Version 6

What

Why it matters

Open questions

• AlphaProof Nexus solved 9 Erdős problems and 44 OEIS conjectures [8][9] — what are the specific problems, how do they compare in difficulty to the OpenAI unit distance disproof, and how has independent verification proceeded?

• If competition math benchmarks near saturation within a year as Rohan Paul predicts [15], what evaluation frameworks exist for research-level AI mathematics that can distinguish degrees of difficulty beyond IMO gold?

• Tao's concern about 'mass-produced mathematics at scale' [18] — has the mathematical community or any institution developed an institutional response to review-capacity pressure as systems resolve dozens of conjectures simultaneously?

• The UW Math AI Lab's dataset of erroneous Lean proofs [14] challenges the trust model behind DeepMind's and Harmonic's formal-verification architectures — how are current systems addressing false proof generation within Lean pipelines?

Narrative

Timeline

• 1946-01-01: Paul Erdős poses the unit distance conjecture in discrete geometry [4]
• 2024-07-01: DeepMind's AlphaProof and AlphaGeometry 2 earn silver medal at IMO 2024 [30]
• 2025-07-21: NYT reports Google AI wins gold at IMO 2025; OpenAI also claims gold — first AI systems to clear this threshold [1][2][3]
• 2025-08-03: Xena Project publishes mathematical community round-up of AI performance at IMO 2025 [21]
• 2026-02-01: The Atlantic publishes longform profile on how Terence Tao uses AI in his research [23]
• 2026-05-20: OpenAI announces unreleased reasoning model disproved the Erdős unit distance conjecture [4][25]
• 2026-05-21: Gil Kalai acknowledges disproof as 'Amazing'; widespread media amplification including The Guardian [6][31][32]
• 2026-05-22: arXiv preprint on the disproof appears; formal verification debate surfaces in coverage [5][11]
• 2026-05-23: Reports of three Erdős problems falling in seven days with Tao verifying each; Gary Marcus publishes critical review of AI math headlines [17][19]
• 2026-05-24: Tao's GitHub wiki tracking AI contributions confirmed; Tao quoted on 'mass-produced mathematics at scale'; AlphaProof Nexus first mentioned [16][18][22]
• 2026-05-28: Zvi Mowshowitz reports AlphaProof Nexus solved 9 Erdős problems and 44 OEIS conjectures; notes landmark result with almost no mainstream media coverage [9][8]
• 2026-06-01: Ars Technica: Fields Medalist Tim Gowers and Daniel Litt explicitly validate OpenAI's Erdős result as substantively exciting [7]
• 2026-06-04: Google research paper: structured proof-writing raises general LLM formal math performance from under 10% to 70% [13]
• 2026-06-07: Rohan Paul predicts competition math benchmarks near obsolescence and expects a model with a perfect IMO score within one year [15]

Perspectives

Tensions

• OpenAI's Erdős disproof came from a general-purpose model with no formal-system grounding; DeepMind's architecture requires every reasoning step to be Lean-verified — both have produced expert-validated results, but they represent different claims about what makes AI mathematical output trustworthy. [4][11][12][5][2][3][7]
• Gary Marcus explicitly audits AI math headlines against underlying results [19], while Fields Medalist Tim Gowers and Daniel Litt have directly endorsed the OpenAI Erdős result as substantively exciting [7] — the most direct clash between the skeptical and endorsing positions. [19][7][4]
• Tao observes 'more and more mass-produced mathematics at scale' [18] as a quality concern; Rohan Paul frames high-volume proof-search as precisely the mechanism for mathematical progress and expects benchmark saturation within a year [15] — the same phenomenon read as a problem versus a feature. [18][15][13]
• AlphaProof Nexus solved 9 Erdős problems and 44 OEIS conjectures — results Zvi calls a landmark milestone — but received almost no mainstream coverage [9], while OpenAI's single Erdős disproof generated sustained press attention; the coverage gap does not track the volume of results. [9][8][4][20]
• The UW Math AI Lab's dataset of erroneous Lean proofs challenges the 'every step formally verified' claim central to DeepMind's and Harmonic's architectures — if the verification layer itself produces false proofs, formal-system grounding may be less reliable than claimed. [14][11][25][12]
• Tudor Achim predicts AI could prove the Riemann Hypothesis by 2028 [25]; Rohan Paul expects a perfect IMO score within one year [15] — both bullish timelines sit against DeepMind's cautious published research and Marcus's ongoing skepticism. [25][15][11][19]