Lindemann, (Carl Louis) Ferdinand von (1852–1939)

German mathematician whose discussion of the nature of π in 1882 laid to rest the old question of ‘squaring the circle’.

Lindemann was born in Hannover and studied at Göttingen, Munich, and Erlangen. He was professor at Würzburg 1879–83, and at Königsberg 1883–93; from 1893 until his death, he taught at Munich.

The question whether π was a transcendental (nonalgebraic) number had never received a satisfactory answer until Lindemann proved it in his 1882 paper. He demonstrated that, except in trivial cases, every expression of the form:

A1ea1 + A2ea2 + ...... + Anean

where A and a are algebraic numbers, must be non-zero. Therefore, since i is a root of x2 + 1 = 0, and since it was known that:

eiπ + e0= 0

(that is eiπ = −1)

then iπ and therefore π (since i is algebraic) must be transcendental.

If π cannot be the root of an equation, it cannot be constructed. Therefore the ‘squaring of a circle’ is impossible.