Bernstein–Kushnirenko theorem

The Bernstein–Kushnirenko theorem, also called Bernstein–Khovanskii–Kushnirenko theorem (BKK theorem), states that the number of nonzero complex solutions of a system of Laurent polynomial equations ${\displaystyle f_{1}=\cdots =f_{n}=0}$ is equal to the mixed volume of the Newton polytopes of such polynomials, assuming that all nonzero coefficients of ${\displaystyle f_{n}}$ are generic.

It was proven by David Bernstein and Anatoliy Kushnirenko in 1975. Askold Khovanskii has found about 15 different proofs of this theorem.