Topological games at Princeton, a mathematical memoir

The games of the title are “Nash” (or Hex), “Milnor” (or Y), “Shapley” (or Projective Plane) and “Gale” (or Bridg-It) all of which were discovered (or re-discovered) in Princeton in 1948-1949. After giving the basic topological connections, I will discuss more recent ramifications related to computational complexity theory. A recurrent theme will be non-constructive proofs, or how we can know something can be done without having the slightest idea of how to do it.