Index of Memorial Resolutions and Biographical Sketches

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It certainly can be argued that each of us is an individual, with special characteristics that set us apart from the rest, but few have been so noticeably successful and taken as much pride in their individuality as did Bill Eaton. While most of us feel compelled to fit in, to conform to our surroundings and quietly adopt the habits and values of those around us, Bill went his own way, with enthusiasm and a margin of defiance. He loved to point out examples in the world of what one might call the Emperor’s New Clothes phenomenon, that is, situations where we all accept an established mode of behavior that really makes little or no sense. He scorned automobile and health insurance as a waste of money. He may not have always been right, but he was never in doubt, and his approach was a constant reminder to look at our own beliefs and ask if we are being completely honest with ourselves.

William T. Eaton was born February 22, 1938, and grew up in Oxnard, California. In high school he was an outstanding athlete; as a single wing tailback he was offered a football scholarship to UCLA, one of the few colleges that still used the single wing offense. He chose instead to attend the University of Utah and major in mathematics. As an undergraduate Bill participated in the Naval ROTC program, but after a tour of summer duty along the coast of South America he came to the conclusion that he would be better off out of the program. When it became clear that he would not be released, he spent a semester skiing, thereby failing all of his classes and resulting in his dismissal from ROTC. While it accomplished his purpose, this strategy may have influenced his choices for graduate school since he remained at Utah for both his M.S. and Ph.D. degrees, studying topology under the supervision of C. E. Burgess. There is a contrasting story as to how this semester occurred that should also be mentioned. It says that Bill encountered the Four Color Problem, a famous conjecture in topology, and it was the conjecture rather than the skiing that took him away from his other academic obligations. Since Bill was likely to be distracted by both skiing and mathematics, perhaps both stories contain a measure of truth.

Following graduate school Bill took a faculty position at the University of Tennessee. Two years later the quality of his research led to his receiving a prestigious Alfred P. Sloan Fellowship, and he used his support for 1969-1970 as a member of the Institute for Advanced Study in Princeton. In the fall of 1970 he joined the faculty of The University of Texas at Austin where he remained for the rest of his career. Bill was quickly promoted to associate professor in 1971 and to professor in 1977. At a time when the Department of Mathematics was entering a period of rapid growth and improvement, Bill played an active role in undergraduate and graduate teaching and the development of a strong research group in topology. A significant step in this expansion was the recruitment of R. H. Bing from Wisconsin back to his original home at The University of Texas, an event in which Bill played a major role.

In June of 1961 Bill married Ann Stacey, and their family grew to include daughters Stacie Marie (1968) and Jennifer Lynn (1971). He loved his family, and their outings in their boat on area lakes were often shared with friends. Bill was an avid bridge player, analytical and competitive while maintaining an engaging sense of humor, and he played tennis with the intensity of a former athlete. His competitiveness extended once to claiming he could outrun a horse over a short distance. The resolution of this debate is now clouded in contemporary memory, but the most reliable sources indicate he lost the race and the wager. But his spirit was not diminished.

Bill did significant research in a field known as geometric topology. His work included the investigation of esoteric objects known as wild surfaces and wild Cantor sets. He was at home constructing these wild objects in dimensions four and higher, and he was able to prove that some wild objects are less wild than one might imagine. In particular, he was able to prove that any wild 2-sphere embedded in 3-space can be sandwiched between two parallel smooth 2-spheres so that the wild sphere sticks out in small spots on each side. This 2-sided approximation theorem was one of the important tools used in understanding the geometric topology of 3-dimensional space. With Carl Pixley, Bill also proved an important theorem about decomposition spaces.

One of the highlights of Bill’s research career occurred in January of 1976. Professor Emeritus H. J. Ettlinger established a prize in honor of two of his most famous colleagues in the Department of Mathematics, R. L. Moore and H. S. Wall. The award of $3,000 was to go to a member of the department in recognition of outstanding research. A selection committee of internationally known mathematicians chose Bill as the recipient for his work in the paper “The sum of solid spheres” published in the Michigan Mathematics Journal in 1972. The presentation of the award occurred at the Annual Meeting of the American Mathematical Society in San Antonio and was attended by many distinguished mathematicians as well as the president of the University and the dean of the college.

In his later years much of Bill’s attention was focused on the PL Schoenfliess Theorem. Given a polygonal closed curve in the plane, one can slide the polygon through some simple maneuvers that will systematically transform the polygon into a triangle. This fact is known as the PL Schoenfliess Theorem in dimension 2. An analogous statement is true in dimension 3, but the question remains unresolved in dimension four or higher. For twenty years Bill worked to prove this theorem in dimension four. He was able to prove some special cases of the theorem, and from time to time he felt close to having a complete proof, a step that would have led to international acclaim, but he was never able to complete the argument. His work was valuable in that it led to greater understanding of the geometry of dimension four, and his dogged determination stands as an example of taste in choosing difficult and important problems and practicing an unrelenting commitment to finding answers to important questions.

As a citizen of the department, Bill argued that the people we hired must be of the best quality. He was willing to take extreme steps, in salary or title, if they had the potential to improve our faculty. One prominent example of this was Bill’s argument that we should offer a chair to a fresh Ph.D. named Donaldson, who eventually became one of the most prominent mathematicians of our time. Bill was something of a maverick in his teaching as well; he taught a number of classes using the Moore method, named for the famous member of the department who produced so many outstanding students, and he was inclined to propose radical revisions of our system of qualifying exams. He did in truth march to the beat of a different drum.

On a personal level Bill and his family were always close to other members of the department. He was a devoted father and friend, with a warm sense of humor, who brought a vibrant honesty, playfulness, and vitality to our lives that we will all miss.

Larry R. Faulkner, President
The University of Texas at Austin

John R. Durbin, Secretary
The General Faculty

This memorial resolution was prepared by a special committee consisting of Professors James W. Vick (chair), Gary C. Hamrick, and Michael P. Starbird.