| IN MEMORIAM
WILLIAM T. EATON
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.
<Signed>
Larry R. Faulkner, President
The University of Texas at Austin
<Signed>
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. |
