I proved it by contradiction - - Let F be a finite, algebraically closed field. Now consider the polynomial p(x) = x^2 - x as a function from F to F.
Since p(x) maps 1 to 0, and 0 to 0, and since F is finite and p is one to one, there must exist an element "a" such that x^2 - x does not equal a for all x in F.
So, x^2 - x - a has no root in F, so F could not be alg. closed, which is a contradiction.
Not sure if this is exactly right, but it made sense to me.
-Tim
