Marshall Stone and duality: from differential equations to Boolean algebras

In this chapter, we investigate the contributions of Marshall Stone (1903-1989) to the study of phenomena of duality in mathematics. In fact, Stone’s name is related to the history of at least two such phenomena, namely adjoint (or dual) operators in functional analysis, and the result known as Stone duality in the theory of Boolean algebras. Note that the two phenomena, although they both mark the scientific work of the same mathematician, are quite different in nature. First of all, they belong to two fields of mathematical research which are quite different, and in fact quite remote of each other—which makes it particularly challenging for a single historian of mathematics to study them both. Second, they belong to different types of what I labelled somewhat helplessly “phenomena”. The notion of adjoint operator is a notion. And historical questions to be asked with respect to such a thing like a notion are: Why was it introduced, what purpose did it serve for, which problems had been solved by its introduction, which other notions might have inspired its introduction, which were the backgrounds of the researchers introducing it and which role might they have played and so on. Stone duality, on the other hand, is a theorem.