# George Daniel Mostow

### Quick Info

Boston, Massachusetts, U.S.A.

Hamden, New Haven, Connecticut, USA

**Dan Mostow**was an outstanding mathematician winning the Leroy Steele Prize in 1993 and the Wolf Prize in Mathematics in 2013 for his fundamental and pioneering contribution to geometry and Lie group theory. He also played a major role in supporting mathematics as president of the American Mathematical Society and in many other leading roles.

### Biography

**Dan Mostow**was the son of Isaac Mostow and Ida Rotman. Sidnie Feit writes [2]:-

Dan's father, Isaac, was born in the Ukraine in 1888. Dan's grandfather Joseph emigrated to the U.S. in 1896, and brought the rest of the family over four years later.There is, however, some confusion over different names and inconsistent dates which we should mention. The 1910 US Census [13] gives Dan's father as Isador Mostow, the son of Joseph and Bessie Mostow. The dates of immigration are given as 1900 for Joseph and 1902 for Bessie, Isador, and Isador's sister Sadie. Joseph's occupation is given as "peddler", and Isador's as working in a jewellery shop. On his World War I Draft Registration Card [8], Dan's father is named Isaac Mostow, born 20 November 1888 in Kiev, living at 45 Leverett Street, Boston, and gives his occupation as lawyer. He is exempted from the draft because of poor eyesight. He married Ida Rotman in 1920 and by the time of the 1930 US Census [14] they had two sons, Jack Mostow, aged 8, and Daniel Mostow, the subject of this biography, aged 7. This 1930 Census names Dan's father as Isidor Mostow (not Isador or Isaac), gives his immigration year as 1896 and his occupation as lawyer. The 1940 US Census [15] gives Dan's father as Isaac Mostow, occupation recorder, and by now there are three children whose names appear as Jechil (previously Jack), George D (previously Daniel) and Morton S who is 9 years old. Jack's occupation is "news worker", seeking work, while Dan has no occupation and is a student. Let us record here that Jechil (or Jack or Jechiel) had been born on 27 April 1922 and, after 4 years of high school, enlisted in US Army Air Corps on 12 December 1940. He served in World War II as a pilot but was shot down over the Mediterranean Sea and died 31 December 1942.

In fact in 1936 Dan had entered the Boston Public Latin School at the same time as Daniel Gorenstein; the two became lifelong friends. It was while he was at this school that he realised that he wanted to become a mathematician. He explained [6]:-

In high school, mathematics was my favourite subject. I especially enjoyed challenging problems. But I did not know that mathematics was a profession. I am indebted to my high school English teacher who, in my senior year, called me up to his desk to ask about my career plans, and told me that his brother was a mathematician. I decided then and there that mathematics was for me.Dan earned money by working as a newsboy and, in addition, as a general helper in a catering hall. For more background about Dan Mostow during these years see the very full biography written by Sidnie Feit at THIS LINK.

Since Sidnie Feit has provided a very full biography, we will give a shorter biography here.

Mostow was awarded the 'Latin School Class of 1898', the prize given to the top pupil. This prize included a one year scholarship and he also won two further minor scholarships. He began his studies at Harvard University in April 1940, living at home to save money. Soon after starting his studies he was offered free tuition, room, and board by Harvard but decided to continue living at home, partly because he could not eat the Harvard college food because it was not Kosher. He was then given a full tuition scholarship to cover his complete course at Harvard. Majoring in mathematics, he graduated in June 1943 and continued his studies in the Harvard Graduate School.

Of course, America was now involved in World War II, and many of the mathematics faculty at Harvard were undertaking war work. As a consequence, Mostow began teaching courses which were part of the training for officers, namely a spherical trigonometry course and a plane trigonometry course. In 1946 he was awarded a Master's Degree from Harvard University. He began research on Lie algebras advised by Garrett Birkhoff and, with the money he was earning from teaching, he was able to rent an attic apartment in Cambridge.

