  In this paper, we consider whether existence of a sums-of-squares formula
depends on the base field. We reformulate the question of existence as a
question in algebraic geometry. We show that, for large enough p, existence of
sums-of-squares formulas over algebraically closed fields is independent of the
characteristic. We make the bound on p explicit, and we prove that the
existence of a sums-of-squares formula of fixed type over an algebraically
closed field is theoretically (though not practically) computable.
