id stringlengths 34 128 | family stringlengths 3 3 | subject stringclasses 17
values | family_title stringlengths 19 102 | family_summary stringlengths 77 1.05k | title stringlengths 23 101 | note stringclasses 1
value | abstract stringlengths 80 1.12k | date stringdate 2026-09-10 00:00:00 2026-10-06 00:00:00 | latex stringlengths 18k 991k | bib stringlengths 1.39k 39.3k ⌀ | num_pages int64 6 262 | has_lean bool 2
classes | pdf_url stringlengths 131 348 | source_dir_url stringlengths 127 221 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Milnes-rationality-conjecture-for-abelian-varieties-September-23-2026 | 001 | Number theory | Milne’s rationality conjecture and algebraic specialization | Proves Milne's rationality conjecture for abelian varieties over $\overline{\mathbb Q}$ with good reduction: specialized Hodge classes pair rationally with complementary divisor products, independently of cohomology theory. Together with result 032, every specialized Hodge class is represented by a single rational alge... | Milne's rationality conjecture for abelian varieties | null | We prove Milne's rationality conjecture for abelian varieties, including residue characteristic 2. After good reduction, the pairing of a rational Hodge class with any complementary product of divisor classes on the reduction is the same rational number in every prime-to-*p* realization and in crystalline cohomology. U... | 2026-09-23 | \documentclass[11pt]{article}
\usepackage[a4paper,margin=28mm]{geometry}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{amsmath,amssymb,amsthm,mathtools}
\usepackage{microtype}
\usepackage{enumitem}
\usepackage{booktabs}
\usepackage[dvipsnames]{xcolor}
\usepackage{tikz}
\usetikzlibrary{arrows.meta,positionin... | null | 36 | false | https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Milnes-rationality-conjecture-for-abelian-varieties-September-23-2026/paper.pdf | https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Milnes-rationality-conjecture-for-abelian-varieties-September-23-2026/build |
Exact-Birch-Swinnerton-Dyer-Formula-from-Low-Selmer-Corank-October-3-2026 | 002 | Number theory | The full BSD formula from low Selmer corank | "Proves the full Birch–Swinnerton-Dyer leading-term formula for every elliptic curve over ℚ whos(...TRUNCATED) | Exact Birch–Swinnerton-Dyer Formula from Low Selmer Corank | null | "We prove the full Birch–Swinnerton-Dyer leading-term formula for every elliptic curve over ℚ wh(...TRUNCATED) | 2026-10-03 | "\\documentclass[11pt]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepacka(...TRUNCATED) | null | 94 | false | https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Exact-Birch-Swinnerton-Dyer-Formula-from-Low-Selmer-Corank-October-3-2026/exact-bsd-low-selmer-corank.pdf | https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Exact-Birch-Swinnerton-Dyer-Formula-from-Low-Selmer-Corank-October-3-2026/build |
The-Selmer-converse-for-elliptic-curves-at-every-prime-September-24-2026 | 002 | Number theory | The full BSD formula from low Selmer corank | "Proves the full Birch–Swinnerton-Dyer leading-term formula for every elliptic curve over ℚ whos(...TRUNCATED) | The Selmer converse for elliptic curves at every prime | null | "We prove the Selmer converse in coranks zero and one for every elliptic curve over ℚ and every pr(...TRUNCATED) | 2026-09-24 | "\\documentclass[11pt]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepacka(...TRUNCATED) | "@article{BertoliniDarmonPrasanna2013,\n author = {Bertolini, Massimo and Darmon, Henri and Prasann(...TRUNCATED) | 82 | false | https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-Selmer-converse-for-elliptic-curves-at-every-prime-September-24-2026/main.pdf | https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-Selmer-converse-for-elliptic-curves-at-every-prime-September-24-2026/build |
The-two-primary-Birch-Swinnerton-Dyer-formula-in-Selmer-corank-at-most-one-September-24-2026 | 002 | Number theory | The full BSD formula from low Selmer corank | "Proves the full Birch–Swinnerton-Dyer leading-term formula for every elliptic curve over ℚ whos(...TRUNCATED) | The two-primary Birch–Swinnerton-Dyer formula in Selmer corank at most one | null | "We prove the two-primary Birch and Swinnerton-Dyer leading-term formula for every elliptic curve ov(...TRUNCATED) | 2026-09-24 | "\\newcommand{\\DoNotLoadEpstopdf}{}\n\\documentclass[11pt]{article}\n\\usepackage[T1]{fontenc}\n\\u(...TRUNCATED) | null | 164 | false | https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-two-primary-Birch-Swinnerton-Dyer-formula-in-Selmer-corank-at-most-one-September-24-2026/paper.pdf | https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-two-primary-Birch-Swinnerton-Dyer-formula-in-Selmer-corank-at-most-one-September-24-2026/build |