While a graduate student, Mostow met Evelyn Beatrice Davidoff (1924-2005), born in Boston on 26 May 1924, the daughter of Sydney Davidoff and Ruth Feinstein. Evelyn, known as "Haavie" was a brilliant musician coming from a family of musicians. Before Mostow had submitted his doctoral thesis, in June 1947, he was offered a 2-year stay at the Institute for Advanced Study in Princeton and, to run in parallel, a one year position as Instructor in Mathematics at Princeton University. There was a problem, however, for [2]:-

... he did not know whether he would have enough income to pay the high Princeton rents. After a consultation, the Institute offered him free rent. He immediately proposed marriage to Evelyn, and after a honeymoon in Nantucket, they moved to the Institute.Let us record that Dan and Evelyn Mostow were married on 1 September 1947. They had four children: Mark Alan Mostow; David Jechiel Mostow (known as Jack); Carol Held Mostow; and Jonathan Carl Mostow. Mark trained as a mathematician, and later became a computer scientist. Jack was the leader of Carnegie Mellon's "RoboTutor" project to enable children in developing countries to read and perform arithmetic. He was awarded a $1 million prize. Carol became an Assistant Professor of Family Medicine and facilitator for the Schwartz Center for Compassionate Healthcare. Jonathan became a Movie Director, screenwriter, and producer.

Mostow's thesis was

*The Extensibility of Local Lie Groups of Transformations and Groups on Surfaces*and he was awarded a Ph.D. for this in 1948. He published the main results of his thesis in a paper with the same title in the

*Annals of Mathematics*which was published in 1950. He writes:-

The results in this paper were obtained by the author in his doctoral dissertation. The author wishes to acknowledge his debt to Prof Garrett Birkhoff for his very valuable advice and encouragement.The Introduction to the paper begins:-

One of the problems early in the history of continuous groups was the determination of all the continuous groups of transformations in the line, plane, and n-space. Sophus Lie derived all the then-called "groups" of transformations in the line and plane. An inspection of his methods reveals that what he obtained was all the local Lie groups of transformations defined in a neighborhood of Euclidean space. It is natural to wonder whether a local group of transformations defined on a neighborhood of the line, plane, or more generally a region of n-space can be extended to a global group of transformations on a manifold of which the given region is a subset. ... In this paper it is proved that a local Lie transitive group of transformations defined in a neighborhood of Euclidean space of dimension less than five can be extended to a global Lie transitive group of transformations on some manifold; if the dimension of the neighborhood is five or greater, the extensibility is not always possible.This was not Mostow's first publication since his paper

*A new proof of E Cartan's theorem on the topology of semi-simple groups*was published in 1949. This paper begins as follows:-

E Cartan has proved that a connected semi-simple Lie group is topologically the direct product of a compact subgroup and a Euclidean space. Cartan first proved this theorem in 1927 by a reduction to special cases, and not until 1929 did he free his proof from the consideration of special cases. As a result Cartan's proof is diffused among several journals. Moreover, Cartan employs in an essential way the theory of symmetric Riemannian spaces and makes use of a result whose proof seems to be lacking. ...Let us give here a summary of Mostow's career. He was appointed as an Assistant Professor of Mathematics at Syracuse University in New York State in 1949. He had been encouraged to accept this position by Atle Selberg who was on the faculty there, but Selberg had left Syracuse by the time Mostow took up his post in 1950. At Syracuse, Mostow became a colleague of Lipman Bers and the two became lifelong friends. There were tensions at Syracuse, however, between researchers and teaching-only members of the Department so when Mostow was offered an Assistant Professorship at Johns Hopkins University in 1952 he was pleased to accept. At Johns Hopkins he was promoted to Associate Professor in 1954, then to full professor three years later. He accepted the position of Professor of Mathematics at Yale Univesity in 1960, taking up the post in 1961. He served as Chairman of the Mathematics Department at Yale University in 1971-73, then in 1981 he was named Henry Ford II Professor

In this paper there will be given a more direct proof which eliminates the use of symmetric Riemannian spaces. The author wishes to acknowledge his debt to Professor C Chevalley who suggested in an oral communication Lemma 1.4 below and to whom a proof of Theorem 1, essentially the same as the one given here, was known.

