Math Makes Sounds... Then Gets Weird

About this video

Math functions make sounds: one sine wave builds into a buzzing voice as odd Fourier harmonics join in. The 3D waveform and original synthesized audio use the same harmonic structure.

The mathematical topic is the L log L Fourier-convergence conjecture. OpenAI, ChatGPT's creator, reports almost-everywhere convergence of ordinary symmetric Fourier partial sums for L log L functions. The finite square-wave example shown here is classical and illustrates the subject; it does not demonstrate the new proof.

Source manuscripts:
Almost-everywhere Fourier convergence in L log L
github.com/openai/math/blob/main/preprints/Almost-everywhere-…

Formalization scope:
github.com/openai/math/blob/main/lean/docs/075.md

Classical Fourier partial sums with 1, 2, 4, 8, 16 and 32 odd harmonics. The summed ordinate is plotted around a circle to show the periodic domain; selected component rings have editorial positions and scales. The audio uses the same harmonic weights. Camera speed and visible phase are slowed for legibility. The finite example illustrates the topic; it is not a proof of the reported general L log L convergence theorem.

Sound and visuals: original code-generated synthesis and Three.js animation. No third-party samples or compositions. Native 2160x3840 at 60 fps.

Source-reported research result, not independently proof-audited in this production. The public ChatGPT product is not claimed to have proved it.
Corrections and withdrawals: github.com/openai/math/blob/main/history.md