The story
Proved independently by James Ax and Alexander Grothendieck.
Etymology from Wiktionary, CC BY-SA 4.0.
Ax-Grothendieck theorem
Today it means: 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. Full definition →