Amazing stuff! Exciting times for math!
However, OpenAI fought dirty on career-making math problem, says NYU mathematician. "OpenAI fought dirty on career-making math problem, says NYU mathematician: There is a $1 million bounty for the first person providing a solution to the Navier-Stokes existence and smoothness problem." OpenAI admits there was apparently an intense competition going in the last few days or so on who would come out first.
"We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. We’re sharing both a writeup of the proof and a formalization in Lean. ...
The agents arrived at their resolution on Saturday, September 5, about 88 hours after the first agents were launched. Lean formalization and verification took an additional 17 hours via GPT‑6 Astra. ...
In the process of resolving the Navier–Stokes problem, the agents sent 2.7 million messages and used approximately 130 billion output tokens. ..."
Credits: The Wall Street Journal What's news
A snapshot of local incompressible motion. Orange marks faster angular rotation; teal marks slower rotation. Circulating speed also depends on radius. The trajectories show inward spiraling and axial stretching.
No comments:
Post a Comment