Stefan Banach

Stefan Banach (1892–1945) was a Polish mathematician and one of the founders of modern functional analysis — the art of treating whole functions as if they were points in a giant space. He was largely self-taught, wildly talented, and did much of his best thinking in a noisy café.

Why it mattered

Banach spaces — complete versions of the metric spaces where you can measure distance — are named after him and are everywhere in advanced maths. With Tarski he also proved the famous Banach–Tarski "paradox": using the axiom of choice, you can (in theory) chop a solid ball into a few pieces and reassemble them into two balls the same size as the first. Impossible in the real world, perfectly valid in the maths.

Banach and his friends held court for hours in the Scottish Café in Lwów, scribbling problems on the marble tabletops. When the waiters wiped them clean each night, the maths vanished — so they bought a thick notebook, kept it with the café staff, and filled it with open problems and prizes (a bottle of wine, a live goose) for anyone who solved them. That "Scottish Book" became legendary. Banach was discovered, too, almost by chance: an older mathematician overheard a young stranger on a park bench casually discussing hard mathematics, and Banach's career began.