Partial differential equations

French mathematician and philosopher who founded dynamics on d'Alembert's principle, solved the wave equation, and co-edited the Encyclopédie.

mechanics, partial differential equations, fluid dynamics

Creator of descriptive geometry and founder of the differential geometry of surfaces, who posed the optimal transport problem and helped found the École Polytechnique.

descriptive geometry, differential geometry, partial differential equations

Founder of the mathematical theory of heat conduction, inventor of Fourier series and the Fourier integral, and the first to describe the atmosphere's warming of the Earth.

mathematical physics, heat conduction, fourier analysis

Prussian mathematician who founded the theory of elliptic and theta functions with Abel, created Hamilton–Jacobi mechanics, and introduced the Jacobian, the Jacobi identity and the Jacobi symbol.

elliptic functions, analytical mechanics, number theory

First woman to earn a modern doctorate in mathematics and to hold a full chair, known for the Cauchy–Kovalevskaya theorem and the integrable Kovalevskaya top.

partial differential equations, mechanics, abelian functions

French analyst who proved the prime number theorem, created the theory of entire functions of finite order, and introduced well-posed problems, Hadamard matrices and the study of chaotic geodesic flows.

complex analysis, analytic number theory, differential geometry

Swedish analyst whose 1903 theory of linear integral equations, with the Fredholm determinant and the Fredholm alternative, launched spectral theory and modern functional analysis.

integral equations, operator theory, partial differential equations

Analyst of variational and eigenvalue problems, co-author of the CFL condition, and founder of the mathematical institutes at Göttingen and New York University.

analysis, partial differential equations, calculus of variations