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Branches of Mathematics

Pure mathematics

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Listen to Ludwig Wittgenstein interviews

Ludwig Josef Johann Wittgenstein (26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He was professor in philosophy at the University of Cambridge from 1939 until 1947. In his lifetime, he published just one book review, one article, a children's dictionary, and the 75-page Tractatus Logico-Philosophicus (1921). In 1999, his posthumously published Philosophical Investigations (1953) was ranked as the most important book of 20th-century philosophy, standing out as "...the one crossover masterpiece in twentieth-century philosophy, appealing across diverse specializations and philosophical orientations".Bertrand Russell described him as "the most perfect example I have ever known of genius as traditionally conceived, passionate, profound, intense, and dominating".

Born in Vienna into one of Europe's wealthiest families, he gave away his entire inheritance. Three of his brothers committed suicide, with Ludwig contemplating it too. He left academia several times: serving as an officer on the frontline during World War I, where he was decorated a number of times for his courage; teaching in schools in remote Austrian villages, where he encountered controversy for hitting children when they made mistakes in mathematics; and working during World War II as a hospital porter in London, where he told patients not to take the drugs they were prescribed, and where no-one knew he was one of the world's most famous philosophers. He described philosophy, however, as "the only work that gives me real satisfaction."

This page contains text from Wikipedia, the Free Encyclopedia - http://en.wikipedia.org/wiki/Ludwig_Wittgenstein

This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.

Listen to Karl Marx interviews

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.

This page contains text from Wikipedia, the Free Encyclopedia - http://en.wikipedia.org/wiki/Karl_Marx

This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.

Listen to Bertrand Russell interviews

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.

Branches of Mathematics

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Applied mathematics

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