He was born in Trelleck, Wales. His parents died when he was 3 years old. He was educated privately and went to Trinity College, Cambridge, where he was a brilliant student of mathematics and philosophy. In 1900, Russell became acquainted with the work of the Italian mathematician Peano, which inspired him to write The Principles of Mathematics (1903), expanded in collaboration with Alfred North Whitehead into three volumes of Principia Mathematica (1910-13). The research, which Russell did during this period together with Whitehead and which is preserved in many books and essays, establishes him as one of the founding fathers of modern analytical philosophy. Throughout his life Russell has also been an extremely outspoken and aggressive moralist in the rationalist tradition of Locke and Hume. His many essays, often in the form of short reflections or observations on moral or psychological topics, are written in a terse, vivid, and provocative style. His greatest literary achievement has been his History of Western Philosophy (1946).
Russell's external career has been chequered. The descendant of one of the great families of the Whig aristocracy, he has always delighted in standing up for his radical convictions with wilful stubbornness. In 1916, he was deprived of his lectureship at Trinity College, Cambridge, after his pacifist activities had brought him into conflict with the government, but in 1946 he was reelected a Fellow. In 1918, he even went to prison for six months, where he wrote his Introduction to Mathematical Philosophy (1919). In 1920, Russell travelled in Russia and, subsequently, taught philosophy at Peking for a year. He went to the United States in 1938 and taught there for several years at various universities. Lord Russell has been a Fellow of the Royal Society since 1908; he succeeded to the earldom in 1931 and, in 1949, received the Order of Merit.
In recent years Lord Russell has been active in political organizations such as the Campaign for Nuclear Disarmament and other groups with similar aims. The first two volumes of his autobiography, covering the years from 1872 to 1944, appeared in 1967 and 1968, respectively.