Schanuel's conjectureSchanuelsConjecutre2003-09-25 17:36:082006-09-08 11:43:16Conjecture% this is the default PlanetMath preamble. as your knowledge
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\renewcommand{\>}{\rangle}Let $x_1, x_2, \ldots, x_n$ be complex numbers linearly independent over $\Q$. Then the set
\begin{align*}
\{x_1,x_2,\ldots,x_n,e^{x_1},e^{x_2},\ldots,e^{x_n}\}
\end{align*}
has \PMlinkname{transcendence degree}{TransendenceDegree} greater than or equal to $n$.
Though seemingly innocuous, a proof of Schanuel's conjecture would prove hundreds of \PMlinkescapetext{open} conjectures in transcendental number \PMlinkescapetext{theory}.