10 lives in this collection worked in foundations of mathematics, from 1781 to today. Each has a full course on their life and the mathematics and physics they made.
Often together with: mathematical logic, set theory, number theory, philosophy, philosophy of mathematics, real analysis. All fields
Prague priest and philosopher who gave the first rigorous definitions of continuity and convergence, proved the intermediate value theorem analytically, and anticipated modern logic and set theory.
real analysis, foundations of mathematics, logic
Hungarian army engineer who independently discovered hyperbolic geometry and published it in 1832 as the Appendix to his father's Tentamen, together with an absolute geometry valid with or without the parallel postulate.
geometry, non-euclidean geometry, foundations of mathematics
Berlin number theorist who stated the Kronecker–Weber theorem, dreamed of class field theory through complex multiplication, and argued that all mathematics should be built from the integers.
number theory, algebra, elliptic functions
Creator of ideal theory, Dedekind cuts and the set-theoretic foundations of the natural numbers.
algebraic number theory, foundations of mathematics, abstract algebra
Creator of set theory who proved that the real numbers are uncountable and built the arithmetic of transfinite ordinals and cardinals.
set theory, real analysis, foundations of mathematics
Founder of modern quantificational logic, author of the logicist programme for arithmetic, and originator of the distinction between sense and reference.
mathematical logic, foundations of mathematics, philosophy of language
Discoverer of Russell's paradox, inventor of the theory of types and the theory of descriptions, and co-author with Whitehead of Principia Mathematica.
mathematical logic, foundations of mathematics, philosophy
Founder of modern topology through the fixed point theorem and invariance of dimension, and creator of intuitionistic mathematics.
topology, intuitionism, foundations of mathematics
Universal mathematician who founded gauge theory and the representation theory of compact Lie groups, and proved the Weyl law and the equidistribution theorem.
analysis, lie groups and representation theory, differential geometry
Logician who proved the completeness of first-order logic, the incompleteness of arithmetic, and the consistency of the axiom of choice and the continuum hypothesis.
mathematical logic, set theory, foundations of mathematics