As part of a project I will be keeping ongoing indefinitely after a suggestion from a teacher of mine, I wish to introduce Mathematical Sinners. The goal is to find physical applications or descriptions of physical phenomena using what would be considered highly "pure" theorems (i.e. from number theory, or abstract algebra or something). A great example would be if someone could find a "use" for the existence of Khinchine's Constant.
Can you think of any?
In 1951, John Nash published a paper in Annals of Mathematics proving the existence of a solution concept for finite, non-cooperative games he termed 'equilibrium points,' that has gone on to bear his name (the so-called 'Nash equilibrium' solution concept of game theory).
His 1951 existence proof makes direct use of the Brouwer fixed point theorem, a piece of machinery usually derived as a consequence of some of easy properties of singular homology.