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Karl Heinrich Marx (5 May 1818 – 14 March 1883) was a German philosopher, economist, sociologist, historian, journalist, and revolutionary socialist. His ideas played a significant role in the development of social science and the socialist political movement. He published various books during his lifetime, with the most notable being The Communist Manifesto (1848) and Capital (1867–1894); some of his works were co-written with his friend and fellow German revolutionary socialist, Friedrich Engels.
Born into a wealthy middle class family in Trier, formerly in Prussian Rhineland now called Rhineland-Palatinate, Marx studied at both the University of Bonn and the University of Berlin, where he became interested in the philosophical ideas of the Young Hegelians. In 1836, he became engaged to Jenny von Westphalen, marrying her in 1843. After his studies, he wrote for a radical newspaper in Cologne, and began to work out his theory of dialectical materialism. Moving to Paris in 1843, he began writing for other radical newspapers. He met Engels in Paris, and the two men worked together on a series of books. Exiled to Brussels, he became a leading figure of the Communist League, before moving back to Cologne, where he founded his own newspaper. In 1849 he was exiled again and moved to London together with his wife and children. In London, where the family was reduced to poverty, Marx continued writing and formulating his theories about the nature of society and how he believed it could be improved, and also campaigned for socialism—he became a significant figure in the International Workingmen's Association.
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these in any profound sense. He was born in Monmouthshire, into one of the most prominent aristocratic families in Britain.
Russell led the British "revolt against idealism" in the early 20th century. He is considered one of the founders of analytic philosophy along with his predecessor Gottlob Frege and his friend Ludwig Wittgenstein, and is widely held to be one of the 20th century's premier logicians. He co-authored, with A. N. Whitehead, Principia Mathematica, an attempt to ground mathematics on logic. His philosophical essay "On Denoting" has been considered a "paradigm of philosophy." His work has had a considerable influence on logic, mathematics, set theory, linguistics, computer science (see type theory and type system), and philosophy, especially philosophy of language, epistemology, and metaphysics.