Short··0:12·Differential geometry
OpenAI's New Math Result: Sphere, Tube or Slab?
Watch on YouTubeAbout the problem →
About this video
OpenAI reports a result for the isoperimetric conjecture in the cubic flat three-torus. This 3D animation shows the sphere, tube and slab configurations.
An original 3D visualization of "The Isoperimetric Conjecture for the Cubic Flat Three-Torus", a manuscript in OpenAI's October 2026 mathematics release.
Opposite cube faces are connected. A region can leave through one face and reappear through the other. As volume changes, the reported minimum-boundary regions are spheres, circular tubes and slabs.
Gold is the physical boundary. Blue hatching marks cuts through the displayed cell, not physical end caps. Brief morphs between shapes are illustrative, not a fluid simulation or an exact sequence of minimizers.
Paper:
github.com/openai/math/blob/main/preprints/The-Isoperimetric-…
Release announcement:
openai.com/index/sharing-ai-progress-in-mathematics/
Formalization scope:
github.com/openai/math/blob/main/lean/docs/354.md
This visualizes the reported result. We have not independently audited the full proof or executed its Lean formalization. Verification stages vary across OpenAI's repository. The reference to ChatGPT means its creators, OpenAI, not a claim that the consumer ChatGPT app produced this proof.
Original Blender render and synthesized music. No borrowed soundtrack or recordings.
About the problem
Differential geometry·OpenAI Math·Result 354
The isoperimetric profile of the cubic three-torus
Determines the isoperimetric profile of the unit cubic flat three-torus and classifies every finite-perimeter minimizer: balls, circular tubes around shortest closed geodesics, coordinate slabs, and their complements. The transition volumes are 4π/81 and 1/π, with exactly the adjacent two types minimizing at each transition. (Lean)
Topics
cubic flat three torusisoperimetric conjectureOpenAI mathematicsChatGPTgeometry3D mathBlender
