# Leonard Jimmie Savage

### Quick Info

Detroit, Michigan, USA

New Haven, Connecticut, USA

**Leonard Jimmie Savage**was an American mathematician and statistician.

### Biography

**Leonard Jimmie Savage**'s parents, Louis Ogashevitz and Mae Rugawitz, were Jewish; Jimmie was the first of their four children. The first question that the reader will naturally ask, therefore, is why Jimmie Savage is named Savage. In fact the reason he was called 'Jimmie Savage' is even more complicated. Louis Ogashevitz, who was in the real estate business, was born in Detroit in 1897 to parents who had emigrated to the United States from Russia. After Jimmie was born, his mother, who had a high school education and was a trained nurse, was seriously ill and, as a consequence, there was a delay in giving him a name. A nurse at the hospital where he was born put the name "Jimmie" against his entry in the hospital records but when his mother recovered he was given the name Leonard Ogashevitz. However, the name 'Jimmie' stuck and he was known as Jimmie as he was growing up. In 1920 his father changed his name from Ogashevitz to Savage but this name change did not apply to his children. Many years later, when Jimmie was undertaking classified war work, he had his name legally changed from Leonard Ogashevitz to Leonard Jimmie Savage. Although known as Jimmie all his life, he wrote his papers under the name Leonard Savage.

Allen Wallis writes in [12] about Jimmie's father:-

His father, Louis, was the most significant figure in Savage's life. His respect and love for his father had extraordinary depth and devotion. Except for Louis's unwavering devotion and support ... Jimmie would not have had as productive a life nor as happy a one.Jimmie had a difficult time growing up. In part this was due to poor eyesight, caused by nystagmus (involuntary eye movement) and extreme myopia, which meant that he had only very limited vision. But there was another problem which was a direct consequence of his parent's fear that their children might be kidnapped - a real possibility in Detroit at this time. Jimmie was confined to his home (which was protected by a surrounding wall) and educated by a governess but this caused much stress and arguments between Jimmie and his two sisters Joan (born 1921) and Barbara (born 1922). His parents tried to improve matters by sending Jimmie to boarding school but he later described the year spent there as one of the worst in his life. He then attended Central High School, Detroit, but his teachers were unimpressed with him and would not recommend him for university studies. Richard, Jimmie's brother born in 1925 who also became a well-known statistician, said in a 1999 interview [10]:-

Central High was a very academic-oriented public high school with mostly Jewish students. Both Jimmie and Joan had rather unpleasant experiences there.Richard also explained why Jimmie had so much trouble at school [10]:-

Jimmie was truly a polymath from a very young age. He was a brilliant child, but he paid no attention to what was going on in school because he couldn't see what was going on in school. The teachers thought he was more or less feebleminded.Jimmie's father Louis did everything he could to get his son an education and persuaded one of his friends to recommend Jimmie to Wayne University in Detroit. He studied engineering for a year at Wayne and did well enough that he was allowed to enter the University of Michigan, Ann Arbor, to study chemical engineering.

At the University of Michigan things again went badly for Savage who, because of his poor eyesight, caused a fire in the chemistry laboratory. He was expelled but again his father intervened and Jimmie was allowed to take some mathematics courses with the aim of majoring in physics. His grades began to improve: C in analytic geometry; B in calculus; B in differential equations; A in Raymond Wilder's foundations of mathematics; and A in Raymond Wilder's point set topology course. Inspired by Wilder he received all A grades from that point on and changed to major in mathematics. He received his BS from the University of Michigan in 1938. In that year he married Jane Kretschmer; they had two sons, Sam Linton and Frank Albert. Their eldest son, Sam Linton Savage, received his Ph.D. in computer science from Yale University in 1973. He has worked in the Management Science Department at Chicago and at Stanford. He is the author of

*The Flaw of Averages: Why we underestimate risk in the face of uncertainty*and

*Decision making with insight*.

