AI This Week: OpenAI Disproves an 80-Year Math Conjecture, Karpathy Joins Anthropic, Google Drops Gemini 3.5, OpenAI Files for IPO

An OpenAI reasoning model autonomously disproved a geometry conjecture from 1946, Karpathy joined Anthropic for pretraining research, Google I/O unveiled Gemini 3.5 Flash and Omni, and OpenAI began filing for an $850B+ IPO.
artificial-intelligence
Author

Kabui, Charles

Published

2026-05-21

Keywords

openai-erdos-conjecture, karpathy-anthropic, gemini-3-5-flash, google-io-2026, openai-ipo

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An OpenAI reasoning model autonomously disproved a conjecture Paul Erdős posed in 1946 about unit-distance pairs among points in a plane. The model constructed configurations yielding n^(1+δ) pairs (δ = 0.014), using algebraic number theory tools no one had thought to apply to this geometry problem. Fields medalist Tim Gowers said he would recommend the proof for publication “without any hesitation.” The model was a general-purpose reasoning system, not trained specifically for math.

Andrej Karpathy joined Anthropic to lead pretraining research. The OpenAI co-founder and former Tesla AI director described the next few years at the LLM frontier as “especially formative.” The same week, Anthropic acquired Stainless, the company behind every official Anthropic SDK, generating SDKs and MCP servers across TypeScript, Python, Go, Java, and Kotlin.

Google I/O 2026 introduced Gemini 3.5 Flash, which outperforms Gemini 3.1 Pro on coding and agentic benchmarks at 4x the speed of other frontier models. Google also launched Gemini Omni Flash for video creation from any input and the Antigravity 2.0 standalone desktop agent. The Gemini app now serves 900 million monthly users. Search AI Mode passed 1 billion.

OpenAI is preparing to file its IPO prospectus with Goldman Sachs and Morgan Stanley at a valuation exceeding $850 billion, days after a jury dismissed all claims in Musk v. Altman. Cursor launched Composer 2.5 on Moonshot’s Kimi K2.5 open-source checkpoint. Stability AI released Stable Audio 3.0 with three open-weight music models trained on fully licensed data.

Capability is no longer the scarce resource. OpenAI proved AI can do original mathematics. Google showed 900 million people already use its AI daily. Anthropic is acquiring the plumbing layer that locks agents into its platform. And OpenAI going public means quarterly earnings pressure will soon shape how frontier AI is built and priced.

Read More: AI Power Shifts: Anthropic, China, Manus, and DeepSeek V4

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BibTeX citation:
@misc{kabui2026,
  author = {{Kabui, Charles}},
  title = {AI {This} {Week:} {OpenAI} {Disproves} an {80-Year} {Math}
    {Conjecture,} {Karpathy} {Joins} {Anthropic,} {Google} {Drops}
    {Gemini} 3.5, {OpenAI} {Files} for {IPO}},
  date = {2026-05-21},
  url = {https://toknow.ai/posts/ai-weekly-openai-erdos-proof-karpathy-anthropic-google-io-gemini-ipo/},
  langid = {en-GB}
}
For attribution, please cite this work as:
Kabui, Charles. 2026. “AI This Week: OpenAI Disproves an 80-Year Math Conjecture, Karpathy Joins Anthropic, Google Drops Gemini 3.5, OpenAI Files for IPO.” https://toknow.ai/posts/ai-weekly-openai-erdos-proof-karpathy-anthropic-google-io-gemini-ipo/.