# algebraic independence

## Schanuel's Conjecture ★★★★

Author(s): Schanuel

\begin{conjecture} Given any $n$ complex numbers $z_1,...,z_n$ which are linearly independent over the rational numbers $\mathbb{Q}$, then the extension field $\mathbb{Q}(z_1,...,z_n,\exp(z_1),...,\exp(z_n))$ has transcendence degree of at least $n$ over $\mathbb{Q}$. \end{conjecture}

Keywords: algebraic independence

## Algebraic independence of pi and e ★★★

Author(s):

\begin{conjecture} $\pi$ and $e$ are \Def[algebraically independent]{Algebraic_independence} \end{conjecture}

Keywords: algebraic independence