Today I am giving the Algebra/Number Theory/Combinatorics Seminar at the Claremont Colleges. This talk, “What is a #P complete problem” is a prequel in a sense to an earlier talk I gave in the Seminar last year. In the earlier talk, I discussed new methods for approximating the permanent of a matrix. In this talk, I will argue that finding the permanent is a hard problem. One way to characterize hardness of a numerical problem is the notion of number P problems, or #P for short. I will define #P problems and give Ben-Dor and Halevi’s 1993 proof that finding the permanent of a matrix is a #P hard problem, so if we could solve it quickly, any problem in #P could also be solved quickly.