Bézout's theorem is named after the French mathematician Etienne Bézout, who stated and gave a (partially correct) proof of the result in 1779. The statement itself is much much older, appearing in the works of Jacques Bernoulli, Colin Maclaurin, and others. The result deals with plane algebraic curves, which are subsets of the plane defined as the solution set of an equation f(x,y)=0, where f(x,y) is a polynomial in two variables. The total degree of the polynomial is called the degree of the curve. Bézout's theorem then states that two plane algebraic curves of degrees m and n intersect in at most mn points unless they have a common component; that is, unless there exists an algebraic curve which is a subset of both curves.

There is a more precise version of the...