Schanuel’s conjecture

Let $x_1,x_2,\mathrm{\dots },x_n$ be complex numbers linearly independent over $\mathbb{Q}$. Then the set

$\mathrm{\{}{x}_1,x_2,\mathrm{\dots },x_n,e^{x_1},e^{x_2},\mathrm{\dots },e^{x_n}\}$

has transcendence degree (http://planetmath.org/TransendenceDegree) greater than or equal to $n$.

Though seemingly innocuous, a proof of Schanuel’s conjecture would prove hundreds of conjectures in transcendental number .

Title	Schanuel’s conjecture
Canonical name	SchanuelsConjecture
Date of creation	2013-03-22 13:58:08
Last modified on	2013-03-22 13:58:08
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	11
Author	mathcam (2727)
Entry type	Conjecture
Classification	msc 11F67
Synonym	Schanuel conjecture
Related topic	LindemannWeierstrassTheorem