Insolvability of the quintic (Abel-Ruffini)
Imposibilidad de resolver la quíntica por radicales
- Date
- 1824 · confidence high
- Place
- Christiania (Oslo), Norway
- Credited to
- Niels Henrik Abel; incomplete proof by Paolo Ruffini (1799)
- People
- 👤 Niels Henrik Abel1802–1829
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
There is no general formula in radicals for equations of degree five or higher. It closes three centuries of searching after Cardano and opens the study of permutations of roots.
Ruffini published a 500-page proof with a gap in 1799; Abel completed it independently and also founded, with Jacobi, the theory of elliptic functions.
What it led to
- Galois theory
- group theory
- elliptic and abelian functions
Built on
- Lagrange (resolvents, 1770)
- Ruffini