Is Bloch’s conjecture for complex surfaces 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 OpenAI posted a preprint on 24 September 2026; it has not been peer reviewed, so treat the result as OpenAI's claim until other mathematicians have checked it.

In OpenAI's preprint Bloch’s conjecture for surfaces with p_g=0 (PDF): https://github.com/openai/math/blob/main/preprints/Blochs-Conjecture-for-Surfaces-with-pg-equals-q-equals-0-September-24-2026/paper.pdf

Yes, Every OpenAI Math Result, Part 1 of 4: Goldfeld's Conjecture and 82 More on YouTube (28:48, chapter 35): https://www.youtube.com/watch?v=HqKGp54O-t0&t=710s

Algebraic and complex geometry·OpenAI Math·Result 040

Bloch’s conjecture for complex surfaces

One of the 372 results in OpenAI's public mathematics catalogue, filed under algebraic and complex geometry: 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 Bloch’s conjecture for complex surfaces (algebraic and complex geometry) 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 It has not been peer reviewed.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.

Compilation · 28:48 · 14 October 2026 · from 11:50Watch on YouTube →

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Chapter 35 of 83 in Every OpenAI Math Result, Part 1 of 4: Goldfeld's Conjecture and 82 More · starts at 11:50 · watch from there on YouTube →

What OpenAI claims

Proves Bloch's conjecture: for every smooth connected projective complex surface S with p_g(S)=0, the Albanese map CH₀(S)⁰ → Alb(S)(ℂ) on integral degree-zero zero-cycles is an isomorphism. This combines the new p_g=q=0 theorem with the classical theorem of Bloch, Kas, and Lieberman.
OpenAI, in its public catalogue of maths results

Paper

Bloch’s conjecture for surfaces with p_g=0
24 September 2026 · Preprint, not peer reviewed · PDF
OpenAI's abstract We prove Bloch's conjecture for smooth connected projective complex surfaces with p_g=0: the Albanese homomorphism on integral degree-zero zero-cycles is an isomorphism.

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?: Proves Bloch's conjecture: for every smooth connected projective complex surface S with p_g(S)=0, the Albanese map CH₀(S)⁰ → Alb(S)(ℂ) on integral degree-zero zero-cycles is an isomorphism. This combines the new p_g=q=0 theorem with the classical theorem of Bloch, Kas, and Lieberman.
Where is the proof?: In the paper, Bloch’s conjecture for surfaces with p_g=0 (PDF).
Is there a video?: Yes, on YouTube (28:48, chapter 35).

Also in

Chapter 5 of 10 in Nagata's Conjecture, Bloch's Conjecture and 8 More in Algebraic and Complex Geometry · starts at 1:23 · 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 35 from 11:50 · description, sources and chapters →

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