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An internal model and thousands of coordinating agents produced a machine-checked argument that smooth three-dimensional flow can reach unbounded speed in finite time.

Agents spent eleven days turning a famous 1990s argument into Lean code so a machine could check every step from the basic rules of mathematics.

By revisiting Apéry’s proof and introducing modern methods, a recent research sheds new light on the irrationality of special values in number theory.

A small model outsmarts the giants. Microsoft’s rStar-Math rewrites the rules of AI math reasoning—no teacher models, just smart self-training and Monte Carlo strategy.

After 66 years, Dijkstra falls. A July 2025 breakthrough shatters the sorting barrier, proving faster shortest paths in directed graphs are possible without sorting everything and rewriting algorithmic theory forever

An examination by a top mathematician of how mathematicians might respond to AI capable of research tasks.