*of mathematics at Yale. He remained at Yale for the remainder of his career.*

Much more information about Mostow's career is available from Sidnie Feit's biography [2] which has the following sections: Dan and the Institute for Advanced Study (IAS); Conference in Mendoza, and Grothendieck; Gerhard Hochschild; Utrecht University; Paris and Travel; Early Years at Yale; 60th Birthday Conference; The International Mathematical Union (IMU); 1972 ICM Panel and Gregory Margulis; The 1974 ICM in Vancouver and 1978 ICM In Helsinki; The 1978 ICM in Helsinki; 1982 and 1983 ICM in Warsaw; The Miraculous Polish Pope; Ludwig Faddeev, the 1986 General Assembly, and A Resolution; A Russian Revolution - and a Redemption; Human Rights; Ilya Piatetsi-Shapiro; Ilya and the Brailovsky Seminar; 1999, A Shared Retirement; Defending Mathematical Research in the U.S.; American Mathematical Society (AMS); National Academy Activities; Reviewer, Adviser, Organizer; Editor; Rigidity and the Steele Prize; The Wolf Prize; and Mostowfest. This biography is available in full at THIS LINK.

Sidnie Feit has also written an article

*Dan Mostow and the ICM, 1972-1990*which is available at THIS LINK.

Mostow retired from his Chair at Yale in 1998 and, in the following year, was made Professor Emeritus. He continued as an active member of the Yale community, retaining his office and attending seminars.

Evelyn Mostow died on 16 September 2005. On 21 June 2007 Mostow married Sidnie Feit. She was an intermittent mathematician, and later, a data communications lecturer, consultant, and author. She had been married to Walter Feit and had two children with him, a son Paul, who became a professor of mathematics, and a daughter Alexandra who became an artist. Walter Feit had died in July 2004. After Dan and Sidnie married, they had two honeymoons. The first was in Niagara on the Lake, in Canada, and the second in Alaska, in Glacier Bay, and then in Haines, where Sidnie's daughter Alexandra was living at that time.

In the interview [6] given in 2013, Mostow explained what his interests were outside mathematics:-

Reading history, especially the history of religion. Trying to understand what is the good life and living a good life. It helps to have a loving wife, four children, and their spouses, as well as 10 grandchildren and 14 great-grandchildren, all fascinating. I enjoy singing in a chorus, and attending the high-definition Metropolitan opera performances at Yale. The University's Koerner Center for Emeritus Faculty - which has a rich program of lectures, films, and parties - keeps me in contact with colleagues from other departments.Mostow received many honours for his outstanding contributions. He served as president of the American Mathematical Society in 1987-88. He was a member of the National Academy of Sciences, elected in 1974, was awarded the American Mathematical Society's Leroy Steele Prize in 1993 and the Wolf Prize in Mathematics in 2013. The citation for the Wolf Prize gives an excellent summary of Mostow's remarkable mathematical achievements [4]:-

George D Mostow made a fundamental and pioneering contribution to geometry and Lie group theory. His most celebrated accomplishment in this fields is the discovery of the completely new rigidity phenomenon in geometry, the Strong Rigidity Theorems. These theorems are some of the greatest achievements in mathematics in the second half of the 20th century. This established a deep connection between continuous and discrete groups, or equivalently, a remarkable connection between topology and geometry. Mostow's rigidity methods and techniques opened a floodgate of investigations and results in many related areas of mathematics. Mostow's emphasis on the "action at infinity" has been developed by many mathematicians in a variety of directions. It had a huge impact in geometric group theory, in the study of Kleinian groups and of low dimensional topology, in work connecting ergodic theory and Lie groups. Mostow's contribution to mathematics is not limited to strong rigidity theorems. His work on Lie groups and their discrete subgroups which was done during 1948-1965 was very influential. Mostow's work on examples of nonarithmetic lattices in two and three dimensional complex hyperbolic spaces (partially in collaboration with P Deligne) is brilliant and lead to many important developments in mathematics. In Mostow's work one finds a stunning display of a variety of mathematical disciplines. Few mathematicians can compete with the breadth, depth, and originality of his works.

