Algebraic solution of cubic and quartic equations
Solución algebraica de las ecuaciones cúbica y cuártica
- Date
- 1545 · confidence high
- Place
- Bologna and Milan, Italy
- Credited to
- Scipione del Ferro, Niccolò Tartaglia, Gerolamo Cardano and Lodovico Ferrari
- People
- 👤 Gerolamo Cardano1501–1576👤 Ludovico Ferrari1522–1565👤 Niccolò Fontana Tartaglia1499–1557👤 Scipione del Ferro1465–1526
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
A formula in radicals for the third-degree equation (and, via Ferrari, the fourth-degree one), published in Cardano's Ars Magna. The first decisive advance beyond Greek and Arabic mathematics, which forced the admission of roots of negative numbers.
Del Ferro solved the reduced case around 1515 and entrusted it to Fior; Tartaglia rediscovered it in 1535 and revealed it to Cardano under an oath of secrecy; Cardano published it in 1545 after finding del Ferro's manuscript, which triggered a famous dispute.
What it led to
- complex numbers
- the insolvability of the quintic (Abel)
- Galois theory
Built on
- Al-Khwarizmi algebrac. 820
- Zero and positional notation in Europe (Fibonacci)1202
- Khayyam's cubic equation
- Fibonacci