# Dan Mostow by Sidnie Feit

The following biography of Dan Mostow was written by Dr Sidnie Feit. We have only made very minor editorial changes to the original material that she sent to us in early 2020.
Click on a link below to go to that section.

Chapter 1
Chapter 2
Chapter 3

### Chapter 1.

Family Background.

George Daniel (Dan) Mostow was born on the 4th of July in 1923, at home on Allen Street, in the West End of Boston.

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. When Joseph was notified that his wealthy uncle had died and he was the only heir, he apprenticed his son Isaac to a goldsmith and left to claim his inheritance. After three years, Joseph returned empty-handed. However, not long afterwards, Joseph obtained an attractive position in a Boston Real Estate firm, moved the family to Boston's West End, and Isaac started night school.

Isaac was valedictorian at his school's graduation exercises. An eminent member of the Boston School Committee was master of ceremonies of the evening. As he handed Isaac his diploma, he said "Some day this young man will be a great lawyer." That was the first time that such a thought had entered Isaac's mind. Isaac went to Suffolk Law School and passed the bar in 1916. He became a leading Jewish Boston lawyer with a distinguished practice.

In 1920 Isaac married Ida Rotman, sister of a friend, and they had three sons. Jack (born in 1922) was the eldest and Morton (born 1930) was the youngest. The initial language in the household was Yiddish and the family called the middle son (born in 1923) by his Hebrew name, Gedalia. But after Jack started school, the family switched to English, and called him George, which was the name on his Birth Certificate. After being teased with the nursery rhyme "Georgy Porgy pudding and pie" George insisted that he wanted to be called Daniel. The family agreed, and he was called Daniel, or Dan. (However, he ran into recurring problems as he passed through school, whenever his birth certificate had to be submitted. His passport says George Daniel Mostow, so he must have made an official change.)

In 1929, Isaac was informed that he had a weak heart. He had to cut down on his practice. The subsequent Depression virtually wiped out the remainder of his practice. Dan's mother went to work as a seamstress, and, when they got a little older, Dan and his elder brother Jack had to find employment.

Teen Years.

In 1936, Dan entered Boston Public Latin School, which was regarded as the gateway to college. [Note. Dan Mostow and his friend Daniel Gorenstein attended Boston Latin and Harvard together.] Until he graduated from Boston Latin, he worked as a newsboy Saturday nights, selling early edition Sunday papers in Dorchester in front of the Franklin Park movie theatre until midnight. And, in the summertime, he sold papers daily from 11 am to 6 pm. He had a prime location, at Charles Street corner Beacon Street, adjacent to Boston Common. At this busy corner, he could sell to pedestrians and also service cars driving to the Suffolk Downs race track.

When he was 16, he also started working Saturday nights and Sundays as a general helper in a catering hall. He manned the coat room when people arrived, aimed the spotlight on the procession down the red carpet, then carried pots from the stove to a dumbwaiter, and finally manned the coat room as people left. He was paid 25 cents per hour, and had to turn over all tips to the management. He kept this job until he obtained his B.A. from Harvard.

Dan was deeply interested in Jewish history and Talmud, and for seven years, concurrently with Boston Latin and his undergraduate years at Harvard, he attended Hebrew College 3 times per week.

Instead of applying for college, Dan's older brother Jack enlisted in the Air Force when he turned 18, shortly before the U.S. had been drawn into the war. [Note. Jack's plane was shot down over the Bay of Tunis, 31 December 1942, on his fiftieth mission, which was supposed to be his last before being sent home to train new recruits.]

Dan applied to only one college - Harvard. In fact, his first choice would have been MIT, but their tuition was $600 per year, and Harvard's was$400. In April of 1940 he was admitted to Harvard - but his family had no money saved for college tuition. Happily, a month after graduation he was informed that he had won the Latin School Class of 1898 prize, which was awarded to the top Latin School Senior Class scorer on the nine 3-hour College Board exams. The prize consisted of a $200 scholarship for the first year of college. And he received two other scholarships:$50 from the Burroughs Newsboys Foundation and \$200 for the Harvard Newsboy Scholarship, given to the newsboy who had been admitted to Harvard and was top scorer for the College Boards. By living at home, he could afford to go to Harvard - for a year.

Dan was assigned to Dudley House, which was the social centre for Harvard undergraduates who were commuters. There they could have lively discussions while they ate their brown bag lunches, could play sports, and could listen to music in comfort.

