TITLE: Can true randomness come out of mathematical rules?
QUESTION [10 upvotes]: For example, prime numbers, they seem very random, and they are defined by a simple set of rules. I can't see how real randomness could exist in the real world, but what about mathematics?

REPLY [2 votes]: I claim that the function $f(n) = $ the digit in the hundredth decimal place of the decimal expansion of $\sqrt{n\pi}$ is a random function from $\mathbb{Z}$ to the set $\{0, 1, \dots, 9\}$, but I would be definitely impressed by anyone who can prove that this function is not random.