OpenAI and Anthropic say AI disproved a 27-year-old computing rule
The Exponential Time Hypothesis says some logic puzzles can't be solved much faster than trying every answer. Hundreds of research papers assume it is true.
On Monday, OpenAI said an internal model proved it false. Hours later, Anthropic posted its own proof, found by an internal Claude model with no human input.
Both proofs come with Lean files, a program that checks every step of the math. An independent replay confirmed both files pass.
What this was not:
- Not a practical speedup. Anthropic says its method is unlikely to beat brute force on any problem with fewer than about 10 million variables.
- Not settled. Lean checks the proof, not whether the formal statement matches the claim. Russell Impagliazzo, who proposed the hypothesis, told Science it is "not 100% certain."
OpenAI also released claimed results on the Kakeya conjecture and part of a Millennium Prize problem, the physics one still held back by expert reviewers.
Nothing changes in your software. What changed is that frontier labs now produce research faster than experts can check it.
Anthropic files for an IPO and shows its numbers
Anthropic filed to list on Nasdaq under the ticker ANT. Share count and price are not set.
The S-1 filing is the first full look at an AI lab's finances:
- Revenue: $16.3 billion in the first half of 2026, up from $1.2 billion a year earlier.
- Operations: a $693 million operating loss, close to break-even.
- Net loss: $80.7 billion, mostly a $72 billion paper charge from revaluing convertible notes.
Growth is slowing. Quarterly revenue rose about 144% in the second quarter but roughly 47% in the third, CNBC reports.
About 80% of revenue comes from usage-based fees rather than subscriptions. Anthropic's growth depends on you running more tasks, so expect it to keep cutting cost per task. It says Opus 5.5 already cut it by about 40% versus Opus 5.
Quick hits 🗞️
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A tampered Claude Code extension tried to backdoor up to 5,000 developers. It sat in Cursor's marketplace for about 11 hours on Thursday. If you installed version 2.1.312 or 2.1.313 there, run Cursor's check script and rotate your keys. Source
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Paid AI plans got more room. OpenAI doubled Work and Codex usage on Pro 100 and Pro 500 and cancelled a planned Pro 200 cut. From December, ChatGPT and Codex will share one token-based allowance on Plus, Pro and Business. Anthropic renamed Max 20x to Ultra, with no five-hour limit for verified accounts. Source
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Mistral released Large 4 as open weights. The trillion-parameter French model is free to use and modify, but companies selling it as a hosted API need a separate license. Source
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A free AI model hacked Firefox using fixes not yet shipped. Epoch AI says Z.ai's GLM 5.3 built file-stealing attacks on six releases for about $1,000 each. Update to Firefox 159. Source
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One robots.txt line may soon block AI training everywhere. OpenAI, Google, Microsoft and Anthropic back a shared opt-out signal. Anthropic already honors it; Google and Microsoft plan support next year. Source
Model leaderboard 🏆
Via Artificial Analysis, which tests models independently.
- Smartest:
- Gemini 4 Carbon (59), cyber defenders only for now
- Claude Opus 5.5 (58)
- GPT-6 Astra (57)
- Best value: GPT-6.1 Terra (51) at about $2 per million tokens, the cheapest top-10 model per task.
- Best open-weights: DeepSeek V4.1 Flash 1017 and Z.ai's GLM-5.3 (32, tied), free to download.
- Moved this week: Artificial Analysis switched to a harder Index v5, so scores don't compare with last week's. Carbon entered at #1 and GPT-6 Astra rose to #3.
See you next week!
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