Mathematician. Born at Stonebyres (South Lanarkshire) and educated at the University of Glasgow, where William Thomson, Lord Kelvin (1824 - 1907) recognised his abilities in mathematics. Muir became a tutor at the University of St. Andrews, taking the opportunity to travel in Europe. He was appointed to the University of Glasgow (1871) then became a teacher at Glasgow High School (1874). Muir became Superintendent General of Education in South Africa (1892), where he introduce many educational reforms and was knighted in 1910. His main work was a History of Determinants, the sixth volume of which he was still completing at the time of his death.
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