In part 2 of his 1885 paper, Weierstrass reproduced Lindemann’s proof that if z is algebraic,

is not zero.

Weierstrass’ proof of Lindemann’s result is concise and elegant, while still displaying its origins in Hermite’s ground-breaking proof that e is transcendental. This contrasts with some of the ‘simplifications’ that have followed, for example the surprisingly cumbersome treatment given by Hardy and Wright.

In the attached pdf (updated 25 July 2013), I reproduce part 2 of Weierstrass’ paper, with some minor modifications and some added material on symmetric polynomials. The latter draws on the description of Waring’s method in Tignol’s book ‘Galois’ Theory of Algebraic Equations’.

### Like this:

Like Loading...

*Related*

This entry was posted on February 16, 2010 at 7:12 am and is filed under Rational and algebraic numbers. You can follow any responses to this entry through the RSS 2.0 feed.
You can skip to the end and leave a response. Pinging is currently not allowed.

## Leave a Reply