The Early 20th Century
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The mathematics of the early 20th century was dominated by Henri Poincaré (1854–1912) and David Hilbert (1862–1943). Poincaré wrote on the “three-body problem” of determining the simultaneous motion of the Sun, Earth, and Moon. One of the most brilliant mathematicians of his time and a gifted popularizer of the subject, Poincaré contributed to many areas of mathematics, including algebraic topology, differential equations, and celestial mechanics. Hilbert’s range was also immense—from abstract number theory and the study of “Hilbert spaces” in analysis to potential theory and the theory of gases. In 1891, he produced a fractal space-filling curve. His celebrated lecture at the Paris International Congress of Mathematicians in 1900 set the agenda for mathematical research over the coming century.
Bertrand Russell (1872–1970) was one of the outstanding figures of the 20th century, who was awarded the Nobel Prize for literature and who made fundamental contributions to mathematical logic. In 1913, he and Albert North Whitehead completed their Principia Mathematica, a pioneering three-volume work on the logical foundations of mathematics.
Srinivasa Ramanujan (1887–1920), one of the most intuitive mathematicians of all time, was mainly self-taught. In 1914, he left India to work with G. H. Hardy in Cambridge, England, and for their spectacular joint papers in analysis and number theory, Ramanujan was elected a Fellow of Trinity College and a Fellow of the Royal Society. He died back in India at the young age of 32.
Two analysts who have been featured on stamps are Constantin Carathéodory (1873–1950), of Greek parentage, and Stefan Banach (1892–1945), of Poland. Carathéodory worked on the theory of functions and the calculus of variations, while Banach helped to create modern functional analysis and develop links between topology and algebra; the terms “Banach space” and “Banach algebra” are named after him.