  We present a new completely effective proof of the Lindemann-Weierstrass
theorem based on algebraic independence methods. Although it is slightly weaker
than the best known estimate due to A. Sert, it improves the best estimate due
to M. Ably obtained by such methods. The novelty of the proof lies in the
simplicity of the construction of auxiliary functions, a fact that we exploit
to introduce the non-specialist to methods of algebraic independence.

Number Theory