Abstract: Let n be a positive integer and f a polynomial of degree n. Then the fundamental theorem of algebra says that for every complex number c, the equation f(z)=c has exactly n roots. Now suppose that f is a polynomial of infinite degree, that is, f is a convergent power series. Picard's big theorem says that for every complex number c (with possibly one exception), the equation f(z)=c has infinitely many roots. In my talk, I'll prove the fundamental theorem of algebra and then I will describe Picard's original proof of his big theorem.