001–031Guide available
Number theory
Proof overviews and connections between papers are available.
Official catalogue · p. 2 ↗Guide: 003 / 004
MATHEMATICS · CLAIMS · PROOFS
A way into
the mathematics.
What does a paper claim, how does its proof unfold, and which results does it use? Explore the OpenAI math collection, one field at a time, in Japanese and English.
Browse the fieldsCreated by Masataka Iwai · The University of Osaka
EXPLORE BY FIELD
Follow the catalogue.
The 17 fields below follow the order and English headings of the official OpenAI Research Catalog. Number ranges refer to the official entries. Catalogue guides are available.
OpenAI Research Catalog ↗6 October 2026 edition · opens in a new tab
032–069Guide available
Algebraic and complex geometry
Proof overviews and connections between papers are available.
Official catalogue · p. 5 ↗Guide: 033 / 034 / 036 / 037 / 038 / 039 / 042 / 046 / 050 / 051 / 052 / 057 / 060 / 063 / 067 / 068
071–086Guide available
Real and complex analysis
Proof overviews and connections between papers are available.
Official catalogue · p. 9 ↗Guide: 074
087–101Guide available
Convex and metric geometry
Proof overviews and connections between papers are available.
Official catalogue · p. 10 ↗Guide: 087
102–142Guide available
Theoretical computer science
A proof overview and its external inputs are available.
Official catalogue · p. 12 ↗Guide: 109
143–154Planned
Dynamical systems and ergodic theory
Expositions in this field are in preparation.
155–192Guide available
Combinatorics
Proof overviews and connections between papers are available.
Official catalogue · p. 17 ↗Guide: 159 / 187
193–210Guide available
Algebra
Proof overviews and connections between papers are available.
Official catalogue · p. 21 ↗Guide: 197
211–239Planned
Probability and statistical mechanics
Expositions in this field are in preparation.
240–245Planned
Mathematical logic
Expositions in this field are in preparation.
246–259Guide available
Group theory
A proof overview and its external inputs are available.
Official catalogue · p. 27 ↗Guide: 246
260–284Planned
Mathematical physics
Expositions in this field are in preparation.
285–303Guide available
Operator algebras
Proof overviews and connections between papers are available.
Official catalogue · p. 31 ↗Guide: 285 / 287
304–321Guide available
Topology
Proof overviews and connections between papers are available.
Official catalogue · p. 33 ↗Guide: 305
322–332Guide available
Functional analysis
A proof overview and its external inputs are available.
Official catalogue · p. 35 ↗Guide: 322
333–361Guide available
Differential geometry
Proof overviews and connections between papers are available.
Official catalogue · p. 36 ↗Guide: 338 / 356 / 357
362–377Planned
Partial differential equations
Expositions in this field are in preparation.
MEET OUR GUIDE
Who is the character at the top right?
Born from ChatGPT, this character is Riefe Elm Verdier—Riefe for short. Riefe is your companion as you read the papers on this site.
The character’s backstory was also created by ChatGPT.
