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Anthropic gave 1,000 AI agents one of the hardest problems in mathematics — a formal, computer-checked proof of Fermat's Last Theorem — and almost no instructions on how to do it. The team finished in 28.7 hours, using one-third of the output tokens and writing a proof one-seventh the length…
A social robot does not say, “Obey.” It says, in effect, “I know you. This choice is good for you.” The person may then experience the resulting preference as personal. This is dangerous. Research supports this concern: studies…
"In particular, we get insights into Lagrangian turbulence," says Björn Birnir, referencing the theory that describes turbulent behavior in a reference fame that moves with the flow, like a raft on a river. (Credit: Ingolf Zeiner Petersen/Flickr) Mathematicians have derived the formulas for boundary layer turbulence 100 years after the…
A computer-checked version of key parts of the Navier–Stokes problem is now public, with every change and every credit spelled out KTS Global has also published a smaller, earlier-stage project linked to the work of mathematician…
This study assesses physics-informed neural networks (PINNs) for the unsteady two-dimensional flow past a rotating circular cylinder confined in a channel (blockage ratio 0.2) at Reynolds numbers of 50, 200 and 500. The networks…
After contributing to the solution of a century-old problem and holding a research position at the University of Michigan, Ma Xiao unexpectedly returned to China to pursue artificial intelligence research. Two years ago…
The notion that some computational problems in math and computer science can be hard should come as no surprise. There is, in fact, an entire class of problems deemed impossible to solve algorithmically. Just below this class lie slightly “easier” problems that are less well-understood — and may be impossible…
OpenAI recently announced that one of its AI models solved one of the hardest problems in modern mathematics: the Navier-Stokes problem. The equations at the heart of this problem describe the movement of fluids like water and…
The University of Chicago’s Division of the Physical Sciences is launching a PhD program in computational and applied mathematics, part of an expansion into a field at the intersection of big data and scientific discovery. The…
Axiom Math has released a machine-checked Lean formalization of the Stacks Project, a roughly 7,500-page open-source reference for algebraic geometry. The startup says coordinated AI agents produced about 16 million lines of code linking thousands of definitions, lemmas and theorems into one reusable library. [1] The claim is narrower than…