The WKB Method

Abstract

Walter Gunther Kaufmann-B/ihler died at 2:30 P.M. on 22 December 1986, as the result of a severe asthma attack. For 13 years, Walter was the mathematics editor at Springer-Verlag New York. His work has had an effect on virtually all contemporary mathematicians. Different people saw Walter in different ways. To some, he was a person at the other end of a phone line who kept his promises and worked quickly and effectively. To those of us who were lucky enough to know him better, he was much more. A personality can't be summarized in a sentence, but Walter was an extraordinary mixture of hard work, humor, intelligence, and creat ivi ty--and fantastic integrity, the like of which I have never observed in any other person. Walter arrived early at the office and worked himself hard, with great concentration. He was certainly not above taking a break now and then, but often, at some point while standing around joking, he would suddenly say rather severely, "All right. Let's do some work now," as though he felt guilty for having taken some time off. Yet Walter had a very strong sense of humor , often bordering on the bizarre. Few people wi th so much responsibility and respect can take pleasure in taping colleagues' phones to their desks, or trapping them in their offices by blocking the door with a large bookcase. Walter was not particularly fashion conscious. His hair seemed to attract static electricity and, more often than not, was standing out at a variety of angles. His usual mode of dress was Levi corduroys, a shirt and tie, and a tweed jacket. Waiter's only extravagance was his Bally shoes; some years ago he had found the exact model and size that fit him perfectly, and thereafter he always bought precisely these. His shoes had to be comfortable because he did a lot of walking. For one thing, he walked back and forth over a mile to Grand Central Station every day, where he took the train to Mount Kisco, NY, and then walked to his home. Accompanying him on this trek was not an Springer-Verlag New York 175 Fifth Avenue New York, NY 10010 USA easy task, as he walked extremely quickly. Walter combined his interest in mathematics with his long-standing interest in history, producing a biography of Gauss, which, in fact, he had just translated into German. He also wrote and translated several articles on the history of mathematics, for example "The Hypergeometric Funct ion--A Biographical Sketch," Mathematical Intelligencer, Vol. 7 (1985), No. 2, 35-40. Walter had just begun to write a biography of Euler; shortly before his death, the volumes of Euler's Opera Omnia that he had ordered began to arrive. Extremely well read, Walter had broad tastes in literature. He liked John Barth and Thomas Berger, and he loved Goethe. Sometimes he enjoyed needling people with pithy little German quotations to suit the occasion. He had recently discovered Aubrey's Brief Lives, a quirky collection of half-finished biographical sketches, which he found most amusing. In fact, before Walter settled on the Euler .project, he had been writing a series of brief lives of imaginary mathematicians. One of them, Polybios Hesse, had "sort of" discovered G6del's incompleteness theorem in the eighteenth century. A good part of Walter's lunch hour was often spent browsing for bargains at Barnes and Noble, where he was somewhat more likely to pick up a history book than a novel. Walter had a flair for languages. Although he spoke with a heavy German accent, his English was excellent, and he had a better feeling for it than most native speakers of the language. He also knew French and Latin, and some Russian, Greek, Italian, and Hebrew. Walter is survived by his wife, Melissa, and two sons, Toby and Phillip. As Aubrey said of John Dee, astrologer and mathematician, "A mighty good man he was."