Elliptic functions (inversion of elliptic integrals)
Funciones elípticas (inversión de las integrales elípticas)
- Date
- 1827-1829 · confidence medium
- Place
- Christiania (Oslo), Norway
- Credited to
- Niels Henrik Abel (independently, also Carl Gustav Jacobi)
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
Abel defined elliptic functions by inverting the elliptic integrals studied since Fagnano, Euler and Legendre, opening a field of its own instead of treating them as mere integrals; Jacobi reached equivalent results almost simultaneously with his 'Fundamenta nova theoriae functionum ellipticarum' (1829).
Wikidata credits only Abel, but Jacobi developed the theory independently and almost simultaneously (1829); Gauss already knew many of its properties decades earlier but never published them. The milestone is placed in Christiania (Oslo), where Abel wrote his 'Recherches sur les fonctions elliptiques' (1827).
What it led to
- Theory of modular functions
- Hyperelliptic functions and their unification as doubly periodic functions (Briot and Bouquet, 1856)
- Later applications in number theory and elliptic-curve cryptography
Built on
- Elliptic integrals of Fagnano, Euler and Legendre