Joseph Kruskal
Early Life and Education
Joseph Bernard Kruskal Jr. was born on January 29, 1928, in New York City, New York. He was born into a family with a strong academic background, with his father, Joseph Kruskal Sr., being a successful fur wholesaler who had a deep interest in mathematics and science. His mother, Lillian Rose Vorhaus Kruskal Oppenheimer, was a noted inventor and artist.
Kruskal attended the University of Chicago, where he received his Bachelor's degree in Mathematics in 1948. He then went on to attend Princeton University, where he completed his Ph.D. in Mathematics in 1952. His doctoral dissertation, titled "The Theory of Well-Partially-Ordered Sets and Their Generalizations", was supervised by Albert W. Tucker.
Career and Contributions
After completing his Ph.D., Kruskal joined the Bell Laboratories in Murray Hill, New Jersey, where he worked as a mathematician from 1952 to 1959. During this period, he developed the Kruskal's algorithm, a significant contribution to the field of Computer Science and Graph Theory. This algorithm is used for finding the minimum spanning tree in a graph, which is a tree that connects all the vertices in the graph and has the smallest possible total edge weight.
In 1959, Kruskal moved to the field of Psychometrics and joined the Educational Testing Service (ETS) in Princeton, New Jersey, where he worked until his retirement in 1993. During his tenure at ETS, he made significant contributions to the field of multidimensional scaling (MDS), a means of visualizing the level of similarity of individual cases of a dataset. His most notable work in this area is the development of the Kruskal's stress formula for MDS, which is widely used in various fields including psychology, marketing, and bioinformatics.
Kruskal also made significant contributions to the field of Statistics. He developed the Kruskal-Wallis one-way analysis of variance by ranks, a non-parametric method used for comparing two or more independent samples of equal or different sample sizes. This method is widely used in various fields including medicine, agriculture, and social sciences.
Awards and Honors
Throughout his career, Kruskal received numerous awards and honors for his contributions to the fields of Mathematics, Computer Science, Psychometrics, and Statistics. Some of the notable ones include:
- In 1989, he was awarded the Wilks Memorial Award by the American Statistical Association for his outstanding contributions to statistics. - In 1993, he was awarded the Samuel J. Wilks Award from the Princeton University Department of Operations Research and Financial Engineering. - In 2002, he was awarded the Psychometric Society Lifetime Achievement Award for his contributions to the field of psychometrics.
Personal Life and Legacy
Joseph Kruskal was known for his love of the outdoors and was an avid hiker and bird watcher. He was also a dedicated family man and is survived by his wife, Judith Kruskal, and their four children.
Kruskal passed away on September 19, 2010, in Princeton, New Jersey. His legacy continues to live on through his significant contributions to various fields, and his algorithms and methods continue to be widely used in research and applications.
See Also
- Graph Theory - Multidimensional Scaling - Kruskal's Algorithm - Kruskal-Wallis Test