Dvoretzky's theorem

In mathematics, Dvoretzky's theorem is an important structural theorem about normed vector spaces proved by Aryeh Dvoretzky in the early 1960s, answering a question of Alexander Grothendieck. In essence, it says that every sufficiently high-dimensional normed vector space will have low-dimensional subspaces that are approximately Euclidean. Equivalently, every high-dimensional bounded symmetric convex set has low-dimensional sections that are approximately ellipsoids.

A new proof found by Vitali Milman in the 1970s was one of the starting points for the development of asymptotic geometric analysis (also called asymptotic functional analysis or the local theory of Banach spaces).