Mark Kac

Mark Kac (1914–1984, pronounced "Kats") was a Polish-American mathematician and one of the great popularisers of probability. Warm, witty and famous for his lecturing, he had a knack for asking questions so simple and vivid that they became instantly famous — like "Can you hear the shape of a drum?"

Why it mattered

Kac spotted a stunning bridge between two worlds that seem to have nothing to do with each other: the deterministic differential equations of physics, and the random wandering of particles. Team up with the physicist Richard Feynman and you get the Feynman–Kac formula, which rewrites the solution of a PDE as an average over random paths:

u(x, t) = \mathbb{E}\!\left[\, \phi(X_T) \;\middle|\; X_t = x \,\right].

In finance, this is exactly why an option's price can be found by simulating thousands of random market scenarios and simply taking the average payoff.

The story goes that Kac was in the audience at a seminar where Feynman described his new "sum over paths" way of thinking about quantum mechanics. Kac, sitting there as a probabilist, realised with a jolt that Feynman was unknowingly describing something very close to a tool he already knew from random walks. He put the two ideas together — and so a physicist and a probabilist who approached the world from opposite ends ended up sharing a single, elegant formula that neither could have written alone.