The four exponentials conjecture states that, if (x₁, x₂) and (y₁, y₂) are two pairs of complex numbers, and each pair is linearly independent over the rationals (i.e., neither element of either pair is a rational multiple of the other), then at least one of e^(x₁y₁), e^(x₁y₂), e^(x₂y₁), and e^(x₂y₂) is transcendental.