The football player and the infinite series

TL;DR

This paper narrates a mathematical story linking a football player's problem to the theory of uniform convergence of Dirichlet series and the analysis of functions with infinitely many variables.

Contribution

It provides an expository account connecting a real-world problem to advanced concepts in the theory of infinite-variable analytic functions.

Findings

Illustrates the connection between a sports problem and Dirichlet series convergence

Highlights the role of infinite-variable analytic functions in understanding the problem

Provides insights into the subtlety of uniform convergence in complex analysis

Abstract

This is the text of an expository talk given at the May 1997 Detroit meeting of the American Mathematical Society. It is a tale of a famous football player and a subtle problem he posed about the uniform convergence of Dirichlet series. Hiding in the background is the theory of analytic functions of an infinite number of variables.