Bertrand Russell was born in 1872 into a British aristocratic family: he was Earl of Kingston and Viscount of Alenby and Arsulk. He was also the grandson of the politician John Russell, who served twice as prime minister. Having lost his parents at a very young age, Russell was raised—contrary to their expressed wishes—by his rigid, puritanical grandmother. Deeply introverted, he had little contact with children his own age and seemed fragile and unhappy, as he recalled in his book La Conquête du bonheur (The Conquest of Happiness; Allen & Unwin, 1930): "As a teenager, I hated life and was continually on the verge of suicide; what stopped me was my desire to become more proficient in mathematics."
Saved by his passion for mathematics, Russell entered Trinity College, Cambridge, where his exceptional abilities were immediately recognized. After winning a mathematics competition in 1893, he turned to metaphysics, graduating in the subject the following year.
Logic first!
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Russell married despite his family's opposition. Apart from politics, he disagreed with them on almost everything. He spent two years in the United States, studying non-Euclidean geometries. He then travelled to Germany, where he learned about economics and discovered Marxism, before returning to Britain to teach political science at Leeds.
It was during this period that Russell produced the bulk of his mathematical work. He became interested in the then-new field of set theory, devised by Georg Cantor but clearly formalized by Giuseppe Peano in his 1888 book Calcolo geometrico. Russell immediately spotted a flaw, which he exposed through a famous paradox. He then published Principles of Mathematics in 1903 (see box) and, with Alfred Whitehead, the Principia Mathematica, whose three volumes appeared between 1910 and 1913.