Black, Max (1909–1988)

Azeri-born US philosopher and mathematician. Investigating the question, ‘What is mathematics?’, he divided the answers into three schools: the logical, the formalist, and the intuitional.

Black, born in Baku, studied philosophy at Cambridge and London universities. Moving to the USA in 1940, he worked from 1946 at Cornell, where he was professor of philosophy 1954–77.

Black described mathematics as the study of all structures whose form may be expressed in symbols. Within that broad spectrum are the three main schools. The logical considers that all mathematical concepts, such as numbers or differential coefficients, are capable of purely logical definition. The formalist 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 intuitional 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's works include The Nature of Mathematics (1950) and Problems of Analysis (1954).