3D animation·Sound·New proofs
Maths you can see. Equations you can hear.
Gradient Damage turns mathematics into 3D animation and sound: geometry, number theory, waves and chaos, and the 372 results OpenAI says its AI has proved. Every video is on YouTube. The explanations, papers and sources are here.
Proofs, explained
The latest write-up
Combinatorics·OpenAI MathThe Harary–Hill conjecture: why 18 dots need 1,008 crossings
Join every dot to every other dot and count where the lines cross. For more than sixty years nobody could prove that the neatest known drawings were the best possible. OpenAI says its AI now has.
Read the write-up →On YouTube
Latest videos
0:21Goldfeld's Conjecture: Half Rank 0, Half Rank 1
0:20Restricted Geometric Langlands: OpenAI Claims Characteristic p
0:22Prime Factors of p−1: OpenAI Claims the Poisson–Dirichlet Law
0:20Milne's Rationality Conjecture: OpenAI Claims a Proof
0:21Erdős–Gallai Conjecture: Every Graph Splits Into Few Loops
0:20Hypercube Ramsey Conjecture: How Many Dots Force a Cube?
0:21Erdős Conjecture on Arithmetic Progressions: OpenAI Claims a Proof
0:20Gotsman–Linial Conjecture: OpenAI Claims Sensitivity ≤ 8d√n
Playlists
Start with a series
OpenAI Math
Short visual explainers of the maths results OpenAI says its AI has proved. Each animation illustrates the statement; it is not the proof.
6 videos · Watch the series →
Visual Math & 3D Animations
Visual maths, geometry and sound brought to life in original 3D animations. Explore pi, mathematical functions, sonification and shapes in short videos from Gradient Damage.
17 videos · Watch the series →
OpenAI Math
Every result, by subject
Theoretical computer science
40 results · 1 with a video
Browse →Combinatorics
37 results · 7 with a video
Browse →Algebraic and complex geometry
36 results
Browse →Number theory
31 results · 8 with a video
Browse →Differential geometry
29 results · 3 with a video
Browse →Probability and statistical mechanics
29 results · 4 with a video
Browse →Mathematical physics
25 results · 3 with a video
Browse →Operator algebras
19 results
Browse →Algebra
18 results
Browse →Topology
18 results · 1 with a video
Browse →Partial differential equations
16 results · 2 with a video
Browse →Real and complex analysis
16 results · 3 with a video
Browse →Convex and metric geometry
15 results · 1 with a video
Browse →Group theory
14 results
Browse →Dynamical systems and ergodic theory
12 results · 2 with a video
Browse →Functional analysis
11 results
Browse →Mathematical logic
6 results
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