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Summary Article: Black, Max (1909-1988)
from The Hutchinson Dictionary of Scientific Biography

Place: United States of America, Russian Federation

Subject: biography, maths and statistics

Russian-born US philosopher and mathematician, one of whose concerns was to investigate the question ‘what is mathematics?’.

Black was born in Baku, Azerbaijan, on 24 February 1909, and he received his higher education in England where he studied philosophy, gaining his BA at Cambridge University in 1930 and his PhD from London University in 1939. From 1936-40 he was a lecturer at the University of London Institute of Education. He went to the USA in 1940 to take up a post in the department of philosophy at the University of Illinois. He became a naturalized US citizen in 1948. He moved from the University of Illinois to Cornell in 1946 and was Susan Lin-Sage Professor of Philosophy and Humane Letters there 1954-77, when he retired. In 1970 he was vice-president of the International Institute of Philosophy.

Black's analysis led him to describe mathematics as the study of all structures whose form may be expressed in symbols. Within that broad spectrum there are three main schools of mathematics: the logical, the formalist, and the intuitional. The logical considers that all mathematical concepts, such as numbers or differential coefficients, are capable of purely logical definition, so that mathematics becomes a branch of logic. The formalist, rejecting the notion that all mathematics can be expressed as logical concepts, looks upon mathematics as the science of the structure of objects and concerns itself with the structural properties of symbols, independent of their meaning. The formalist approach has been especially fruitful in its application to geometry. The third school, the intuitional, by laying less emphasis on symbols and more on thought, considers mathematics to be grounded on the basic intuition of the possibility of constructing an infinite series of numbers. This approach has had most influence in the theory of sets of points.

Black has thus done little work in mathematics itself, but his writings, such as The Nature of Mathematics (1950) and Problems of Analysis (1954), have been a major contribution to the philosophy of mathematics.

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