GPE
Oil painting of a scholar at a desk with a compass and globe

Follow the proof.

Step-by-step maps of OpenAI's math papers, in plain English.
Browse the papersStart with the ETH disproof

Featured digests

Fully mapped papers. Each one took a careful model pass; the rest of the catalog is read-only until it gets its turn.All digested (5)
Theoretical computer scienceLean
The Exponential Time Hypothesis is False
Family 378 · 67 ppFor fixed kk, counts kk-CNF solutions deterministically in 2Ok(nlog⁡log⁡n/log⁡n)2^{O_k(n\log\log n/\sqrt{\log n})} time, refuting ETH
89 nodes5 novel68 sections
Theoretical computer scienceLean
Exact Derandomization of Logarithmic Space: L = RL = BPL
Family 103Deterministic logarithmic space equals randomized logarithmic space: L=RL=BPL\mathsf{L}=\mathsf{RL}=\mathsf{BPL}
164 nodes4 novel66 sections
Theoretical computer science
Integer multiplication below n log n
Family 109Multiplies nn-bit integers in deterministic time O(n(lg⁡n)1−κ)O(n(\lg n)^{1-\kappa}), κ=2−182\kappa=2^{-182}, on a multitape Turing machine
95 nodes3 novel55 sections

How a paper reads here

The source PDFs are dense and unsigned. The explorer gives each one three handles.
  • The map
    Every theorem, lemma and in-proof claim becomes a node; "uses" edges are drawn as a layered DAG with the main result on top. Click a node and its whole support lights up.
  • The node
    Each step has a name, the paper's statement, a plain-English version, why it is here, and a classification: novel, routine, or a known result with its citation.
  • Ask the paper
    A chat that only knows the map. Every claim in an answer cites a node, and clicking the citation opens that step. It will not assert anything that is not in the map.

Browse by discipline

373 result families. The count is families; the second number is how many are digested so far.
Number theory
31 families
Algebraic and complex geometry
36 families · 1 digested
Real and complex analysis
16 families
Convex and metric geometry
15 families
Theoretical computer science
41 families · 3 digested
Dynamical systems and ergodic theory
12 families
Combinatorics
37 families · 1 digested
Algebra
18 families
Probability and statistical mechanics
29 families
Mathematical logic
6 families
Group theory
14 families
Mathematical physics
25 families
Operator algebras
19 families
Topology
18 families
Functional analysis
11 families
Differential geometry
29 families
Partial differential equations
16 families