12 lives in this collection worked in set theory, from 1831 to today. Each has a full course on their life and the mathematics and physics they made.
Often together with: foundations of mathematics, measure theory, real analysis, topology, ergodic theory, functional analysis, general topology, graph theory, mathematical logic, mathematical physics. All fields
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 general topology and of the theory of ordered sets, creator of Hausdorff measure and dimension, who also wrote philosophy and literature as Paul Mongré.
set theory, general topology, measure theory
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
Founder of modern functional analysis, who introduced complete normed spaces and proved its fundamental theorems, and co-author of the Banach–Tarski paradox.
functional analysis, measure theory, real analysis
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
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 logician who gave the semantic definition of truth, proved the decidability of real closed fields and elementary geometry, co-discovered the Banach–Tarski paradox, and founded the Berkeley school of model theory.
mathematical logic, model theory, set theory
Mathematician who founded the Hilbert-space formulation of quantum mechanics, operator algebras and game theory, and defined the stored-program computer.
set theory, mathematical physics, functional analysis
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
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
Itinerant Hungarian mathematician, author of some 1,500 papers with over 500 co-authors, who founded the probabilistic method and the theory of random graphs.
number theory, combinatorics, graph theory