The-Quasi-Riemann-Hypothesis-October-5-2026 | 003 | Number theory | The quasi-Riemann hypothesis | "Proves that every Dirichlet *L*-function, including $\\zeta(s)$, is zero-free in $\\Re s> 7/8$, res(...TRUNCATED) | The Quasi-Riemann Hypothesis (alternate 11/12 proof) | null | "We establish the quasi-Riemann hypothesis by proving that every Dirichlet *L*-function, including R(...TRUNCATED) | 2026-10-05 | "\\documentclass[11pt,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\(...TRUNCATED) | null | 49 | true | https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-Quasi-Riemann-Hypothesis-October-5-2026/paper2.pdf | https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-Quasi-Riemann-Hypothesis-October-5-2026/build |
The-Quasi-Riemann-Hypothesis-September-30-2026 | 003 | Number theory | The quasi-Riemann hypothesis | "Proves that every Dirichlet *L*-function, including $\\zeta(s)$, is zero-free in $\\Re s> 7/8$, res(...TRUNCATED) | The Quasi-Riemann Hypothesis: A Zero-Free Half-Plane $\Re s> 7/8$ | null | "We prove that all finite-order Hecke *L*-functions over $\\mathbb Q(\\sqrt{-3})$ and all Dirichlet (...TRUNCATED) | 2026-09-30 | "\\documentclass[11pt,a4paper]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\(...TRUNCATED) | null | 199 | true | https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-Quasi-Riemann-Hypothesis-September-30-2026/paper.pdf | https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-Quasi-Riemann-Hypothesis-September-30-2026/build |
Uniform-exclusion-of-Landau-Siegel-zeros-October-1-2026 | 003 | Number theory | The quasi-Riemann hypothesis | "Proves that every Dirichlet *L*-function, including $\\zeta(s)$, is zero-free in $\\Re s> 7/8$, res(...TRUNCATED) | Uniform exclusion of Landau–Siegel zeros | null | "We prove the uniform exclusion of Landau–Siegel zeros. There is an absolute constant *c* > 0 such(...TRUNCATED) | 2026-10-01 | "\\documentclass[11pt,a4paper]{amsart}\n\\usepackage[a4paper,margin=1in]{geometry}\n\\usepackage[T1](...TRUNCATED) | null | 9 | true | https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Uniform-exclusion-of-Landau-Siegel-zeros-October-1-2026/paper.pdf | https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Uniform-exclusion-of-Landau-Siegel-zeros-October-1-2026/build |
A-pointwise-2-converse-for-elliptic-curves-with-rational-two-torsion-September-24-2026 | 004 | Number theory | Hilbert’s tenth problem over ℚ | "Proves that no algorithm decides whether an integer-coefficient polynomial in an arbitrary number o(...TRUNCATED) | A pointwise 2-converse for elliptic curves with rational two-torsion | null | "We prove a pointwise 2-converse for elliptic curves over $\\mathbf Q$ with nonzero rational two-tor(...TRUNCATED) | 2026-09-24 | "\\documentclass[11pt]{article}\n\\pdftrailerid{}\n\\input{glyphtounicode}\n\\input{glyphtounicode-c(...TRUNCATED) | "@article{BCDT2001,\n author={Breuil, Christophe and Conrad, Brian and Diamond, Fred and Taylor, Ric(...TRUNCATED) | 91 | false | https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/A-pointwise-2-converse-for-elliptic-curves-with-rational-two-torsion-September-24-2026/paper.pdf | https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/A-pointwise-2-converse-for-elliptic-curves-with-rational-two-torsion-September-24-2026/build |
Hilberts-tenth-problem-over-the-rational-numbers-September-24-2026 | 004 | Number theory | Hilbert’s tenth problem over ℚ | "Proves that no algorithm decides whether an integer-coefficient polynomial in an arbitrary number o(...TRUNCATED) | Hilbert’s tenth problem over the rational numbers | null | "We give a negative answer to Hilbert's tenth problem over the rational numbers: no algorithm decide(...TRUNCATED) | 2026-09-24 | "\\documentclass[11pt]{article}\n\\pdfinfoomitdate=1\n\\pdftrailerid{}\n\\pdfsuppressptexinfo=15\n\\(...TRUNCATED) | "@article{SilverbergZarhin1995,\n author = {Silverberg, Alice and Zarhin, Yuri G.},\n title = {Sem(...TRUNCATED) | 62 | false | https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Hilberts-tenth-problem-over-the-rational-numbers-September-24-2026/main.pdf | https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Hilberts-tenth-problem-over-the-rational-numbers-September-24-2026/build |
Catalans-constant-is-irrational-September-24-2026 | 005 | Number theory | Irrationality of Catalan’s constant | Proves that Catalan's constant $G=\sum_{j\ge0}(-1)^j/(2j+1)^2$ is irrational. | Catalan's constant is irrational | null | We prove that Catalan's constant $G=\sum_{j\geq0}(-1)^j/(2j+1)^2$ is irrational. | 2026-09-24 | "\\documentclass[11pt]{article}\n\\usepackage[T1]{fontenc}\n\\usepackage{lmodern}\n\\usepackage[marg(...TRUNCATED) | "@article{RivoalZudilin2003,\n author = {Rivoal, Tanguy and Zudilin, Wadim},\n title = {Diophan(...TRUNCATED) | 44 | true | https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Catalans-constant-is-irrational-September-24-2026/paper.pdf | https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Catalans-constant-is-irrational-September-24-2026/build |
End of preview. Expand in Data Studio
OpenAI Math Manuscripts
This dataset is a machine-readable copy of openai/math at commit
adc7f12. That
repository holds research manuscripts produced by an internal OpenAI model.