In 1941 Savage received his PhD with a thesis was on metric and differential geometry. Writing in 1950 he described his doctoral thesis

*The Application of Vectorial Methods to the Study of Distance Spaces*as follows (see [12]):-

My dissertation for the Ph.D. degree at the University of Michigan was on applications of vectorial methods to metric geometry (in the sense of the Menger school), especially with a view to the merging of metric geometry in that sense with differential geometry. Professor S B Myers at the University of Michigan sponsored my dissertation, but I was particularly close to R L Wilder there.He spent session 1941-42 at the Institute for Advanced Study at Princeton as a Rackham fellow, and there he continued to work on pure mathematics. While at the Institute he solved an open problem in the calculus of variations suggested to him in discussions with John von Neumann and Marston Morse. He published this result in

*On the crossing of extemals at focal points*(1943). He was then appointed as an Instructor in Mathematics at Cornell University where he spent the academic year 1942-43, following which he spent a year at Brown University as a Research Mathematician in the classical mechanics group as part of his contribution to the war effort. In 1944, still undertaking war work, he joined the Statistical Research Group at Columbia University as a Research Associate - this move into statistics was suggested by von Neumann who had recognised Savage's talents when he was at Princeton.

Following the end of World War II in 1945, Savage spent a year working with Richard Courant at the Institute of Applied Mathematics at New York University and then he was awarded a Rockefeller Fellowship to spend time at the Institute of Radiobiology and Biophysics at the University of Chicago. He went to Chicago in the autumn of 1946 and began one of the most productive periods of his life being appointed as a Research Associate at Chicago in 1947. He published a joint paper with the economist Milton Friedman

*The Utility Analysis of Choices Involving Risk*in 1948 in the

*Journal of Political Economy*and, in the following year, a joint paper with Paul Halmos

*Application of the Radon-Nikodym theorem to the theory of sufficient statistics*. Remaining at Chicago, Savage was one of the founders of the Statistics Department there in 1949. An interesting snapshot of Savage at this time can be had from a reference written to support his application for a Guggenheim Foundation Fellowship in 1950 (see [2]):-

Dr Savage is brilliant and scholarly, has broad and varied interests, and knows a number of fields rather deeply. He is in addition a remarkable personality, vitally stimulated and interested by, and stimulating and interesting to, others. His basic training is in pure mathematics, but fundamentally he is equally interested in empirical science, whether physical, biological, or social. Statistics, in which he began to work about 1944, has provided a suitable meeting ground for his formal-abstract and his empirical-inductive interests. At least two of the several contributions he has already made to statistics are of major importance, and have stimulated a flow of papers by others. In addition, he has published significant papers in economics, biology, and medicine. It is quite possible, though obviously too early to predict, that he will become one of the great figures of his generation in the field of statistics.He was awarded the Guggenheim Foundation Fellowship and, in addition, was a Fulbright grantee allowing him to spend the academic year 1951-52 in Paris and in Cambridge, England. In 1954 Savage was promoted to professor at Chicago and he served as Chairman of the Statistics Department from 1956 to 1959.

Savage wrote on the foundations of statistics which led him into deep philosophical questions both about statistics and knowledge in general. The other main direction of his work was to study gambling as a source to stimulate problems in probability and decision theory. Savage's book

*The Foundations of Statistics*(1954) is perhaps his greatest achievement. It shows von Neumann's influence and also that of Ramsey. The book starts with six axioms, which are both motivated and discussed, and from these are deduced the existence of a subjective 'personal' probability and a utility function. A special case of a utility function had been introduced by von Neumann and Morgenstern in their theory of games.

*The Foundations of Statistics*sets out Savage's ideas on Bayesian statistics and, in particular, explains his theory of subjective and personal probability. These important ideas did, however, lead to difficult relations with his colleagues. William Kruskal, one of these Chicago colleagues, wrote [11]:-

In his development of personal probability, Savage moved more and more to a proselytizing position. Personal probability was not only useful and interesting to study; it became for him the only sensible approach to probability and statistics. Thus, orthodoxy of neoradicalism developed: if one were not in substantial agreement with him, one was inimical, or stupid, or at the least inattentive to an important scientific development. This attitude, no doubt sharpened by personal difficulties and by the mordant rhetoric of some anti-Bayesians, exacerbated relationships between Jimmie Savage and many old professional friends. The problem had a special poignancy for those who, like myself, took an eclectic point of view.Savage left Chicago in 1960 and took up a professorship at the University of Michigan. Chicago had tried hard to keep him and, in a letter he wrote before leaving Chicago, he expressed his appreciation for the Chicago Department (see [12]):-

For a person who wants to do original, realistic, and critical work in statistics there is no atmosphere anywhere in the world today to compare with this Department.He remained at Michigan for four years before moving to Yale University where he was named Eugene Higgins Professor of Statistics. An important work by Savage, published in 1965 after he took up the chair at Yale, is

