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 ...
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 ...
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 ...
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
In
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
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 ...
. 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 ...
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
*
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 ...
(1956)
*
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)
*
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)
* ...