Early in his spring term at Harvard, the Dean of the College offered Dan free tuition, room, and board. Dan replied that he had responsibilities at home. His mother was extremely upset because his brother Jack was in constant jeopardy, having volunteered to join the Air Force. Also, Dan was attending Hebrew College. And further, he could not eat the Harvard college food because it was not Kosher. The Dean agreed to grant Dan a full tuition scholarship for his remaining years at Harvard.

At the end of his freshman year, Dan was assigned a tutor, Dr Putnam, who introduced him to more advanced mathematics, and Dan became a mathematics major. Because of the war, all science majors were assembled in Memorial Hall and urged to take extra courses and graduate in three years. Dan succeeded, gained his Bachelor's degree in June 1943, and was accepted to Harvard Graduate School.

More than half of the Harvard mathematics professors were on leave for war work. As a result, Dan was appointed Instructor at Harvard while he was a graduate student. He started to teach when he was 20 years old, but looked a lot younger. He taught two courses: a spherical trigonometry course in the Navy V12 program for future officers who navigate by the stars, and a plane trigonometry course in the Army Specialized Training Program for future artillery officers.

In 1943, his mother still worked as a seamstress and his father had a wartime job as a machinist in the Watertown Arsenal. With his teaching salary, Dan could afford to move into an attic apartment in Cambridge.

Early in his first semester of graduate school, he became intrigued with Lie Groups, and approached Professor Garrett Birkhoff with the request that he give a course on Lie Groups. Birkhoff replied that he had to be away on war work but would be able to present three lectures on the subject. After these lectures, Dan studied his notes, fell in love with the subject, and Garrett Birkhoff became his thesis adviser. By 1947, Dan had completed his thesis work, although it had not yet been typed.

In the meantime, he had met and fallen in love with "Haavie" (Evelyn) Davidoff, a brilliant student who came from a family of musicians. On Saturday nights, the Davidoff house was open for visits, conversation, jokes, and music they played on violins, cellos, and piano. Haavie was an accomplished pianist who could sight-read complex compositions with ease. Evenings ended with sing-alongs and hot-out-of-the-oven bagels.

In June of 1947, Dan had an offer of a 2-year membership at the Institute for Advanced Study in Princeton and a concurrent 1-year instructorship at Princeton University, but 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.

Dan and the Institute for Advanced Study (IAS).

The following section outlines Dan's long affiliation with the IAS from 1947 to his death in 2017.

Their furnished apartment at the Institute was one of two in a remodelled carriage house, and the other tenants were Atle and Hedi Selberg, also newlyweds. The couples got along very well. During this stay, Dan met many other mathematicians at the Institute, including Deane Montgomery and Harish-Chandra both of whom became lifelong friends.

In 1949, Selberg accepted a professorship at Syracuse University, scheduled to begin in 1950, when his visiting membership at the Institute would expire. When Dan received an assistant professorship offer from Syracuse, Selberg urged him to accept it, which he did. But by the time that Dan arrived in Syracuse in July 1949, Selberg had been appointed a permanent member of the Institute. At Princeton, Dan attended a course by Emil Artin on Number Theory, a course by Claude Chevalley on Lie Algebras, and a course by Norman Steenrod on Fiber Bundles. Dan's first published paper was written while attending Chevalley's course.

Dan remained connected to the Institute for the rest of his life. He was a visiting member for the year 1956-57, and spent terms there in 1975 and 1990. He served as Academic Trustee of the IAS from 1982 to 1992. During 1985 and 1986, Trustee Mostow was Chairman of a Visiting Committee to the School of Mathematics, tasked with reviewing their activities and making recommendations

The review of the School of Mathematics was complete in 1986. Dan's recommendations were as follows:

1. To adopt a structural change: an annual program consisting of eight senior and junior year-long visitors, led by a distinguished Visiting Professor in an area not covered by the Institute's faculty expertise.

2. To construct a new building for the School of Mathematics which would provide offices, seminar rooms, and a Common room.
The first recommendation resulted in the successful "Special Year" programs - each led by one or more Distinguished Visiting Professors at the peak of their careers. These programs continue today.

The second recommendation led to immediate fund-raising for the mathematics building (and for an additional large general auditorium). James Wolfensohn, Chairman of the Board of Trustees, got the fund-raising started with a million-dollar gift.

Mostow was appointed head of Buildings and Grounds, and (as an amateur architect who had designed his own home) enjoyed watching the new mathematics building rise. He also was a member of the Budget Committee, and had to deal with the demands of the local Princeton administrators who were searching for a way to levy new taxes on Institute property. In addition, he participated in fund-raising, participated in outreach meetings, and wrote letters of thanks to donors.

