Cauchy–Riemann equations
Ecuaciones de Cauchy-Riemann
- Date
- 1752 · confidence high
- Place
- Paris, France
- Credited to
- Jean le Rond d'Alembert
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
D'Alembert introduced these equations in his essay on fluid resistance, decades before Cauchy and Riemann turned them into a cornerstone of complex analysis: they are the condition a function must satisfy to be complex-differentiable.
Despite bearing the names of Cauchy and Riemann, d'Alembert had already written them down in 1752 and Euler connected them to analytic functions in 1797; Cauchy (1814) and Riemann (1851) built the modern theory of complex functions on them, and the name stuck with the latter two.
What it led to
- Cauchy's theory of complex-variable functions (1814)
- Riemann's dissertation on function theory (1851) and the geometry of Riemann surfaces