Topology

Leipzig astronomer and geometer who introduced barycentric and homogeneous coordinates, the Möbius function and Möbius transformations, and described the one-sided Möbius band.

projective geometry, astronomy, topology

French mathematician whose Traité des substitutions (1870) founded group theory as a discipline, and who introduced the Jordan normal form, composition series, functions of bounded variation, Jordan content and the Jordan curve theorem.

group theory, linear algebra, analysis

Creator of Lebesgue measure and the Lebesgue integral, the foundation of modern analysis and probability.

real analysis, measure theory, fourier analysis

Founder of modern topology through the fixed point theorem and invariance of dimension, and creator of intuitionistic mathematics.

topology, intuitionism, foundations of mathematics

Leader of the Warsaw school of mathematics, pioneer of set theory and the continuum hypothesis, and creator of the Sierpiński triangle, carpet and numbers.

set theory, number theory, topology

Warsaw topologist who axiomatized closure, defined the set-theoretic ordered pair, characterized planar graphs, and led the post-war rebuilding of Polish mathematics.

topology, set theory, graph theory

Polish-American mathematician of the Lwów school who introduced measurable cardinals, conjectured the Borsuk–Ulam theorem, invented the Monte Carlo method, co-designed the hydrogen bomb and ran the Fermi–Pasta–Ulam–Tsingou experiment.

set theory, measure theory, topology

Geometer who founded topological K-theory, proved the index theorem with Isadore Singer, and joined geometry to gauge theory and quantum field theory.

geometry, topology, k-theory

Theoretical physicist and first physicist to win the Fields Medal, whose work on supersymmetry, topological field theory and string theory reshaped geometry and topology.

theoretical physics, string theory, quantum field theory