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 largest city in the U.S. state of Oregon. Situated at the confluence of the Willamette and Columbia rivers, Portland is the county seat of Multnomah County, the most populous ...

, the son of an army officer from Isbell, a town in Franklin County, Alabama... He attended several undergraduate institutions, including the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...

, 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 Oklahoma (; Choctaw: ; chr, ᎣᎧᎳᎰᎹ, ''Okalahoma'' ) is a state in the South Central region of the United States, bordered by Texas on the south and west, Kansas on the north, Missouri on the northeast, Arkansas on the east, New M ...

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 Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...

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 ...

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 w ...

, 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 Seatt ...

and

Case Western Reserve University Case Western Reserve University (CWRU) is a private research university in Cleveland, Ohio. Case Western Reserve was established in 1967, when Western Reserve University, founded in 1826 and named for its location in the Connecticut Western Reser ...

. 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
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 individu ...

s. Isbell published the first paper by

John Rainwater The fictitious mathematician John Rainwater was created as a student prank but has become known as the author of important results in functional analysis. At the University of Washington in 1952, John Rainwater was invented and enrolled in a mat ...

, 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 defi ...

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 Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, ca ...

: *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; a standard example is the

Stone duality In mathematics, there is an ample supply of categorical dualities between certain categories of topological spaces and categories of partially ordered sets. Today, these dualities are usually collected under the label Stone duality, since they f ...

between sober spaces 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 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 setti ...

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 19 ...

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 groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The ter ...

, Isbell found a rigorous formulation for the Pierce–Birkhoff conjecture on piecewise-polynomial functions. He also made important contributions to the theory of median algebras. 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 associ ...

the points of the plane in such a way that no two points at unit distance from each other have the same color..

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

Biography

Research

See also

References

External resources

Mathematical Reviews