*How to gamble if you must : Inequalities for stochastic processes*, written jointly with Lester Dubins. They describe their motivation in the Introduction:-

Imagine yourself at a casino with $1,000. For some reason, you desperately need $10,000 by morning; anything less is worth nothing for your purpose. What ought you to do? ... As is well known, any policy of compounding bets that are subfair to you must decrease your expected wealth. Consequently, no matter how you play, your chance of converting $1,000 into $10,000 will be less than $\large\frac{1}{10}\normalsize$. How close to $\large\frac{1}{10}\normalsize$ can you make it and by what strategy?Other articles written by Savage relate to statistical inference, in particular the Bayesian approach. He introduced Bayesian hypothesis tests and Bayesian estimation. His Bayesian approach, however, opposed the views of Fisher and Neyman. In his later years he wrote on the philosophy of statistics.

Jimmie Savage was divorced in 1964 and, on 10 July of that year, he married Jean Strickland. Sadly, Savage only had seven years at Yale before he died at the early age of fifty-three. However, these were good years [12]:-

Yale proved much to his liking, especially the close association with Frank Anscombe, whom he had held in high personal and professional regard from the time they first met and to whom, in fact, Savage had enthusiastically offered a professorship at Chicago. The agreeable professional circumstances during the seven Yale years, and above all his great happiness with Jean, combined to make the last period of Savage's life personally the happiest.He was president of the Institute of Mathematical Statistics (1957-58), invited to give the Fisher lecture

*On rereading R A Fisher*in 1970, and due to give the 1972 Wald lectures at the time of his death. In 1963 he was awarded an doctorate by the University of Rochester. His early death, however, prevented him receiving many honours which would almost certainly have been given to him. He has been honoured with the establishment in 1977 of the Savage Award made each year to two outstanding doctoral dissertations in Bayesian econometrics and statistics. The American Statistical Association and the Institute of Mathematical Statistics decided to sponsor the publication of a memorial volume [2] for Savage which was published in 1981. Also in his honour was

*Studies in Bayesian econometrics and statistics*published as

*Contributions to Economic Analysis*No 86 (1975).

Finally, let us quote Milton Friedman writing in 1964 (see [2]):-

Jimmie is one of the few really creative people I have met in the course of my intellectual life. He has an original, independent mind capable of throwing new light on whatever problems he looks at. He also has a wide-ranging curiosity. In whatever fields he turns his mind to, he gets new insights, ideas, and approaches. ... Here is one of those extraordinary people of whom there are only a handful in any university at any time.

### References (show)

- B M Hill, Biography in
*Dictionary of Scientific Biography*(New York 1970-1990). See THIS LINK. - The Writings of Leonard Jimmie Savage: A Memorial Selection (Washington, D.C., 1981).
- D A Berry, L J Savage,
*The American Statistician***26**(1) (1972), 47. - W A Ericson, Preface, in
*The Writings of Leonard Jimmie Savage: A Memorial Selection*(Washington, D.C., 1981), 3-5. - B de Finetti, Un modo di pensare fruttuoso: quello di Leonard Jimmie Savage,
*Period. Mat*. (5) (1-2)**49**(1972), 63-65. - Leonard Jimmie Savage Memorial Service tributes, in
*The Writings of Leonard Jimmie Savage: A Memorial Selection*(Washington, D.C., 1981), 9-34. - D V Lindley, L J Savage : His work in probability and statistics, in
*The Writings of Leonard Jimmie Savage: A Memorial Selection*(Washington, D.C., 1981), 35-60. - D V Lindley, L J Savage : His work in probability and statistics,
*Annals of Statistics***8**(1980), 1-24. - D V Lindley, L J Savage,
*Journal of the Royal Statistical Society***A135**(1972), 462-463. - A R Sampson and B Spencer, A conversation with I Richard Savage,
*Statistical Science***14**(1) (1999), 126-148. - Tales of Statisticians, Jimmie Savage, 20 Nov 1917 - 1 Nov 1971. http://www.umass.edu/wsp/statistics/tales/savage.html
- W A Wallis, Leonard Jimmie Savage 1917-1971, in
*E Shils (ed.), Remembering the University of Chicago: teachers, scientists, and scholars*(University of Chicago Press, Chicago, 1991), 436-451.

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Written by J J O'Connor and E F Robertson

Last Update November 2010

Last Update November 2010