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Arthur Black was born in Brighton, the eldest of 8 children. His sister Constance, later Constance Garnett, was to become famous for her translations of the novels of Tolstoy and Dostoyevsky. Arthur Black studied mathematics under William Kingdon Clifford, Professor of Applied Mathematics at University College London. He was a favourite pupil of Clifford, who was impressed by Black's brilliance. He took his degree by private study and achieved his BSc in 1877. After this he worked as an army coach and tutor in Brighton, while pursuing his mathematical and philosophical interests. His marriage was allegedly unhappy. He took his own life in January 1893, having not published any of his mathematical work. The main focus of Black's work seems to have been an attempt to use his mathematical skills to develop a quantitative theory of evolution.