10 lives in this collection worked in real analysis, from 1781 to today. Each has a full course on their life and the mathematics and physics they made.
Often together with: set theory, complex analysis, differential geometry, foundations of mathematics, functional analysis, measure theory, potential theory, topology. 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
Founder of rigorous modern analysis, who introduced the epsilon-delta style, uniform convergence and power-series foundations of complex function theory.
real analysis, complex analysis, elliptic and abelian functions
Founder of Riemann surfaces and Riemannian geometry, and author of the 1859 paper linking the primes to the zeros of the zeta function.
complex analysis, differential geometry, analytic number theory
French geometer whose work on surfaces, orthogonal systems, integration and Pfaffian forms shaped classical differential geometry, and who led the Paris Faculty of Science and the Academy of Sciences.
differential geometry, real analysis, differential equations
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
Creator of Lebesgue measure and the Lebesgue integral, the foundation of modern analysis and probability.
real analysis, measure theory, fourier analysis
Hungarian analyst, a founder of functional analysis, known for the Riesz–Fischer and Riesz representation theorems, the L^p spaces, the theory of compact operators and subharmonic functions.
functional analysis, operator theory, real analysis
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 axiomatic probability theory whose work also shaped turbulence, Hamiltonian dynamics, ergodic theory and algorithmic complexity.
probability theory, real analysis, turbulence