Augustin-Louis Cauchy made fundamental contributions to analysis, including the Cauchy-Riemann equations and the Cauchy integral theorem.

Nikolai Lobachevsky developed a non-Euclidean geometry that challenged the traditional Euclidean axioms.

Evariste Galois' work on group theory laid the foundation for modern algebra.

Carl Jacobi's work on elliptic functions and number theory had a profound impact on mathematics.

William Rowan Hamilton introduced quaternions and developed vector analysis, which laid the groundwork for modern physics.

Arthur Cayley's work on algebraic invariants and covariants had a significant impact on algebraic geometry.

Bernhard Riemann's work on complex analysis, including the Riemann surface and the Riemann zeta function, revolutionized the field.

Felix Klein's work on projective geometry and non-Euclidean geometry had a profound impact on mathematics.

Peter Gustav Lejeune Dirichlet's contributions to number theory, including Dirichlet's theorem on primes, were groundbreaking.

Élie Cartan's work on the theory of characteristics and differential geometry had a profound impact on mathematics and physics.

Évariste Galois' work on Galois theory revolutionized the study of algebraic equations.

Henri Poincaré's work on manifolds and topology laid the foundation for modern differential geometry and algebraic topology.

Henri Lebesgue's work on measure theory revolutionized the study of functions of real variables.

Sophus Lie's work on Lie groups and their applications to differential geometry had a profound impact on mathematics and physics.

Fredholm Ivar's work on integral equations and functional analysis laid the foundation for modern functional analysis.