# 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 |