John Rolfe Isbell (October 27, 1930 – August 6, 2005) was an American mathematician, for many years a professor of mathematics at the
University at Buffalo (SUNY).
Biography
Isbell was born in
Portland, Oregon
Portland (, ) is a port city in the Pacific Northwest and the list of cities in Oregon, largest city in the U.S. state of Oregon. Situated at the confluence of the Willamette River, Willamette and Columbia River, Columbia rivers, Portland is ...
, the son of an army officer from Isbell, a town in
Franklin County, Alabama
Franklin County is a county located in the U.S. state of Alabama. As of the 2020 census, the population was 32,113. Its county seat is Russellville. Its name is in honor of Benjamin Franklin, famous statesman, scientist, and printer. It is a ...
.
[.][.] He attended several undergraduate institutions, including the
University of Chicago
The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...
, where professor
Saunders Mac Lane
Saunders Mac Lane (4 August 1909 – 14 April 2005) was an American mathematician who co-founded category theory with Samuel Eilenberg.
Early life and education
Mac Lane was born in Norwich, Connecticut, near where his family lived in Taftville ...
was a source of inspiration.
He began his graduate studies in mathematics at Chicago, briefly studied at
Oklahoma A&M University and the
University of Kansas
The University of Kansas (KU) is a public research university with its main campus in Lawrence, Kansas, United States, and several satellite campuses, research and educational centers, medical centers, and classes across the state of Kansas. T ...
, and eventually completed a Ph.D. in
game theory at
Princeton University
Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ...
in 1954 under the supervision of
Albert W. Tucker.
After graduation, Isbell was drafted into the
U.S. Army
The United States Army (USA) is the land service branch of the United States Armed Forces. It is one of the eight U.S. uniformed services, and is designated as the Army of the United States in the U.S. Constitution.Article II, section 2, cl ...
, and stationed at the
Aberdeen Proving Ground
Aberdeen Proving Ground (APG) (sometimes erroneously called Aberdeen Proving ''Grounds'') is a U.S. Army facility located adjacent to Aberdeen, Harford County, Maryland, United States. More than 7,500 civilians and 5,000 military personnel work a ...
.
In the late 1950s he worked at the
Institute for Advanced Study
The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent schola ...
in
Princeton, New Jersey
Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...
, from which he then moved to the
University of Washington
The University of Washington (UW, simply Washington, or informally U-Dub) is a public research university in Seattle, Washington.
Founded in 1861, Washington is one of the oldest universities on the West Coast; it was established in Seattl ...
and
Case Western Reserve University. He joined the
University at Buffalo
The State University of New York at Buffalo, commonly called the University at Buffalo (UB) and sometimes called SUNY Buffalo, is a public research university with campuses in Buffalo and Amherst, New York. The university was founded in 18 ...
in 1969, and remained there until his retirement in 2002.
[Announcement of Isbell's death](_blank)
in ''Topology News'', October 2005.
Research
Isbell published over 140 papers under his own name, and several others under
pseudonym
A pseudonym (; ) or alias () is a fictitious name that a person or group assumes for a particular purpose, which differs from their original or true name (orthonym). This also differs from a new name that entirely or legally replaces an individua ...
s. Isbell published the first paper by
John Rainwater, a fictitious mathematician who had been invented by graduate students at the University of Washington in 1952. After Isbell's paper, other mathematicians have published papers using the name "Rainwater" and have acknowledged "Rainwater's assistance" in articles.
[The seminar on ]functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined o ...
at the University of Washington has been called the "Rainwater seminar". Isbell published other articles using two additional pseudonyms, M. G. Stanley and H. C. Enos, publishing two under each.
Many of his works involved
topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...
and
category theory:
*He was "the leading contributor to the theory of
uniform space
In the mathematical field of topology, a uniform space is a set with a uniform structure. Uniform spaces are topological spaces with additional structure that is used to define uniform properties such as completeness, uniform continuity and unifo ...
s".
