# Samuel Karlin

### Quick Info

JanÃ³wa, Poland

Palo Alto, California, USA

**Samuel Karlin**was a Polish-born American mathematician who worked in game theory and its application in statistics and economics.

### Biography

Although**Samuel Karlin**was born in Poland, his family emigrated to the United States when he was two months old. The family settled in Chicago, but found difficulties which became much worse due to the Great Depression which began in 1929. By 1933 the Depression had reached its most severe stage and Karlin, although only nine years old, started working in a store to help with the family's finances.

Karlin's father wanted his son to study religion, but after Karlin won a scholarship he was able to attend the Illinois Institute of Technology. He then went to Princeton University where he studied for a Ph.D. with Salomon Bochner as his advisor. Karlin was awarded his doctorate in 1947 for his thesis

*Independent Functions*. He was appointed to the California Institute of Technology in 1948 and began publishing papers on functional analysis such as

*Unconditional convergence in Banach spaces*(1948),

*Bases in Banach spaces*(1948),

*Orthogonal properties of independent functions*(1949), and (with L S Shapley)

*Geometry of reduced moment spaces*(1949).

From about 1950 his research interests changed and he began to work on game theory. This interest had arisen through his years at Princeton when he had been influenced by John von Neumann who published his classic text

*Theory of Games and Economic Behaviour*, written with Oskar Morgenstern, at about the time Karlin arrived at Princeton. Karlin published papers such as

*Solutions of discrete, two-person games*;

*Polynomial games*; and

*Games with continuous, convex pay-off*all in 1950. In 1956 he was appointed to Stanford University. His interest in game theory continued and he worked for the RAND Corporation, in addition to lecturing at Stanford. At RAND he [1]:-

... applied game theory to the analysis of games of pursuit and evasion like a dogfight between warplanes.In 1958 he published the book

*Studies in the mathematical theory of inventory and production*which was written jointly with Kenneth Arrow and Herbert Scarf. This book made a major contribution to mathematical economics and operations research. In 1959 he published the book

*Mathematical methods and theory in games, programming and economics*. This was a major two volume work, the first volume being

*Matrix games, programming, and mathematical economics*while the second volume was

*The theory of infinite games*. Karlin wrote in the Introduction:-

We may summarize our aims as an attempt to unify the mathematical techniques of the field and to help crystallize the concepts underlying these kinds of decision problems. It is not our purpose to propose a formal structure which will encompass all the problems in the areas covered. ... The coverage of these volumes is in no sense exhaustive; I have stressed most what appeals to me.Large numbers of papers and books on a wide range of topics continued to flow from his pen. We indicate the range of the work by listing some of the books. In addition to those already mentioned, he wrote: (with William Studden)

*Tchebycheff systems: With applications in analysis and statistics*(1966);

*A first course in stochastic processes*(1966); and

*Total positivity. Vol. I*. (1968); (with Howard Taylor)

*An introduction to stochastic modeling*(1984). The aim of this last mentioned book is described in the Preface being:-

... to bridge the gap between basic probability know-how and an intermediate level course in stochastic processes, for example, 'A first course in stochastic processes' by the present authors.Total positivity is a subject in which Karlin played a major role. The importance of the subject is described by I I Hirschman, Jr:-

These ideas play a basic role in problems involving convexity, moment spaces, orthogonal polynomials, Chebyshev systems, the oscillation properties of linear differential equations, and the theory of approximation. They figure in an essential and elegant way in the theory of stochastic processes, especially in linear diffusion processes. Finally, they are important in various applications - in statistics where they are fundamental to the understanding of statistical decision procedures, and also in such topics as inventory control and reliability theory.Karlin received many honours throughout his career including a lifetime achievement award from the National Academy of Sciences in 1973, the John von Neumann Theory Prize in 1987, and the National Medal of Science in 1989. The citation for the John von Neumann Theory Prize reads:-

Samuel Karlin has been awarded the ORSA/TIMS John von Neumann Theory Prize for 1987 for his contributions to the theory of games, inventory theory, decision theory, birth-death and diffusion processes, total positivity and the theory of approximations.As this quote indicates, Karlin moved towards applying mathematical techniques in biology in the last portion of his career. In particular he concentrated on the development of mathematical and computational techniques and tools for the analysis of DNA and protein sequences. He worked on descriptive and statistical analysis of protein structure properties, including methods for characterizing and comparing protein structures and sequences. Papers in this area include

Through his sustained research productivity over the past forty years at The California Institute of Technology and at Stanford University, he has contributed richly to the methodology of operations research and management science at a deep and fundamental level. His many books have influenced teaching and research in all areas of operations research and have provided a standard of excellence greatly admired. Over the years, his vitality, scholarship and industry have generated more than fifty research students with spin-off in such diverse areas as reliability theory and queuing theory.

His important contributions to genetics, though peripheral to operations research and management science, attest to the great breadth of his contributions. As a tribute to this breadth and vitality, we award Samuel Karlin the John von Neumann Theory Prize.

*Distinctive features of large complex virus genomes and proteomes*,

*A Theoretical and Numerical Assessment of Genetic Variability*, and

*Some Natural Viability Systems for a Multiallelic Locus: A Theoretical Study*. We should note that the papers and books we have listed form a very small fraction of Karlin's total output since he published over 450 works.

Karlin married Dorit Carmelli; they had three children - Kenneth (a chemistry professor at Johns Hopkins University), Manuel and Anna.

He continued to undertake research despite becoming physically frail towards the end of his life. In [2] his death is described as taking place:-

... at Stanford Hospital after a massive heart attack.As to his character, he is described in [1] as follows:-

He was known for the emotional force, not to mention volume, with which he argued scientific points.In the same article, Russ Altman, a professor of bioengineering at Stanford, is quoted as saying:-

I would not say he was intellectually gentle.Perhaps we should end with a quotation from Karlin. This well-know quote is from the eleventh R A Fisher Memorial Lecture which Karlin delivered at the Royal Society of London on 20 April 1983:-

The purpose of models is not to fit the data but to sharpen the questions.

### References (show)

- D Martin, Samuel Karlin, Versatile Mathematician, Dies at 83,
*The New York Times*(21 February 2008). - Sam Karlin, influential math professor, dead at 83,
*Stanford Report*(December 21, 2007).

### Additional Resources (show)

Other websites about Samuel Karlin:

### Honours (show)

Honours awarded to Samuel Karlin

Written by J J O'Connor and E F Robertson

Last Update July 2008

Last Update July 2008