Today on the Brief: A Decade-Old Math Problem Falls

OpenAI disclosed that an internal version of its next model, Astra, solved ten open problems in math and theoretical computer science — each unsolved for at least a decade. The headline: the first explicit construction proving non-sofic groups exist, a question open since 1999. It also disproved a major conjecture on von Neumann algebras and cracked several problems from Paul Erdős's list.

OpenAI posted the full proofs on GitHub in Lean, a formal language where every logical step is machine-checked — zero unfinished steps, and they compiled. Total compute cost for all ten: about $2,000. In the same stretch, ChatGPT crossed 1 billion weekly active users, the fastest any app has ever hit that number.

DeepSeek is rolling out peak/off-peak pricing on V4 Pro. Output tokens at peak hours (1–4AM and 6–10AM UTC) jump to about $3.96 per million — more than 4x the previous rate. Off-peak is roughly half that. Input pricing on a cache miss climbs to about $1.32/M at peak, up from $0.43/M.

Google shipped Gemini 3.7 Flash just three weeks after 3.6 — a real intelligence jump from algorithmic improvements, not just more compute, and meaningfully better at coding and debugging. It's priced at $0.75 in / $3.75 out per million tokens through the end of the year, half of the previous model's launch price.

xAI shipped Grok 4.6, built for long-running agents that don't need babysitting — research, whole-codebase coding, building an app from an idea. It ties OpenAI's GPT-5.6 Sol on the main intelligence index, at $2 in / $6 out per million tokens.

Anthropic told investors it pulled in over $11.5 billion in revenue last quarter, with positive operating income for the first time. But the more interesting story is in their new safety risk report: Anthropic raised its own estimate of catastrophic misalignment risk from "very low" to "low" — not because a model failed a safety test, but because of rising uncertainty, partly from how they disclosed handling cybersecurity evaluations. They also revealed an internal model, "Model Two," more capable than their current flagship, with no plans to release it publicly.

OpenAI's CFO told shareholders enterprise revenue has now overtaken ChatGPT's consumer business for the first time — a crossover originally predicted for the end of this year, arriving months early. Annualized revenue run rate: $40 billion, up 20% in a single month, with business customers growing 32% over the same stretch.

Nvidia released Nemotron 3.5 Lightning, a 30B-parameter open-weight model that runs on a single consumer GPU with up to 4x the output speed of similar-sized models. DARPA and the Air Force flew an F-16 under AI control for the first time — a safety pilot remains in the cockpit with override control, so it's not fully unmanned yet. And the EU AI Act's transparency rules are now actively enforced: any chatbot operating in the EU legally has to disclose it's AI, not a human.