For a historical perspective we provide some brief information about the pioneers of the areas of investigation we have touched upon.

Abel, Niels Henrik (1802–1829): Norwegian mathematician with pioneering contributions to quintic equations and mathematical analysis

Alaoglu, Leonidas (1914–1981): Canadian mathematician of Greek origin, with contributions to functional analysis

Arzelà, Cesare (1847–1912): Italian mathematician with contributions to the theory of functions

Ascoli, Giulio (1843–1896): Italian mathematician with contributions to the theory of functions of a real variable and to Fourier series

d'Alembert, Jean-Baptiste le Rond (1717–1783): French mathematician and philosopher (he played an important role in the intellectual ferment leading to the French Revolution)

Archimedes (c. 287 B.C. – 212 B.C.): Greek mathematician, physicist, engineer, and astronomer (active in Syracuse, Sicily), regarded as one of the leading scientists in classical antiquity

Baire, René-Louis (1874–1932): French mathematician with important contributions to mathematical Analysis

Banach, Stefan (1892–1945): Polish mathematician; one of the founders of functional analysis, with major contributions to integration theory and set theory

Bergman, Stefan (1895–1977): Polish-born American mathematician with important contributions to complex analysis

Bernoulli, Daniel (1700–1782): Swiss mathematician and physicist, famous for his applications of mathematics to fluid mechanics and for his pioneering work in probability and statistics

Bernstein, Sergei Natanovich (1880–1968): Russian mathematician known for contributions to constructive function theory, a field studying the connection between smoothness properties of a function and its approximations by polynomials

Bessel, Friedrich Wilhelm (1784–1846): German mathematician and astronomer

Blaschke, Wilhelm Johann Eugen (1885–1962): Austrian mathematician with important contributions to complex analysis and geometry

Bloch, André (1893–1948): French mathematician known for his contributions to complex analysis

Bochner, Salomon (1899–1982): American mathematician known for his wide-ranging work in mathematical analysis

du Bois-Reymond, Paul David (1831–1889): German mathematician with notable contributions to the calculus of variations and Fourier series

Borel, Félix Édouard Justine Émile (1871–1956): French mathematician; one of the pioneers of measure theory and probability theory

Cantelli, Francesco Paolo (1875–1966): Italian mathematician with important contributions to probability theory and mathematical finance