If algebraic integers α_1, ..., α_n are linearly independent over Q, then e^(α_1), ..., e^(α_n) are algebraically independent over Q. The Lindemann-Weierstrass theorem is implied by Schanuel's conjecture.

algebraically independent | Hermite-Lindemann theorem | Schanuel's conjecture

Ferdinand von Lindemann | Karl Weierstrass