The theme of the talk is analogies between number theory and topology and everything will be elementary and discussed in the context of simple examples. I will focus on the space of configurations of points in the complex plane, and how basic ideas from algebraic topology, representation theory and analytic number theory interact in this example, to yield arithmetic statistics of polynomials over finite fields. In fancier language, I will discuss how the cohomology of the pure braid groups as representations of the permutation groups corresponds to special values of L-functions, and how the Riemann zeta function is related to the second iterated loop space of the two-sphere!