Mostow spent the 1990 fall term at the Institute, keeping an eye on the construction, and working with Pierre Deligne on a paper that grew into their book: Commensurabilities among lattices in $PU(1, n)$, Annals of Mathematics Studies, 132.

Dan retired as Trustee in 1992. At the retirement ceremony, he concluded his comments with:
The Institute has played a special role in my career, in both the professional and personal phases. Many of the faculty and their families have been good friends, some for almost 45 years. The school for mathematics occupies an extraordinary position in my chosen profession. The thought that I may have made a positive contribution is very satisfying. I thank you all for the kind sentiments expressed this evening.
He was presented with the following Citation:
To G D Mostow, whose two terms as Academic Trustee have made us all more aware of the beauty and architecture of mathematics, the Board of Trustees herein expresses its gratitude.

Deft Chairman of the Visiting Committee to the School of Mathematics in 1985-86, vigorous Chairman of the Buildings and Grounds Committee since 1988, especially in the past two years as the new mathematics building has taken shape and substance, he has sustained and explained the unique role of the Institute in enhancing the quality of mathematics not only in this country but throughout the world.

Gifted interpreter for the less numerate, Dan was able to take every Board Member with him into those magic realms he frequents.

We came to know something of the adventure, the excitement, and the satisfaction of this field which lies at the foundations of our civilization as it does at the foundations of the Institute.

Colleague and friend, we wish him Godspeed and hope that he will continue to visit us as before, enlarging our comprehension and illuminating our minds.
The new mathematics building was dedicated in 1993, and Dan presented a speech entitled Space, Time, Mathematics to an audience of Trustees, members, and other well-wishers. Given the title, the audience probably was braced for a technical lecture, but Dan had a gift for crafting speeches that could be understood by non-mathematicians. He stated:
... I feel that this occasion calls for remarks in the converse direction: how mathematics gets shaped over time and space.
and presented a lively history of mathematics that made a case for the value of the expansion of mathematical knowledge.

The speech concluded:
The building we are dedicating today was designed to optimize the mathematical productivity of its faculty and its 60 odd members visiting from all parts of the world, by providing them with space and time for both private concentration, planned interactions, and chance encounters. Eliminating as it does the dispersal of its members, we can at last provide optimal conditions for the School of Mathematics.

What about the future? Some of the mathematical advances made here may supply the missing link of an ambitious algorithm and result at once in dramatic technological advances, as well as intellectual and material rewards, for the inventor. Other of the advances, if not most, may be destined to have pragmatic effects centuries from now. Guided by history, we can conjecture with confidence that the benign influence of this new mathematics building will project far into the future.
Until the end of his life, Dan was frequently invited to special events and ceremonies at the Institute, and visited old friends.

[Note: Dan's other favourite location for academic leaves was the Institut des Hautes Études Scientifiques (IHES), in Bures-sur-Yvette, France. He visited IHES four times.]

#### Chapter 2.

In 1949, Dan arrived in Syracuse as an Assistant Professor. The family's first social call was to the home of Lipman (Lipa) Bers, and the families started a life-long friendship. Bers soon left for a year at the Institute for Advanced Study.

At that time, there were many stars on the Syracuse faculty, but the situation was unstable because of friction between the research and non-research faculty. In 1952, Dan was relieved to accept an Assistant Professorship at Johns Hopkins University, which strongly supported research.

In the summer of 1953, Dan was invited to speak at the first American Mathematical Society Summer Institute, directed by A Adrian Albert and Irving Kaplansky. There were two important outcomes. He met Armand Borel, with whom he began a collaboration and a lifelong friendship, and also met Irving Kaplansky, who asked if Dan would be willing to spend the academic year 1953-1954 at the 'Instituto Nacional de Matematica Pura e Aplicada' (IMPA) in Rio de Janeiro, Brazil. Dan checked with the Hopkins mathematics chairman, who encouraged him to accept.

[Note: This was the first of many journeys. Dan was eager to see the world. He learned languages easily, and over the years, he lectured in Portuguese Dutch, French, Hebrew, and German, (but sometimes had to speak in English).]

Dan, Evelyn, and their two sons travelled to Rio de Janeiro by boat. They decided to travel to Brazil by steamship because Evelyn had been frightened by a bumpy flight from Boston to New York that she had taken as a college student. Dan wrote that:
The boat trip, on the Moore-McCormack Line, from New York City to Rio De Janeiro, lasted two weeks that were filled with good food, good weather, games, and most pleasurably for the women, dancing with handsome partners arranged by the social director.
See the photo of Evelyn dancing with the ship's Valentino at THIS LINK.

