Brouwer had similar inspiration from a cup of coffee. In his case, the intuition was that if you stir coffee, there's a "part" of it that stays fixed. In math

Brouwer had similar inspiration from a cup of coffee. In his case, the intuition was that if you stir coffee, there's a "part" of it that stays fixed. In math terms, f:X->X where X is compact and convex, and f is continuous, has a fixed point (exists x_0 in X, f(x_0)=x_0)