Victor LaRue Klee, Jr. (September 18, 1925 – August 17, 2007) was a

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

specialising in

convex set In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset contains the whole line segment that joins them. Equivalently, a convex set or a convex r ...

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 space#Definition, inner product, Norm (mathematics)#Defini ...

analysis of algorithms In computer science, the analysis of algorithms is the process of finding the computational complexity of algorithms—the amount of time, storage, or other resources needed to execute them. Usually, this involves determining a function that re ...

optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...

, and

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many appl ...

. He spent almost his entire career at 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 Seattle a ...

Seattle Seattle ( ) is a seaport city on the West Coast of the United States. It is the seat of King County, Washington. With a 2020 population of 737,015, it is the largest city in both the state of Washington and the Pacific Northwest regio ...

Life

Born in

San Francisco San Francisco (; Spanish language, Spanish for "Francis of Assisi, Saint Francis"), officially the City and County of San Francisco, is the commercial, financial, and cultural center of Northern California. The city proper is the List of Ca ...

, Vic Klee earned his

B.A. Bachelor of arts (BA or AB; from the Latin ', ', or ') is a bachelor's degree awarded for an undergraduate program in the arts, or, in some cases, other disciplines. A Bachelor of Arts degree course is generally completed in three or four yea ...

degree in 1945 with high honors from

Pomona College Pomona College ( ) is a private liberal arts college in Claremont, California. It was established in 1887 by a group of Congregationalists who wanted to recreate a "college of the New England type" in Southern California. In 1925, it became ...

, majoring in mathematics and chemistry. He did his graduate studies, including a thesis on Convex Sets in Linear Spaces, and received his PhD in mathematics from the

University of Virginia The University of Virginia (UVA) is a Public university#United States, public research university in Charlottesville, Virginia. Founded in 1819 by Thomas Jefferson, the university is ranked among the top academic institutions in the United S ...

in 1949. After teaching for several years at the University of Virginia, he moved in 1953 to the

Seattle, Washington Seattle ( ) is a port, seaport city on the West Coast of the United States. It is the county seat, seat of King County, Washington, King County, Washington (state), Washington. With a 2020 population of 737,015, it is the largest city in bo ...

, where he was a faculty member for 54 years. He died in

Lakewood, Ohio Lakewood is a city in Cuyahoga County, Ohio, Cuyahoga County, Ohio, United States, on the southern shore of Lake Erie. Established in 1889, it is one of Cleveland's historical streetcar suburbs and part of the Greater Cleveland, Greater Clevelan ...

Research

Klee wrote more than 240 research papers. He proposed

Klee's measure problem In computational geometry, Klee's measure problem is the problem of determining how efficiently the measure of a union of ( multidimensional) rectangular ranges can be computed. Here, a ''d''-dimensional rectangular range is defined to be a Cart ...

and the

art gallery problem The art gallery problem or museum problem is a well-studied visibility problem in computational geometry. It originates from the following real-world problem: In the geometric version of the problem, the layout of the art gallery is represented ...

Kleetope In geometry and polyhedral combinatorics, the Kleetope of a polyhedron or higher-dimensional convex polytope is another polyhedron or polytope formed by replacing each facet of with a shallow pyramid. Kleetopes are named after Victor Klee. Exam ...

s are also named after him, as is the

Klee–Minty cube The Klee–Minty cube or Klee–Minty polytope (named after Victor Klee and George J. Minty) is a unit cube, unit hypercube of variable dimension whose corners have been perturbed. Klee and Minty demonstrated that George Dantzig's simplex algorith ...

, which shows that the

simplex algorithm In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming. The name of the algorithm is derived from the concept of a simplex and was suggested by T. S. Motzkin. Simplices are n ...

for

linear programming Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear function#As a polynomial function, li ...

does not work in

polynomial time In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by ...

in the worst–case scenario.

Service and recognition

Klee served as president of the

Mathematical Association of America The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure a ...

from 1971 to 1973. In 1972 he won a

Lester R. Ford Award Lester is an ancient Anglo-Saxon surname and given name. Notable people and characters with the name include: People Given name * Lester Bangs (1948–1982), American music critic * Lester W. Bentley (1908–1972), American artist from Wisc ...

Notes

External links

Applied Geometry and Discrete Mathematics
a volume dedicated to Klee on his 65th birthday.

* ttp://www.ams.org/featurecolumn/archive/klee.html AMS column: People Making a Difference*
MAA presidents: Victor LaRue Klee
* Shapes of the Future: Some unsolved problems in geometry.
Two dimensionsThree dimensions
{{DEFAULTSORT:Klee, Victor 1925 births 2007 deaths Writers from San Francisco University of Virginia alumni University of Washington faculty 20th-century American mathematicians Fellows of the American Academy of Arts and Sciences Fellows of the American Association for the Advancement of Science Institute for Advanced Study visiting scholars Presidents of the Mathematical Association of America Educators from California American science writers Pomona College alumni

Life

Research

Service and recognition

Notes

Further reading

External links