After moving into their apartment in Rio, they discovered that there was a problem. At some times of day, the water would start out clear, but then turn brown. Sometimes, it just started brown. All of these starts and stops apparently were under the control of the superintendent of the building and the city water system. One day, the water stopped completely and did not return. A helpful neighbour told them:
Go to the corner garage. Brazilians have their cars washed there every day and they have lots of water. A government Minister lives on that street and he arranges that there is always water there.
The year in Brazil turned out to be productive mathematically. Dan submitted three papers for publication in the American Journal of Mathematics, which was sponsored by Johns Hopkins. His Brazilian teaching duties consisted of giving a course on his research in their spring term. He learned to speak Portuguese before the term began and lectured in Portuguese.

Conference in Mendoza, and Grothendieck.

UNESCO had organised a July conference on the mathematics being done in Latin America. The conference was held in the city of Mendoza, Argentina, high in the Andes, on the border of Chile and Argentina.

Dan was invited to give a lecture, and he planned to speak in English. However, when he arrived, his host said "We hear that you are lecturing in Portuguese in Rio. Most of the mathematicians here in Argentina do not know English and would understand you better if you spoke in Portuguese." He did so, attempting to improve communication by using Spanish verb endings. Dan reported:
At my talk, I met Alexander Grothendieck, who was 26 years old, for the first time. Grothendieck had received his PhD in France, and he had a job at the University of Sao Paulo. He was beginning to learn algebraic geometry, which was quite different from his dissertation, a massive study of topological vector spaces.

As I lectured, Grothendieck asked a question after almost every sentence - good questions requesting clarifications, and about possible generalizations. Not surprisingly, my lecture went overtime.

After the afternoon talks, Grothendieck, I, and a guide from Mendoza, took an exhilarating walk along one of the mountain trails. As we strode, Grothendieck asked me "How long were you in Brazil before you started to lecture in Portuguese?" I replied, "Around a month." Then he said "I have been in Brazil for more than a year and I am still lecturing in French." Just a few weeks later I learned that Grothendieck had started to lecture in Portuguese!

We kept in touch by mail and our friendship strengthened in 1966 during my sojourn at the Institute des Hautes Etudes Scientifique where he was a professor. For years thereafter, every time that I visited Paris, he invited me to his home for dinner. I saw him in action at some Bourbaki seminars. I was amazed at the dominant standing in Algebraic Geometry that he enjoyed.
After Dan returned to Hopkins in 1954, he was promoted to Associate Professor, and in 1957, he was raised to full Professor.

Gerhard Hochschild.

During the academic year 1957-58, Dan was a member at the Institute for Advanced Study. There he met Gerhard Hochschild and began a partnership that lasted until 1973. In his 2010 Hochschild memorial article, Dan said:
Our mathematical backgrounds were quite different. Gerhard had published papers on the theory of bi-modules, cohomology groups of associative algebras, and the application of cohomology to Number Theory. My previous publications were on geometric aspects of Lie Groups and had virtually no overlap with his at that time. Also, our temperaments were very different, hardly predictive of a joint collaboration that produced 17 papers.
The Mostow family spent many summers in Berkeley, visiting the Hochschilds.

Utrecht University.

After Dan received a reprint from Willem Titus van Est of Utrecht University, they began to correspond. Van Est suggested that Dan should apply for a Fullbright fellowship and visit Utrecht in 1957-58. The fellowship was awarded, and Hopkins granted a leave.

Dan, Evelyn, their two sons, and young daughter travelled to Utrecht by boat. On arrival, they were taken to a resort hotel, and given courses on Dutch language, history, art, and geography. Dan noted:
We had water available 24 hours each day. Milk did not need to be boiled. Our two boys attended public schools and could speak English with the teacher.
And he reported:
Mathematical life in the Netherlands was centrally organized. There was a colloquium each week, followed by lunch at one of the many nearby Indonesian restaurants. Some weeks, there was a seminar reporting on the Bourbaki Paris seminars. The Dutch mathematicians were eager to participate in current advanced mathematics.

The senior mathematicians at Utrecht were Hans Freudenthal, Anthony Springer, and Willem Titus van Est - a distinguished group. Nicolaas Kuiper, at the University of Amsterdam, was not far away. I had useful conversations with all of them.
Paris and Travel.

