Are the digits of $\pi$ (or anything like it) random?

Richard E. Crandall

A theory of digit randomness has been proposed (jointly, by D. Bailey and the lecturer) to "explain" the apparent randomness of the expansions of fundamental constants such as $\pi$, $\log 2$, $\zeta(3)$. At the core of the theory is a general hypothesis connecting chaotic phenomena with the older theory of normal numbers. In particular, on the general hypothesis we can prove that each of the aforementioned constants is normal to base 2 (i.e., has "random" binary bits).