Real and complex analysis·OpenAI Math·Result 078
The three-dimensional Bochner–Riesz conjecture
One of the 372 results in OpenAI's public mathematics catalogue, filed under real and complex analysis: 1 preprint, the latest dated 24 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 three-dimensional Bochner–Riesz conjecture (real and complex analysis) in a preprint dated 24 September 2026. It has not been peer reviewed. The channel's animation, Every OpenAI Math Result, Part 1 of 4: Goldfeld's Conjecture and 82 More, is on YouTube.
Chapter 55 of 83 in Every OpenAI Math Result, Part 1 of 4: Goldfeld's Conjecture and 82 More · starts at 18:45 · watch from there on YouTube →
What OpenAI claims
Resolves the three-dimensional Bochner–Riesz conjecture in its strict range: the Bochner–Riesz multipliers of order δ are bounded on Lp(ℝ3) for every 1 ≤ p ≤ ∞ whenever δ > max {3|1/p-1/2|-1/2,0}.
Paper
Bochner–Riesz multipliers in three dimensions
OpenAI's abstract We prove the three-dimensional Bochner–Riesz conjecture in its strict-order formulation. The main result is boundedness of the Bochner–Riesz multipliers on L3(ℝ3) for every positive order. Interpolation and duality then give the full conjectured strict range.
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 OpenAI posted a preprint on 24 September 2026; it has not been peer reviewed, so treat the result as OpenAI's claim until other mathematicians have checked it.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?
- Resolves the three-dimensional Bochner–Riesz conjecture in its strict range: the Bochner–Riesz multipliers of order δ are bounded on Lp(ℝ3) for every 1 ≤ p ≤ ∞ whenever δ > max {3|1/p-1/2|-1/2,0}.
- Where is the proof?
- In the paper, Bochner–Riesz multipliers in three dimensions (PDF).
- Is there a video?
- Yes, on YouTube (28:48, chapter 55).
Also in
- Chapter 4 of 10 in Falconer Distance Conjecture, Bochner–Riesz Conjecture and 8 More · starts at 1:03 · watch from there on YouTube →
The video
Every OpenAI Math Result, Part 1 of 4: Goldfeld's Conjecture and 82 More · Compilation · 28:48 · chapter 55 from 18:45 · description, sources and chapters →
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