In one of the posters on the math department bulletin board in Utrecht, Dan noticed that Jean Braconnier was speaking on his paper, Equivariant Embeddings In Euclidian Space.
Listening to my work in French - at the Bourbaki Seminar in Paris - was an experience that I did not want to miss, so I booked a room in a hotel recommended by Nathan Jacobson, at 44 Rue Madame.

A few days later, I received a letter from Harish-Chandra, saying that he was spending the academic year in Paris, and inviting me to visit him and meet his new bride. He gave me explicit instructions on how to get from my hotel to his apartment on Ligne de Sceaux. I look back on that evening, and my conversation with Lily, with much pleasure.
During summer vacation, the Mostow family set off on a six week Grand Tour of Western Europe by car. They visited sites in Luxembourg, France, Switzerland, and Italy, before returning to Utrecht.

After the 1958 academic year, the family travelled to Edinburgh, Scotland for the 1958 International Congress of Mathematicians, and then, finally, home.

Early Years at Yale.

Late in 1960, Dan accepted a professorship at Yale and, in 1961, moved to New Haven. He served as Chairman in 1971-74, and in 1983, was named Henry Ford II Professor.

In the early 1960's, Dan presented a long series of lectures on Lie Groups and Lie Algebras. Notes were taken and typed by his student, Harvey Hyman. In 1963, the 506-page lectures were bound in Yale Math Department cardboard covers and widely distributed. They eventually were digitised and placed on the Internet at:

https://archive.org/details/lecturesonliegro00most/page/n1/mode/2up

In the mid to late sixties, Dan proved his first global rigidity results, which culminated in his 1973 book, Strong Rigidity of Locally Symmetric Spaces, which will be discussed later.

In the early 1970s, Dan's Yale Lie Group Seminar was under way, featuring lectures by many outside speakers. Roger Howe often collaborated in organizing the seminars, which continued until 2002.

60th Birthday Conference.

In March of 1984, a 60th Birthday Conference to honour Dan was held at Yale. Lectures were presented by Pierre Deligne, Jun-Ichi Igusa, Robert P Langlands, John Millson, Mark Mostow, (Dan's eldest son), Yum Tong Siu, Dennis Sullivan, and Robert Zimmer. Roger Howe edited a book based on six of the lectures. In Dan's remarks of thanks, he stated:
... I have been privileged to earn my livelihood by working at a labour of love. I need not tell the mathematicians here that doing mathematics is its own reward. Over and above the pleasure we receive in working on fascinating problems and even solving them occasionally, we have the satisfaction of participating in a construction of central importance to the human spirit: it is only through the eyes of mathematics that our bewildered existence in a Universe of seemingly random motions and perplexing changes can be perceived as the unfolding of a very simple scheme.
The International Mathematical Union (IMU).

Note: Dan Mostow's IMU Positions:
1971-74: Alternate delegate for the U.S. National Committee to the IMU for the 1974 International Congress of Mathematicians (ICM).

1972-74: Convener, to organise and lead a panel to recommend ICM speakers.

1975-78: Member of the U.S. IMU National Committee for Mathematics - to guide the planning for the 1978 ICM.

1979-83: Chair of the U.S. IMU National Committee, attended the 1982 Assembly and 1983 ICM in Warsaw.

1983-86: Member of the IMU Executive Committee.
The IMU organises the quadrennial International Congresses of Mathematicians (ICMs). Each country is represented by a National Committee, usually chosen by the country's National Academy. IMU regulations state that member countries must:
... observe the basic policy of non-discrimination and affirm the rights of scientists throughout the world to adhere to or to associate with international scientific activity without regard to race, religion, political philosophy, ethnic origin, citizenship, language, or sex.
They also require:
... freedom of movement, association, expression and communication for scientists, as well as equitable access to data, information, and other resources for research.
However, the Russian mathematics establishment paid no attention to these rules. During the 1970's and 1980's, influential Russians exerted mounting restrictions on Russian mathematicians who were Jewish, belonged to certain other ethnic groups, or were otherwise out of political favour. Gradually, Jews and the other targeted groups were blocked from University jobs, their travel was prevented, and sometimes, they even were denied the right to publish their work.

ICM lecture sessions are organised by topic. Speakers for a topic are nominated by an international panel of experts in that area. A final decision is made by the Congress Program Committee, which makes choices from each panel's list.

Until the end of the Cold War, there was an effort, led by Russian mathematicians Lev Pontryagin and Ivan Vinogradov, to gain control over the choice of all Russian ICM lecturers and medal winners, taking this duty away from the international panels. They already exerted iron control over which mathematicians were allowed to travel to an ICM. And only favoured mathematicians were allowed to travel for other purposes, especially to countries outside the Eastern Bloc.

