Joseph Bernard Kruskal, Jr. (; January 29, 1928 – September 19, 2010) was an

American American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, pe ...

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 ...

statistician A statistician is a person who works with theoretical or applied statistics. The profession exists in both the private and public sectors. It is common to combine statistical knowledge with expertise in other subjects, and statisticians may wor ...

computer scientist A computer scientist is a person who is trained in the academic study of computer science. Computer scientists typically work on the theoretical side of computation, as opposed to the hardware side on which computer engineers mainly focus (al ...

and

psychometrician Psychometrics is a field of study within psychology concerned with the theory and technique of measurement. Psychometrics generally refers to specialized fields within psychology and education devoted to testing, measurement, assessment, and ...

Personal life

Kruskal was born to a

Jewish Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...

family in

New York City New York, often called New York City or NYC, is the List of United States cities by population, most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the L ...

to a successful fur wholesaler, Joseph B. Kruskal, Sr. His mother,

Lillian Rose Vorhaus Kruskal Oppenheimer Lillian Rose Vorhaus Kruskal Oppenheimer (October 24, 1898 in New York City – July 24, 1992) was an American origami pioneer. She popularized origami in the West starting in the 1950s, and is credited with popularizing the Japanese term ''origami ...

, became a noted promoter of

origami ) is the Japanese paper art, art of paper folding. In modern usage, the word "origami" is often used as an inclusive term for all folding practices, regardless of their culture of origin. The goal is to transform a flat square sheet of pape ...

during the early era of television. Kruskal had two notable brothers,

Martin David Kruskal Martin David Kruskal (; September 28, 1925 – December 26, 2006) was an American mathematician and physicist. He made fundamental contributions in many areas of mathematics and science, ranging from plasma physics to general relativity and ...

, co-inventor of

soliton In mathematics and physics, a soliton or solitary wave is a self-reinforcing wave packet that maintains its shape while it propagates at a constant velocity. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium ...

s, and

William Kruskal William Henry Kruskal (; October 10, 1919 – April 21, 2005) was an American mathematician and statistician. He is best known for having formulated the Kruskal–Wallis one-way analysis of variance (together with W. Allen Wallis), a widely used ...

, who developed the

Kruskal–Wallis one-way analysis of variance The Kruskal–Wallis test by ranks, Kruskal–Wallis ''H'' testClyde Kruskal.

Education and career

He was a student at 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 ...

earning a bachelor of science in mathematics in the year of 1948, and a master of science in mathematics in the following year 1949. After his time at the University of Chicago Kruskal attended

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

, where he completed his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

in 1954, nominally under Albert W. Tucker and

Roger Lyndon Roger Conant Lyndon (December 18, 1917 – June 8, 1988) was an American mathematician, for many years a professor at the University of Michigan.. He is known for Lyndon words, the Curtis–Hedlund–Lyndon theorem, Craig–Lyndon interpolation a ...

, but de facto under

Paul Erdős Paul Erdős ( hu, Erdős Pál ; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in ...

with whom he had two very short conversations. Kruskal worked on

well-quasi-ordering In mathematics, specifically order theory, a well-quasi-ordering or wqo is a quasi-ordering such that any infinite sequence of elements x_0, x_1, x_2, \ldots from X contains an increasing pair x_i \leq x_j with i x_2> \cdots) nor infinite sequenc ...

s and

multidimensional scaling Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a dataset. MDS is used to translate "information about the pairwise 'distances' among a set of n objects or individuals" into a configurati ...

. He was a Fellow of the

American Statistical Association The American Statistical Association (ASA) is the main professional organization for statisticians and related professionals in the United States. It was founded in Boston, Massachusetts on November 27, 1839, and is the second oldest continuousl ...

, former president of the

Psychometric Society The Psychometric Society is an international nonprofit professional organization devoted to the advancement of quantitative measurement practices in psychology, education, and the social sciences. The society publishes a scientific journal calle ...

, and former president of the Classification Society of North America. He also initiated and was first president of the Fair Housing Council of

South Orange South Orange, officially the Township of South Orange Village, is a suburban township in Essex County, New Jersey, United States. As of the 2010 United States Census, the village's population was 16,198, reflecting a decline of 766 (4.5%) fro ...

and Maplewood in 1963, and actively supported civil rights in several other organizations such as

CORE Core or cores may refer to: Science and technology * Core (anatomy), everything except the appendages * Core (manufacturing), used in casting and molding * Core (optical fiber), the signal-carrying portion of an optical fiber * Core, the centra ...

. He worked at

Bell Labs Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial research and scientific development company owned by mult ...

from 1959 to 1993.

Research

statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

, Kruskal's most influential work is his seminal contribution to the formulation of

. In computer science, his best known work is

Kruskal's algorithm Kruskal's algorithm finds a minimum spanning forest of an undirected edge-weighted graph. If the graph is connected, it finds a minimum spanning tree. (A minimum spanning tree of a connected graph is a subset of the edges that forms a tree that i ...

for computing the minimal spanning tree (MST) of a

weighted graph This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes or vertices connected in pairs by lines or edges. Symbols A B ...

. The algorithm first orders the edges by weight and then proceeds through the ordered list adding an edge to the partial MST provided that adding the new edge does not create a cycle. Minimal spanning trees have applications to the construction and pricing of communication networks. In

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 is known for

Kruskal's tree theorem In mathematics, Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under homeomorphic embedding. History The theorem was conjectured by Andrew Vázsonyi and proved b ...

(1960), which is also interesting from a

mathematical logic Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of for ...

perspective since it can only be proved nonconstructively. Kruskal also applied his work in

linguistics Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure. Linguis ...

, in an experimental

lexicostatistical Lexicostatistics is a method of comparative linguistics that involves comparing the percentage of lexical cognates between languages to determine their relationship. Lexicostatistics is related to the comparative method but does not reconstruct a p ...

study of

Indo-European languages The Indo-European languages are a language family native to the overwhelming majority of Europe, the Iranian plateau, and the northern Indian subcontinent. Some European languages of this family, English, French, Portuguese, Russian, Dutc ...

, together with the linguists

Isidore Dyen Isidore Dyen (16 August 1913 in Philadelphia – 14 December 2008 in Newton, Massachusetts) was an American linguist, Professor Emeritus of Malayo-Polynesian and Comparative Linguistics at Yale University. He was one of the foremost scholars i ...

and Paul Black. Their database is still widely used.

Concepts named after Joseph Kruskal

(1956) *

(1960) *

Kruskal–Katona theorem In algebraic combinatorics, the Kruskal–Katona theorem gives a complete characterization of the ''f''-vectors of abstract simplicial complexes. It includes as a special case the Erdős–Ko–Rado theorem and can be restated in terms of uniform ...

(1963) * Kruskal rank or k-rank (1977), closely related to the

spark Spark commonly refers to: * Spark (fire), a small glowing particle or ember * Electric spark, a form of electrical discharge Spark may also refer to: Places * Spark Point, a rocky point in the South Shetland Islands People * Spark (surname) * ...

References

External links

*
The Dyen, Kruskal and Black lexicostatistical database
: the 200-meaning Swadesh lists for 95 Indo-European languages.
MacTutor biography of Joseph Kruskal
{{DEFAULTSORT:Kruskal, Joseph Bernard 20th-century American mathematicians 21st-century American mathematicians Jewish American scientists American statisticians University of Chicago alumni Princeton University alumni Scientists at Bell Labs 1928 births 2010 deaths Fellows of the American Statistical Association Scientists from New York City Mathematicians from New York (state) Combinatorialists 21st-century American Jews University of Michigan faculty People from New York City