Ax-Grothendieck theorem

Etymology
Proved independently by James Ax and Alexander Grothendieck.

Proper noun

 * 1)  A result about injectivity and surjectivity of polynomials, often given as this special case: If P is an injective polynomial function from an n-dimensional complex vector space to itself then P is bijective. The full theorem generalizes to any algebraic variety over an algebraically closed field.