Theodore Samuel Motzkin (; 26 March 1908 – 15 December 1970) was an
Israel
Israel, officially the State of Israel, is a country in West Asia. It Borders of Israel, shares borders with Lebanon to the north, Syria to the north-east, Jordan to the east, Egypt to the south-west, and the Mediterranean Sea to the west. Isr ...
i-
American 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, mathematical structure, structure, space, Mathematica ...
.
Biography
Motzkin's father
Leo Motzkin
Leo Motzkin (also ''Mozkin''; 1867 – 7 November 1933) 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 ...
, a
Ukrainian Jew, went to
Berlin
Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...
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
Leopold Kronecker (; 7 December 1823 – 29 December 1891) was a German mathematician who worked on number theory, abstract algebra and logic, and criticized Georg Cantor's work on set theory. Heinrich Weber quoted Kronecker
as having said, ...
, but left the field to work for the
Zionist
Zionism is an Ethnic nationalism, ethnocultural nationalist movement that emerged in History of Europe#From revolution to imperialism (1789–1914), Europe in the late 19th century that aimed to establish and maintain a national home for the ...
movement before finishing a dissertation.
Motzkin grew up in Berlin and started studying mathematics at an early age as well, entering university when he was only 15.
He received his
Ph.D. in 1934 from the
University of Basel
The University of Basel (Latin: ''Universitas Basiliensis''; German: ''Universität Basel'') is a public research university in Basel, Switzerland. Founded on 4 April 1460, it is Switzerland's oldest university and among the world's oldest univ ...
under the supervision of
Alexander Ostrowski
Alexander Markowich Ostrowski (; ; 25 September 1893 – 20 November 1986) was a mathematician.
Biography
His father Mark having been a merchant, Alexander Ostrowski attended the Kiev College of Commerce, not a high school, and thus had an ins ...
for a thesis on the subject of
linear programming
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear function#As a polynomia ...
(''Beiträge zur Theorie der linearen Ungleichungen'', "Contributions to the Theory of Linear Inequalities", 1936
).
In 1935, Motzkin was appointed to the
Hebrew University
The Hebrew University of Jerusalem (HUJI; ) is an Israeli public research university based in Jerusalem. Co-founded by Albert Einstein and Chaim Weizmann in July 1918, the public university officially opened on 1 April 1925. It is the second-ol ...
in
Jerusalem
Jerusalem is a city in the Southern Levant, on a plateau in the Judaean Mountains between the Mediterranean Sea, Mediterranean and the Dead Sea. It is one of the List of oldest continuously inhabited cities, oldest cities in the world, and ...
, contributing to the development of
mathematical terminology
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
in
Hebrew
Hebrew (; ''ʿÎbrit'') is a Northwest Semitic languages, Northwest Semitic language within the Afroasiatic languages, Afroasiatic language family. A regional dialect of the Canaanite languages, it was natively spoken by the Israelites and ...
.
In 1936 he was an Invited Speaker at the
International Congress of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).
The Fields Medals, the IMU Abacus Medal (known before ...
in Oslo. During
World War II
World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...
, he worked as a
cryptographer
Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or '' -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adversarial behavior. More gen ...
for the British government.
In 1948, Motzkin moved to the United States. After two years at
Harvard
Harvard University is a private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher lear ...
and
Boston College
Boston College (BC) is a private university, private Catholic Jesuits, Jesuit research university in Chestnut Hill, Massachusetts, United States. Founded in 1863 by the Society of Jesus, a Catholic Religious order (Catholic), religious order, t ...
, he was appointed at
UCLA
The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California, United States. Its academic roots were established in 1881 as a normal school then known as the southern branch of the C ...
in 1950, becoming a professor in 1960.
He worked there until his retirement.
Motzkin married Naomi Orenstein in Jerusalem. The couple had three sons:
* Aryeh Leo Motzkin - Orientalist
* Gabriel Motzkin -
philosopher
Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...
* 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.
Apart from this, Motzkin published about diverse problems in
algebra
Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...
,
graph theory
In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...
,
approximation theory
In mathematics, approximation theory is concerned with how function (mathematics), functions can best be approximation, approximated with simpler functions, and with quantitative property, quantitatively characterization (mathematics), characteri ...
,
combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...
,
numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...
,
algebraic geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...
and
number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
.
The
Motzkin transposition theorem,
Motzkin number
In mathematics, the th Motzkin number is the number of different ways of drawing non-intersecting chords between points on a circle (not necessarily touching every point by a chord). The Motzkin numbers are named after Theodore Motzkin and have ...
s,
Motzkin–Taussky theorem and the
Fourier–Motzkin elimination
Fourier–Motzkin elimination, also known as the FME method, is a mathematical algorithm for eliminating variables from a system of linear inequalities. It can output real solutions.
The algorithm is named after Joseph Fourier who proposed the ...
are named after him. He first developed the "double description" algorithm of
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.
Research in polyhedral co ...
and
computational geometry. He was the first to prove the existence of
principal ideal domain
In mathematics, a principal ideal domain, or PID, is an integral domain (that is, a non-zero commutative ring without nonzero zero divisors) in which every ideal is principal (that is, is formed by the multiples of a single element). Some author ...
s that are not
Euclidean domain
In mathematics, more specifically in ring theory, a Euclidean domain (also called a Euclidean ring) is an integral domain that can be endowed with a Euclidean function which allows a suitable generalization of Euclidean division of integers. Th ...
s,