**Joseph Kruskal** was an American mathematician, statistician and computer scientist who worked in combinatorics and graph theory.

- Kruskal studied mathematics at the University of Chicago.
- Joseph Bernard Kruskal Sr. died in 1950.
- In 1954, Kruskal was awarded a Ph.D. by Princeton for his thesis The Theory of Well-Partially-Ordered Sets.
- We should explain that while Kruskal was working towards his Ph.D., he was also employed at the US Office of Naval Research.
- After the award of his doctorate, Kruskal continued to work for the US Office of Naval Research, spending the years 1954-1956 working on Princeton's Analytical Research Project.
- During the three years 1956-59, Kruskal lectured at the University of Wisconsin at Madison and at the University of Wisconsin at Ann Arbor.
- For example 'Kruskal's algorithm', a graph theory algorithm which finds a minimal spanning tree of a weighted graph, was described in his 1956 paper On the shortest spanning subtree of a graph and the traveling salesman problem.
- The 'Kruskal's tree theorem' is the name now given to Kruskal's proof of the Vazsonyi's Conjecture which he published in Well-Quasi-Ordering, The Tree Theorem, and Vazsonyi's Conjecture (1960).
- The 'Kruskal-Katona theorem' appears in Kruskal's 1963 paper The number of simplices in a complex and in Gyula O H Katona's 1968 paper A theorem of finite sets.
- The 'Kruskal rank' or 'kkk-rank' appears in Kruskal's 1977 paper Three-way arrays rank and uniqueness of trilinear decompositions, with applications to arithmetic complexity and statistics.
- In 1978 Kruskal published the book Multidimensional Scaling which was co-authored by Myron Wish.
- There is another area to which Kruskal has made a major contribution, namely a field known as lexicostatistics or glottochronology which is a form of comparative linguistics.
- Working with Isidore Dyen and Paul Black, Kruskal published the monograph An Indoeuropean Classification, a Lexicostatistical Experiment in the Transactions of the American Philosophical Society in 1992.
- In 1997 Kruskal announced that the 'Comparative Indoeuropean Data Corpus' was available.
- Kruskal's interest in languages extended to an interest in how to write good scientific articles.
- Kruskal was a fellow of the American Statistical Association and was honoured by being elected president of both the Psychometric Society and the Classification Society of North America.

Born 29 January 1928, New York City, New York, USA. Died 19 September 2010, Maplewood, New Jersey, USA.

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Origin Usa

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive