Lindemann–Weierstrass theorem
Teorema de Lindemann–Weierstrass
- Date
- 1882-1885 · confidence medium
- Place
- Berlin, Germany
- Credited to
- Karl Weierstraß y Ferdinand von Lindemann
- Field
- Knowledge & symbols
What was discovered
A theorem proving that if α₁,…,αₙ are distinct algebraic numbers, then e^α₁,…,e^αₙ are linearly independent over the algebraic numbers, which allows the transcendence of e and π to be proved. Proved by Ferdinand von Lindemann in 1882 and generalized by Karl Weierstraß in 1885.
What it led to
- Proof of the transcendence of π and the impossibility of squaring the circle
- Development of the theory of transcendental numbers
- Precedent for Hilbert's seventh problem (Gelfond–Schneider theorem)