Errett A. Bishop, Mathematics: San Diego
(A) Mathematics is common sense. (B) Do not ask whether a statement is true until you know what it means. (C) A proof is any completely convincing argument. (D) Meaningful distinctions deserve to be preserved. These principles of constructivism were elucidated by Errett Bishop in a 1973 paper with the title “Schizophrenia in contemporary mathematics.” Errett Bishop is universally recognized as an outstanding mathematician, one of the great analysts of the present time. By the mid 1960s, there were theorems and methods attributed to him in many areas of mathematicssimply beautiful results which remain as a seminal influence. About 1964 his interests turned toward the foundations of mathematics. Indeed, the above principles from Errett's paper are epitaphial since constructivism dominated his research from about 1964 until his illness in 1982. These principles certainly lend a rough sculpture of his personality. Errett Bishop died of cancer on April 14, 1983. The epitaph only hints of the power and concentration Errett brought to bear on the problems he worked on and of the originality, depth, and insight he displayed in his research. It does speak, however, of simplicity and honesty, and it surely speaks of a clear mind and fierce independence. Errett was a sincere and compassionate friend to many of us in the department. To us who knew him well, his epitaph speaks, further, of the strong principles by which he lived. He had a strong feeling for fairness in the treatment of other peoplehis colleagues, his students. He treated people with kindness and consideration. We shall never forget him. It is appropriate to mention Errett's father, Albert T. Bishop, before discussing Errett's career in more detail. Albert T. Bishop graduated from West Point and served in the U.S. Army during World War I. Later on, he was a professor of mathematics at several universities: at career's end, at the University of Wichita until failing health forced early retirement. Errett himself was born in Newton, Kansas, on July 24, 1928. It is noteworthy ― 25 ―
that Errett began serious study by picking his way through a pile of textbooks which remained in the family home after Albert's
death in 1933.
It was clear early on that Errett was a brilliant student. Undoubtedly he was not challenged by high school work. When he learned of a special scholarship program at the University of Chicago, he applied and was accepted at the age of 16. He received the B.S. degree at the age of 19 and the M.S. two years later (finishing the M.S. in 1949). As only a sophomore, he took a graduate level course in probability taught by Paul Halmos, who eventually became his thesis advisor. It is remembered that Halmos once suggested to this class that they find one example of a certain unusual phenomenon. Errett was not satisfied to do this; his paper contained a general theorem, a necessary and sufficient condition for that phenomenon to occur! The theorem was new to Halmos. Finally, any recollection of the Chicago years should include Errett's sister, Mary Weiss, who was two years young than himself. Mary was also a child prodigy. She was accepted by the (same) special scholarship program at the University of Chicago and received the Ph.D. in mathematics in 1957. Mary Weiss died in 1966. From 195052 Errett served in the U.S. Army. The Army showed good judgment by assigning him (after basic training) to do mathematical research at the National Bureau of Standards. This work was recognized by an award: he received a “Commendation ribbon with pendant for mathematical research in Army Ordnance.” In 1952 he returned to the University of Chicago and obtained his Ph.D. in 1954. Halmos, his advisor, said: “As a student he was outstanding and with the writing of his thesis he became spectacular.” Errett's thesis was a penetrating study of a generalized version of spectral theory. Errett began his teaching career at Berkeley in 1954, where he remained until 1965, with the exception of one and onehalf years spent at Princeton as a member of the Institute for Advanced Study. His academic career was absolutely brilliant. In his first eight years at Berkeley, he advanced from instructor to a full professor in their very distinguished mathematics department. He had a Sloan fellowship during three of those years. Also, he spent the years 196465 as a member of the Miller Institute for Basic Research in Berkeley. At the Miller Institute, he devoted full time to research in preparation for his remarkable book, which we describe later on. Errett accepted an offer from our young Department of Mathematics at UCSD in 1965. He remained at UCSD until his illness and death in 1983. It is not easy to summarize Errett's work. Many mathematicians earn their reputation by doing outstanding work in one area, but Errett made his mark in many. He had the ability of going into a new field and in two or three papers advancing it in an essential way. He has many times succeeded in unifying and extending a field by introducing the right kind ― 26 ―
of imaginative new concepts. He did that first in operator theory in Hilbert space and in Banach space; next in the theory
of polynomial approximation in the complex plane and on Riemann surfaces. The latter led Errett to his outstanding work in
function algebras. This work in turn led him to his highly original approach to the theory of functions of several complex
variables. He applied here the methods of functional analysis as a new and powerful tool. This work had a strong impact on
the theories of mathematicians in Europe.
We mentioned that Errett began struggling with foundational issues in 1964 or so (about the time he was at the Miller Institute). Despite his extraordinary successes in so many fieldswhich brought him recognition and acclaim of his peershis independent mind drove him to think about the basic meaning of it all. He felt there is a crisis in mathematics due to our neglect of philosophical issues. His motivation was to explore the meaning of mathematics: he felt, particularly, that we are proving many theoremsmore today than ever beforewithout knowing what they mean. He asked “Is pure mathematics simply a game which we play or do our theorems describe an external reality?” The occupation with these ideas lead to the appearance of his book on Foundations of Modern Analysis in 1968 in which he develops a large part of modern analysis by socalled “constructive” methods. The leading protagonist of the constructivist cause in the early part of this century was the Dutch mathematician, J. L. E. Brouwer. Brouwer and his followers, the “intuitionists,” introduced methods which appeared unacceptable to most mathematicians. In view of this situation it was a most remarkable achievement that Errett produced a simple and systematic treatment showing that almost all of the important material of modern analysis can be dealt with by methods not far removed from the classical approach. In many cases it deepens the understanding of the theorems. Errett Bishop will be remembered as one of the outstanding mathematicians in the world. He will be remembered for his sense of justice, for the integrity and dignity of his personal life. He is survived by his wife, Jane, their two sons, Edward and Thomas, and by their daughter, Rosemary. He is survived, also, by his mother, Helen. Errett will be sorely missed by his colleagues and by his friends who both respected him and loved him deeply.
Leonard R. Haff
Murray Rosenblatt
Stefan E. Warschawski
