issues and will fix such problems quickly.
No — results sit at different stages of verification and not all have Lean formalizations yet; the authors warn that some unformalized results could have issues and will fix such problems quickly.How were these results actually produced?Almost all followed one fixed procedure: an unreleased internal OpenAI model was posed roughly 4,000 problems, with each result taking on average three hours of ChatGPT Pro thinking compute. Outputs were then aggregated into families and manuscripts that met a significance bar. A handful, including a zero-free region for the Riemann zeta function and the Hodge Conjecture for CM abelian varieties, deviated from this procedure.
Almost all followed one fixed procedure: an unreleased internal OpenAI model was posed roughly 4,000 problems, with each result taking on average three hours of ChatGPT Pro thinking compute. Outputs were then aggregated into families and manuscripts that met a significance bar. A handful, including a zero-free region for the Riemann zeta function and the Hodge Conjecture for CM abelian varieties, deviated from this procedure.Which results come with the model's reasoning summaries?Abridged reasoning summaries are published for ten families, among them the irrationality exponent of pi, the symmetric and general Mahler conjectures, quasipolynomial bounds for arithmetic progressions, Kaplansky's direct-finiteness conjecture in characteristic two, and the three-dimensional relativistic Vlasov-Maxwell system.
Abridged reasoning summaries are published for ten families, among them the irrationality exponent of pi, the symmetric and general Mahler conjectures, quasipolynomial bounds for arithmetic progressions, Kaplansky's direct-finiteness conjecture in characteristic two, and the three-dimensional relativistic Vlasov-Maxwell system.What areas of mathematics does it cover?Each family is classified by mathematical discipline, and the overview describes them all. The published summaries alone range across analytic number theory, statistical physics, quantum many-body theory, operator algebras, complexity theory, and relativistic field equations.
Each family is classified by mathematical discipline, and the overview describes them all. The published summaries alone range across analytic number theory, statistical physics, quantum many-body theory, operator algebras, complexity theory, and relativistic field equations.Will the collection keep changing?Yes. Lean formalizations will keep being added as they are obtained, and the release history is preserved: corrections and revisions become new versions while earlier versions stay accessible. The team is also exploring community-hosted repositories for these materials.
Yes. Lean formalizations will keep being added as they are obtained, and the release history is preserved: corrections and revisions become new versions while earlier versions stay accessible. The team is also exploring community-hosted repositories for these materials.What are similar projects?NavierStokesAndEuler, gpt-3, fermats-last-theorem, awesome-rsi, gpt-2, Engram, MSA, bdh
NavierStokesAndEuler, gpt-3, fermats-last-theorem, awesome-rsi, gpt-2, Engram, MSA, bdhWhich topics is it in?lean, theorem-proving, research-tools, science, math, reasoning, mathematics, catalog, papers, paper, dataset, gpt
lean, theorem-proving, research-tools, science, math, reasoning, mathematics, catalog, papers, paper, dataset, gpt