Theodore Motzkin

Theodore Motzkin
Born	(1908-03-26)March 26, 1908 Berlin, German Empire
Died	October 15, 1970(1970-10-15) (aged 62) Los Angeles
Nationality	American
Alma mater	University of Basel
Known for	Motzkin transposition theorem Motzkin number PIDs that are not EDs Linear programming Fourier–Motzkin elimination
Scientific career
Institutions	UCLA
Doctoral advisor	Alexander Ostrowski
Doctoral students	John Selfridge Rafael Artzy

Theodore Samuel Motzkin (26 March 1908 – 15 December 1970) was an Israeli-American mathematician.[1]

Biography

Motzkin's father Leo Motzkin, a Ukrainian Jew, went to Berlin at the age of thirteen to study mathematics. He pursued university studies in the topic and was accepted as a graduate student by Leopold Kronecker, but left the field to work for the Zionist movement before finishing a dissertation.[2]

Motzkin grew up in Berlin and started studying mathematics at an early age as well, entering university when he was only 15.[2] He received his Ph.D. in 1934 from the University of Basel under the supervision of Alexander Ostrowski[3] for a thesis on the subject of linear programming[2] (Beiträge zur Theorie der linearen Ungleichungen, "Contributions to the Theory of Linear Inequalities", 1936[4]).

In 1935, Motzkin was appointed to the Hebrew University in Jerusalem, contributing to the development of mathematical terminology in Hebrew.[4] In 1936 he was an Invited Speaker at the International Congress of Mathematicians in Oslo.[5] During World War II, he worked as a cryptographer for the British government.[2]

In 1948, Motzkin moved to the United States. After two years at Harvard and Boston College, he was appointed at UCLA in 1950, becoming a professor in 1960.[4] He worked there until his retirement.[2]

Motzkin married Naomi Orenstein in Jerusalem. The couple had three sons:

• Aryeh Leo Motzkin - Orientalist
• Gabriel Motzkin - philosopher
• Elhanan Motzkin - mathematician

Contributions to mathematics

Motzkin's dissertation contained an important contribution to the nascent theory of linear programming (LP), but its importance was only recognized after an English translation appeared in 1951. He would continue to play an important role in the development of LP while at UCLA.[4] Apart from this, Motzkin published about diverse problems in algebra, graph theory, approximation theory, combinatorics, numerical analysis, algebraic geometry and number theory.[4]

The Motzkin transposition theorem, Motzkin numbers, Motzkin–Taussky theorem and the Fourier–Motzkin elimination are named after him. He first developed the "double description" algorithm of polyhedral combinatorics and computational geometry.[6] He was the first to prove the existence of principal ideal domains that are not Euclidean domains, ${\textstyle \mathbb {Z} \left[{\frac {1+{\sqrt {-19}}}{2}}\right]}$ being his first example.[7]

He found the first explicit example of a nonnegative polynomial which is not a sum of squares, known as the Motzkin polynomial ${\displaystyle X^{4}Y^{2}+X^{2}Y^{4}-3X^{2}Y^{2}+1}$, and showed that it was positive using the AM–GM inequality.[8]

The quote "complete disorder is impossible," describing Ramsey theory, is attributed to him.[9]

See also

• Cyclic polytope
• Pentagram map, a related concept

References

1. Motzkin, Theodore S. (1983). David Cantor; Basil Gordon; Bruce Rothschild (eds.). Theodore S. Motzkin: Selected papers. Contemporary Mathematicians. Boston, Mass.: Birkhäuser. pp. xxvi+530. ISBN 3-7643-3087-2. MR 0693096.
2. O'Connor, John J.; Robertson, Edmund F. "Theodore Motzkin". MacTutor History of Mathematics Archive. University of St Andrews.
3. Theodore Motzkin at the Mathematics Genealogy Project
4. Joachim Schwermer (1997). "Motzkin, Theodor Samuel". Neue Deutsche Biographie. Vol. 18. pp. 231 ff.
5. Motzkin, Th. (1936). "Sur le produit des spaces métriques". In: Congrès International des Mathématiciens. pp. 137–138.
6. Motzkin, T. S.; Raiffa, H.; Thompson, G. L.; Thrall, R. M. (1953). "The double description method". Contributions to the theory of games. Annals of Mathematics Studies. Vol. 2. Princeton, N. J.: Princeton University Press. pp. 51–73. MR 0060202.
7. Motzkin, Th (December 1949). "The Euclidean algorithm". Bulletin of the American Mathematical Society. 55 (12): 1142–1146. doi:10.1090/S0002-9904-1949-09344-8. ISSN 0002-9904.
8. Motzkin, T. S. (1967). "The arithmetic-geometric inequality". Inequalities (Proc. Sympos. Wright-Patterson Air Force Base, Ohio, 1965). New York: Academic Press. pp. 205–224. MR 0223521.
9. Hans Jürgen Prömel (2005). "Complete Disorder is Impossible: The Mathematical Work of Walter Deuber". Combinatorics, Probability and Computing. 14. Cambridge University Press: 3–16. doi:10.1017/S0963548304006674. S2CID 37243306.