6 lives in this collection worked in algebraic topology, from 1854 to today. Each has a full course on their life and the mathematics and physics they made.
Often together with: algebraic geometry, differential equations. All fields
Universal mathematician who created automorphic functions, the qualitative theory of dynamical systems and algebraic topology, discovered chaos in the three-body problem, and formulated the Lorentz group of relativity.
complex analysis, differential equations, celestial mechanics
Engineer turned mathematician who brought topology into algebraic geometry, proved the Lefschetz fixed-point theorem, and founded an American school of nonlinear differential equations.
algebraic geometry, algebraic topology, differential equations
Topologist who discovered the Hopf fibration and Hopf invariant, proved the Poincaré–Hopf and Hopf degree theorems, and founded the theory of Hopf algebras and group homology.
algebraic topology, differential geometry, homological algebra
Founder of the Moscow school of topology, who with Pavel Urysohn created the theory of compact spaces and who introduced the nerve of a covering.
general topology, algebraic topology, dimension theory
French mathematician who transformed algebraic topology, algebraic geometry and number theory, youngest Fields medallist and first Abel laureate.
algebraic topology, algebraic geometry, number theory
Topologist who computed the classifying space of surgery theory, founded minimal-model rational homotopy theory, proved the no-wandering-domains theorem and launched string topology.
algebraic topology, geometric topology, rational homotopy theory