### References (show)

- O Aderet, Enlightenment at a Red Traffic Light,
*HAARETZ.com*.

https://www.haaretz.com/.premium-enlightenment-at-a-red-traffic-light-1.5242531 - S Feit, George Daniel (Dan) Mostow,
*Personal Communication*(27 March 2020). - G Daniel Mostow Papers, 1935-2019,
*Dolph Briscoe Center for American History, The University of Texas at Austin*(February 2020). - George D Mostow Wolf Prize in Mathematics 2013,
*The Wolf Foundation*.

https://wolffund.org.il/2018/12/11/george-d-mostow/ - George Daniel Mostow,
*Institute for Advanced Study*.

https://www.ias.edu/scholars/george-daniel-mostow - E Gershon, In Conversation: George Daniel Mostow, Geometer of the nth dimension,
*SHAMSKM.com*.

https://www.shamskm.com/in-conversation-george-daniel-mostow-geometer-of-the-nth-dimension/ - In Memoriam: George Daniel Mostow 1923-2017,
*Department of Mathematics, Yale University.*

https://web.archive.org/web/20180101014859/http://math.yale.edu/memoriam-george-daniel-mostow-1923-2017 - Isaac Mostow, World War I Draft Registration Cards,
*ancestry.com*.

https://www.ancestry.co.uk/imageviewer/collections/6482/images/005216203_04422?treeid=&personid=&hintid=&queryId=a88d85470ff782dba9bc191b5150da1f&usePUB=true&_phsrc=qxG10&_phstart=successSource&usePUBJs=true&pId=341248 - Isaac Mostow, World War II Draft Registration Cards,
*ancestry.com.*

https://www.ancestry.co.uk/imageviewer/collections/1002/images/2wwii_2251539-4575?usePUB=true&_phsrc=qxG11&_phstart=successSource&usePUBJs=true&pId=8713877 - E Kehoe, Mostow and Artin Awarded 2013 Wolf Prize,
*Notices Amer. Math. Soc*.**60**(5) (2013), 602-603. - J Mandell, Yale Mathematician George Mostow Wins Wolf Prize,
*Yale Scientific*(31 March 2013).

https://www.yalescientific.org/2013/03/yale-mathematician-george-mostow-wins-wolf-prize/ - Mostow, master of geometry, wins Wolf Prize,
*Yale News*(8 January 2013).

https://news.yale.edu/2013/01/08/mostow-master-geometry-wins-wolf-prize - Mostow Family, 1910 US Census,
*ancestry.com*.

https://www.ancestry.co.uk/imageviewer/collections/7884/images/31111_4330099-00168?usePUB=true&_phsrc=qxG1&_phstart=successSource&usePUBJs=true&pId=106216563 - Mostow Family, 1930 US Census,
*ancestry.com*.

https://www.ancestry.co.uk/imageviewer/collections/6224/images/4607688_00787?usePUB=true&_phsrc=qxG8&_phstart=successSource&usePUBJs=true&pId=14272878 - Mostow Family, 1940 US Census,
*ancestry.com*.

https://www.ancestry.co.uk/imageviewer/collections/2442/images/m-t0627-01672-00650?usePUB=true&_phsrc=qxG12&_phstart=successSource&usePUBJs=true&pId=95492684

### Additional Resources (show)

Other pages about Dan Mostow:

Other websites about Dan Mostow:

### Honours (show)

Honours awarded to Dan Mostow

Written by J J O'Connor and E F Robertson

Last Update September 2021

Last Update September 2021