Note dell’episodio
How can a collection of line segments point in every direction and still fit into a surprisingly small space? The Kakeya conjecture asks what dimension such a set must have—and its answer connects geometry to the way waves concentrate. We explore OpenAI’s new proof of local smoothing for the Euclidean wave equation, whose consequences reach Kakeya sets, Fourier analysis, and the mathematics of wave propagation. The key intuition is wonderfully approachable: a wave can focus intensely at one...
