Errett Bishop: Reflections on Him and His Research

This book is the proceedings of the Memorial Meeting for Errett Bishop, held at the University of California, San Diego, 24 September 1983. During his early days as a mathematician, Errett Bishop made distinguished contributions in many branches of analysis---first in operator theory in Hilbert and Banach spaces, then in the theory of polynomial approximation in the complex plane and on Riemann surfaces, and thence to his outstanding research in function algebras. This work in turn led him to his highly original approach to the theory of functions of several complex variables. About 1964 Bishop turned his interests toward the foundations of mathematics. Whereas L. E. J. Brouwer's intuitionism took as basic the integers and the real numbers, Bishop proposed that the integers are the only basic, irreducible mathematical construct. His remarkable 1968 book, "Foundations of Constructive Analysis", was devoted to the development of a large part of modern analysis, suitably modified, on this one concept. The object of the present book is to present a view of Errett Bishop, who died suddenly in 1983 at the age of 54, as a human being, a colleague, and a mathematician. An eloquent statement of his philosophy is contained in his paper, "Schizophrenia in Contemporary Mathematics", which resulted from his AMS Colloquium Lectures in 1973 and which occupies about one-third of the book.