Galois theory and group theory
Teoría de Galois y teoría de grupos
- Date
- 1832 · confidence high
- Place
- Paris, France
- Credited to
- Évariste Galois (manuscripts of 1830-1832, published by Liouville in 1846)
- People
- 👤 Évariste Galois1811–1832
- Field
- Knowledge & symbols
What was discovered
Associating to each equation the group of permutations of its roots and characterising solvability by radicals through the structure of that group. It introduces the concept of group and the structural method that would come to dominate algebra.
Galois died in a duel at the age of 20; he wrote the letter summarising his theory the night before. Cayley gave the abstract definition of a group in 1854.
What it led to
- abstract algebra
- field theory
- the impossibility of angle trisection and cube duplication
- Lie groups
- the classification of finite simple groups
Built on
- Insolvability of the quintic (Abel-Ruffini)1824
- Lagrange
- Abel
- Cauchy (permutations)
Made possible
- Erlangen program1872
- Theory of Lie groups1873-1874
- Rejewski's break into the Enigma cipher1932
- Error-correcting codes (Hamming, Reed-Solomon)1950-1960
- Public-key cryptography (Diffie-Hellman)1976
- Monster group1973-1982
- Faltings' theorem1983
- Classification of finite simple groups1983 (completada en 2004)
- crystallography and particle physics (symmetry)