Fundamental theorem of algebra
Teorema fundamental del álgebra
- Date
- 1799 · confidence high
- Place
- Helmstedt and Brunswick, Germany
- Credited to
- Carl Friedrich Gauss (doctoral thesis); earlier attempts by d'Alembert (1746), Euler and Lagrange; Argand's proof (1806)
- People
- 👤 Carl Friedrich Gauss1777–1855👤 Leonhard Euler1707–1783
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
Every non-constant polynomial with complex coefficients has at least one complex root, and so factorises completely. It establishes that the complex numbers are algebraically closed and that no further numbers are needed to solve polynomial equations.
Gauss's 1799 proof had a topological gap; d'Alembert gave the first almost-complete proof, which is why in France it is called the d'Alembert-Gauss theorem.
What it led to
- field theory
- complex analysis
- Galois theory
Built on
- Complex numbers1572
- Cardano's formulas