He attended several undergraduate institutions, including the University of Chicago, where professor Saunders Mac Lane was a source of inspiration. He began his graduate studies in mathematics at Chicago, briefly studied at Oklahoma Agricultural and Mechanical University and the University of Kansas, and eventually completed a Doctor of Philosophy in game theory at Princeton University in 1954 under the supervision of Albert West. Tucker.
After graduation, Isbell was drafted into the United States. Army, and stationed at the Aberdeen Proving Ground. In the late 1950s he worked at the Institute for Advanced Study in Princeton, New Jersey, from which he then moved to the University of Washington and Case Western Reserve University. He joined the University at Buffalo in 1969, and remained there until his retirement in 2002.
Isbell published over 140 papers under his own name, and several others under pseudonyms.
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
Isbell published other articles using two additional pseudonyms, M. G. Stanley and H. C. Enos, publishing two under each. He was "the leading contributor to the theory of uniform spaces".
Isbell was the first to study the category of metric spaces defined by metric spaces and the metric maps between them, and did early work on injective metric spaces and the tight span construction.
In abstract algebra, 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, Isbell was the first to prove the bound χ ≤ 7 on the Hadwiger–Nelson problem, the question of how many colors are needed to color the points of the plane in such a way that no two points at unit distance from each other have the same color.
Mathematical Reviews "M. G. "H. C.
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 between sober spaces and complete Heyting algebras with sufficiently many points.