In college I remember being fascinated by the Clay mathematical institute's problems. One of these is the Navier-Stokes problem, which basically means figuring out whether fluid dynamical equations always give sensible answers or whether they break down in some cases.
Fascinating news today. Apparently researches working with Claude and Codex, and then OpenAI itself - have all announced varying degrees of "solutions". OpenAI is claiming to have a result that shows "blowups" (i.e. equations breaking down) in some cases.
Human researchers (Levent Alpöge and Tristan Buckmaster) demonstrated a "blowup" for forced Euler equations, a sort of simpler cousin of the Navier-Stokes set of equations.
Apparently OpenAI got wind that Anthropic and these researchers were close to a solution, then simply threw 10,000 agents at the problem, who worked for 88 hours to produce the result, verified using lean. Mind you, this is a problem that human experts have been working on for over 100 years.
I have many takeaways from this. One is that any domain with the possibility of solution-verification is a compute allocation away from "done". Or the domain itself as a mostly-human endeavor is "cooked", as the kids say.
I think this loosely resembles another one of the Clay mathematical problems, P vs NP. If a lot of human knowledge-work turns out to be "NP" (meaning incredibly hard to solve but relatively simple to verify solutions), then this opens a path to basically throwing compute at the problem and brute-finding solutions.