Appears in collection : Mikefest : A conference in honor of Michael Douglas’ 60th birthday

In the early 2000s, one often heard that the vacuum counting problem in string theory was like a spin glass problem. My talk will review results of Douglas, Shiffman, and myself on probabilistic methods for counting vacua of certain string theories. I then review some more recent results by various mathematicians on critical points of p-spin Hamiltonians. These results do not seem to be well known to physicists but may have analogs for string theory vacua.