daily notes

previous notes →

Signals

We’re sharing a solution to the Navier-Stokes Millennium Prize Problem, one of the deepest problems at the frontier of mathematics. The proof was produced by a group of agents, using an OpenAI next-generation model significantly more capable than GPT-6 Astra. The problem concerns whether the description of smooth three-dimensional fluid motion modeled by the Navier-Stokes equations can break down. It has remained unresolved for roughly 90 years.

discussion2 selected replies
@OpenAIreply ↗

This model represents a step-function improvement on many benchmarks, and its training is ongoing. Our internal model group arrived at the Navier–Stokes solution in 88 hours, using around 10,000 coordinating AI agents. Throughout the effort, we maintained the strict safeguards—including monitoring and isolation—that we apply to all our frontier evaluations.

@OpenAIreply ↗

The group produced an analytical proof and Lean formalization that via Navier-Stokes dynamics a fluid can develop a singularity in finite time. The solution is a vortex, a spinning swirl of fluid, that spirals inward and gets increasingly elongated, like spaghetti. https://t.co/tz1shoCZZo

OpenAI says a group of agents produced a solution to the Navier–Stokes Millennium Prize Problem with a next-generation model. The post describes the problem as unresolved for roughly 90 years; it is a producer claim rather than an independent verification.

Sentiment

Capability evidence with deployment constraints +0.18

71 source items · 55% editorial confidence

Must read

What determines banks' excess demand for reserves?Per Asberg-Sommar, Mathias Drehmann, Denise Hansson, and Vatsala Shreeti

The 38-page BIS paper uses bank-level specifications, robustness tables, institutional detail, and policy implications to identify what shapes banks' excess reserve demand.

Sentiment

Rates, credit, and infrastructure risk -0.08

396 source items · 55% editorial confidence