*Isbell duality is a form of
duality arising when a mathematical object can be interpreted as a member of two different
categories
Category, plural categories, may refer to:
Philosophy and general uses
*Categorization, categories in cognitive science, information science and generally
*Category of being
* ''Categories'' (Aristotle)
*Category (Kant)
* Categories (Peirce)
* ...
; a standard example is the
Stone duality between
sober space In mathematics, a sober space is a topological space ''X'' such that every (nonempty) irreducible closed subset of ''X'' is the closure of exactly one point of ''X'': that is, every irreducible closed subset has a unique generic point.
Definitio ...
s and
complete Heyting algebra
In mathematics, especially in order theory, a complete Heyting algebra is a Heyting algebra that is complete as a lattice. Complete Heyting algebras are the objects of three different categories; the category CHey, the category Loc of locales, ...
s with sufficiently many points.
*Isbell was the first to study the
category of metric spaces In category theory, Met is a category that has metric spaces as its objects and metric maps (continuous functions between metric spaces that do not increase any pairwise distance) as its morphisms. This is a category because the composition of two ...
defined by
metric space
In mathematics, a metric space is a set together with a notion of '' distance'' between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are the most general set ...
s and the
metric map In the mathematical theory of metric spaces, a metric map is a function between metric spaces that does not increase any distance (such functions are always continuous).
These maps are the morphisms in the category of metric spaces, Met (Isbell 1 ...
s between them, and did early work on
injective metric space In metric geometry, an injective metric space, or equivalently a hyperconvex metric space, is a metric space with certain properties generalizing those of the real line and of L∞ distances in higher-dimensional vector spaces. These properties ca ...
s and the
tight span
In metric geometry, the metric envelope or tight span of a metric space ''M'' is an injective metric space into which ''M'' can be embedded. In some sense it consists of all points "between" the points of ''M'', analogous to the convex hull of a ...
construction.
In
abstract algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include group (mathematics), groups, ring (mathematics), rings, field (mathematics), fields, module (mathe ...
, Isbell found a rigorous formulation for the
Pierce–Birkhoff conjecture In abstract algebra, the Pierce–Birkhoff conjecture asserts that any piecewise-polynomial function can be expressed as a Supremum, maximum of finite Infimum, minima of finite collections of polynomials. It was first stated, albeit in non-Mathemati ...
on piecewise-polynomial functions. He also made important contributions to the theory of
median algebra In mathematics, a median algebra is a set with a ternary operation \langle x,y,z \rangle satisfying a set of axioms which generalise the notions of medians of triples of real numbers and of the Boolean majority function.
The axioms are
# \lang ...
s.
In
geometric graph theory
Geometric graph theory in the broader sense is a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. In a stricter sense, geometric graph theory studies combinatorial and geometric properties of geome ...
, Isbell was the first to prove the bound χ ≤ 7 on the
Hadwiger–Nelson problem
In geometric graph theory, the Hadwiger–Nelson problem, named after Hugo Hadwiger and Edward Nelson, asks for the minimum number of colors required to color the plane such that no two points at distance 1 from each other have the same color. ...
, the question of how many colors are needed to
color
Color (American English) or colour (British English) is the visual perceptual property deriving from the spectrum of light interacting with the photoreceptor cells of the eyes. Color categories and physical specifications of color are assoc ...
the points of the plane in such a way that no two points at unit distance from each other have the same color.
[.]
See also
*
Isbell conjugacy
References
External resources
Mathematical Reviews
*
*Pseudonyms used by Isbell (and other mathematicians):
**
**
**
{{DEFAULTSORT:Isbell, John Rolfe
1930 births
2005 deaths
20th-century American mathematicians
21st-century American mathematicians
Category theorists
Game theorists
Topologists
University of Chicago alumni
Princeton University alumni
University of Washington faculty
Case Western Reserve University faculty
University at Buffalo faculty
American operations researchers
Lattice theorists
Mathematicians from Oregon