# Schanuel’s conjecture

Let $x_{1},x_{2},\ldots,x_{n}$ be complex numbers linearly independent over $\mathbb{Q}$. Then the set

 $\displaystyle\{x_{1},x_{2},\ldots,x_{n},e^{x_{1}},e^{x_{2}},\ldots,e^{x_{n}}\}$

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 SchanuelsConjecture 2013-03-22 13:58:08 2013-03-22 13:58:08 mathcam (2727) mathcam (2727) 11 mathcam (2727) Conjecture msc 11F67 Schanuel conjecture LindemannWeierstrassTheorem