Real and complex analysis·OpenAI Math·Result 075·Lean formalisation listed
The L log L Fourier-convergence conjecture
One of the 372 results in OpenAI's public mathematics catalogue, filed under real and complex analysis: 1 preprint, the latest dated 23 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and embeds the animation.
In one line: OpenAI reports a proof of the L log L Fourier-convergence conjecture (real and complex analysis) in a preprint dated 23 September 2026. It has not been peer reviewed. The channel's animation, Math Makes Sounds... Then Gets Weird, is on YouTube.
What OpenAI claims
Proves that the ordinary symmetric Fourier partial sums of every complex-valued function in L log L(𝕋) converge almost everywhere along the full sequence. This resolves the classical sufficiency conjecture at the L log L scale. (Lean)
Paper
Almost-everywhere Fourier convergence in L log L
OpenAI's abstract We prove that the ordinary symmetric Fourier partial sums of every complex-valued function in L log L on the circle converge almost everywhere to the function along the full sequence. This establishes the classical L log L sufficiency conjecture.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
Quick answers
- Is it proven?
- Not independently yet. OpenAI posted a preprint on 23 September 2026; it has not been peer reviewed, so treat the result as OpenAI's claim until other mathematicians have checked it.
- What exactly does OpenAI claim?
- Proves that the ordinary symmetric Fourier partial sums of every complex-valued function in L log L(𝕋) converge almost everywhere along the full sequence. This resolves the classical sufficiency conjecture at the L log L scale. (Lean)
- Where is the proof?
- In the paper, Almost-everywhere Fourier convergence in L log L (PDF).
- Is there a video?
- Yes, on YouTube (0:12).
Also in
- Chapter 54 of 83 in Every OpenAI Math Result, Part 1 of 4: Goldfeld's Conjecture and 82 More · starts at 18:23 · watch from there on YouTube →
- Chapter 3 of 10 in Falconer Distance Conjecture, Bochner–Riesz Conjecture and 8 More · starts at 0:41 · watch from there on YouTube →
The video
Math Makes Sounds... Then Gets Weird · Short · 0:12 · description, sources and transcript →
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