| Config | Rows | Content |
|---|---|---|
papers (default) |
722 | Full LaTeX source of every manuscript in preprints/ (372 result families, 17 subjects, 34,815 PDF pages, ~36.4M tokens with o200k_base) |
reasoning_summaries |
10 | Abridged summaries of the model's reasoning from reasoning_traces/, transcribed to Markdown + LaTeX (~149k tokens) |
overview |
1 | LaTeX source of the catalogue overview.pdf |
from datasets import load_dataset
papers = load_dataset("ituperceptron/openai-math", "papers", split="train")
summaries = load_dataset("ituperceptron/openai-math", "reasoning_summaries", split="train")
How the text was produced
Papers: from the source, not the PDFs. Every manuscript is published with its LaTeX source
under build/. We take the root file (the one containing \begin{document}) and inline every
\input and \lstinputlisting recursively. We remove % comments, but leave verbatim and listing
environments untouched. One manuscript bundles two standalone documents with \includepdf, so its
latex field holds both documents one after the other. The text is never OCR'd, so formulas are
exactly as the authors wrote them. Bibliographies are either inline thebibliography blocks in
latex or the referenced .bib files in bib. Figures are left as TikZ code or
\includegraphics references.
Reasoning summaries: OCR with a vision model. OpenAI released 9 of the 10 summaries only as
PDFs. We sent each page (rendered at 150 dpi) together with the PDF text layer to gpt-6-sol
(OpenAI). The text layer supplies exact spelling. The image supplies structure and math, which plain
text extraction breaks: flattened sub/superscripts, Unicode italic letters, lost spaces, split
ligatures. The model was told to transcribe the page verbatim:
- prose as Markdown, with math as
$…$/$$…$$; - original-prompt excerpts and
VERBATIM EXCERPTpassages as```textblocks, copied as written; - running headers and page numbers dropped.
Page outputs were then joined, continuing paragraphs and code blocks across page breaks. A
word-level comparison with the text layer shows no dropped content. The only differences are
hyphenation and ligature fragments that the text layer had split. The Mézard–Parisi summary also
has an official LaTeX source, which is included in its latex field.
Fields
papers
| Field | Description |
|---|---|
id |
Manuscript directory name in preprints/ |
family |
Result family number (001–372); a family groups a main result with companions and alternative proofs |
subject |
Subject heading from overview.tex (e.g. Number theory, Combinatorics) |
family_title, family_summary |
Family title and description from CONTENTS.md |
title, abstract |
Manuscript title and abstract from CONTENTS.md (Markdown with $…$ math) |
note |
Annotation next to the link in CONTENTS.md (e.g. secondary writeup), otherwise null |
date |
Release date from the directory name (ISO) |
latex |
Flattened LaTeX source of the whole document, including the preamble and macros |
bib |
Contents of the .bib files referenced by \bibliography, otherwise null |
num_pages |
Page count of the published PDF |
has_lean |
Whether the family has a Lean formalization in the source repository |
pdf_url, source_dir_url |
Published PDF and source directory at the pinned commit |
reasoning_summaries
| Field | Description |
|---|---|
family, subject, title |
Result family, subject, and title from the source README |
slug |
Source file name without extension |
markdown |
Transcribed text (Markdown + LaTeX) |
latex |
Official LaTeX source when published (only mezard-parisi-formula), otherwise null |
num_pages, ocr_model, pdf_url |
PDF page count, transcription model, and source PDF |
Limitations
- OpenAI notes that some results have not been formalized and could contain errors. The text here is reproduced as published; it has not been checked.
- The
latexdocuments are flattened but not normalized. Package files, figures, and the pdfTeX-only\input glyphtounicodelines are still referenced but not included, so not every document compiles as-is. - Model transcription of the reasoning summaries can still contain small errors in math. When an
exact formula matters, check it against
pdf_url. - The
reasoning_summariesare OpenAI's abridged third-person summaries ("the assistant considered…"), not raw chains of thought.
Reproduction
The build scripts are in this repository under scripts/. Steps:
build_papers.pyclones the pinned commit without the Lean library and writes thepapersandoverviewconfigs.ocr_reasoning.pytranscribes the summary PDFs page by page and caches each page.build_reasoning.pyjoins the cached pages intoreasoning_summaries.
License
Apache License 2.0, the same as the source repository. Content © OpenAI. The reasoning-summary
transcriptions were produced with an OpenAI model (gpt-6-sol). Packaged by
ITU Perceptron.
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