Theodore Motzkin
Theodore Samuel Motzkin (26 March 1908–15 December 1970) was an Israeli
The State of Israel is a parliamentary republic located in the Middle East, along the eastern shore of the Mediterranean Sea...

United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....



Motzkin's father, Leo Motzkin
Leo Motzkin
Leo Motzkin was a Russian Zionist leader. A leader of the World Zionist Congress and numerous Jewish and Zionist organizations, Motzkin was a key organizer of the Jewish delegation to the 1919 Paris Peace Conference and one of the first Jewish leaders to organize opposition to the Nazi Party in...

, was a noted Russian Zionist leader.

Motzkin received his Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...

 in 1934 from the University of Basel
University of Basel
The University of Basel is located in Basel, Switzerland, and is considered to be one of leading universities in the country...

 under the supervision of Alexander Ostrowski
Alexander Ostrowski
Alexander Markowich Ostrowski , was a mathematician.His father Mark having been a merchant, Alexander Ostrowski attended the Kiev College of Commerce, not a high school, and thus had an insufficient qualification to be admitted to university...


He was appointed at UCLA in 1950 and worked there until retirement.

Contributions to mathematics

The Motzkin transposition theorem, Motzkin number
Motzkin number
In mathematics, a Motzkin number for a given number n is the number of different ways of drawing non-intersecting chords on a circle between n points. The Motzkin numbers have very diverse applications in geometry, combinatorics and number theory...

s and the Fourier–Motzkin elimination
Fourier–Motzkin elimination
Fourier–Motzkin elimination, FME method, is a mathematical algorithm for eliminating variables from a system of linear inequalities. It can look for both real and integer solutions...

 are named after him. Motzkin first developed the "double description" algorithm of polyhedral combinatorics
Polyhedral combinatorics
Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher dimensional convex polytopes....

 and computational geometry
Computational geometry
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational...

. He was the first to prove the existence of principal ideal domain
Principal ideal domain
In abstract algebra, a principal ideal domain, or PID, is an integral domain in which every ideal is principal, i.e., can be generated by a single element. More generally, a principal ideal ring is a nonzero commutative ring whose ideals are principal, although some authors refer to PIDs as...

s that are not Euclidean domain
Euclidean domain
In mathematics, more specifically in abstract algebra and ring theory, a Euclidean domain is a ring that can be endowed with a certain structure – namely a Euclidean function, to be described in detail below – which allows a suitable generalization of the Euclidean algorithm...

s, being his first example.

The quote "complete disorder is impossible," describing Ramsey theory
Ramsey theory
Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that studies the conditions under which order must appear...

 is attributed to him.

External links

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