1972 ICM Panel and Gregory Margulis.

Gregory Margulis had been an undergraduate and graduate student at Moscow State University. After graduation, he obtained a job as a Junior scientific worker at the 'Institute for Problems in Information Transmission' in Moscow.
Margulis' mathematical research was closely related to Dan Mostow's, and in 1972, they started to correspond, exchanging papers and discussing ideas. Dan was delighted and impressed to discover that Margulis was creating important mathematics at the highest level.

In 1972, Dan was asked to organise and lead the panel to nominate 1974 ICM speakers for 'Algebraic Groups and Discrete Subgroups'. He was determined that Margulis should be invited to speak at the 1974 Congress.

All of the members of his panel, except for Russian mathematician Anatoli Andrianov, agreed that Russians Gregory Margulis and David Kazhdan (both Jewish) should be invited to speak. Andrianov chose Russian mathematician Platonov as his highest choice and disparaged Kazhdan and Margulis. He also claimed that Platonov had found a gap in a proof by Margulis.

When the "final" program was circulated, Kazhdan's name was included, but Margulis' name was missing. Dan protested, stating that Margulis' "result on arithmeticity would be the most spectacular announcement of the Section." Finally, an updated program appeared, with Margulis scheduled to talk in the Section on 'Differential Geometry & Analysis on Manifolds' - whose panel had no Russian members.

The 1974 ICM in Vancouver and 1978 ICM In Helsinki.

Dan was not surprised when Margulis wrote him a letter saying that the Soviets would not permit him to attend and asking Dan to present his paper. Later, Dan described what happened next:
I was the chairman of one of the first-day sessions. On that evening, I received an envelope from the chairman of the meeting committee containing a hand-written paper by Margulis entitled "On Some Motions On Spaces Of Negative Curvature." I looked at the paper and recognised that it was a proof of the arithmeticity of Lattices of Rank > 1 [Note: An achievement that had been unsuccessfully attempted by some of the world's top mathematicians]. I spent the night reading the paper. David Kazhdan, who was scheduled the next day, had not been able to attend, so I took the liberty of presenting Margulis's paper at a special seminar at the time of Kazhdan's scheduled talk. The front row included Atiyah, Deligne, Borel, Sinai, and Tits - and there were gasps of surprise and admiration.
The 1978 ICM in Helsinki.

Four years later, attendees at the 1978 ICM were shocked when Margulis, who had won the prized Fields medal, was not allowed to go from Russia to nearby Helsinki to receive it. After the meeting, Dan and Evelyn Mostow flew to Russia and spent two weeks with Margulis in Leningrad and Moscow. Dan writes:
In order to visit us at our hotel, he had to call me from a public telephone booth near the hotel so that I could come down to the front door and escort him past the guard. Whenever he came to my room, I had to keep in mind that our conversation was being monitored.
1982 and 1983 ICM in Warsaw.

Warsaw, Poland was chosen for the next 1982 ICM, but it turned out to be a fateful choice.

Lech Walesa was a Polish electrician who worked in the Lenin (now Gdansk) Shipyard. His role as a Trade Union activist caused the authorities in Poland to arrest him several times. Walesa continued his activities and became a strike leader, and the strikes spread across Poland. In 1980, Walesa co-founded and led the Solidarity Trade Union. Many people who wished to replace Communism with a democratic government joined, and Solidarity grew into a powerful political force with over 10 million members that included workers, professionals, and scientists.

In December, 1981, Polish leader Wojciech Jaruzelski imposed Martial Law on Poland, and set out to destroy Solidarity. It was harsh. Streets were patrolled by military vehicles, independent newspapers were closed, communications were cut off, and many were detained or imprisoned without trials.

There was no hope of holding an International Congress in Poland in 1982. Governments were unwilling to provide travel funds to send their mathematicians into a dangerous situation. As Dan Mostow, now Chairman of the U.S. IMU Committee, wrote in a report to the IMU Executive Committee on 15 March of 1982:
In response to the inquiry of President Lennart Carleson about the expected attendance of U.S. mathematicians at the scheduled Warsaw conference, the members of the U.S. National Committee have undertaken to solicit the views of mathematicians in various parts of our country. Although many different views are expressed, there is a broad consensus on the following points.

1. A Congress taking place under martial law would be very poorly attended.

2. The outlook of a 1982 Congress in Warsaw is made even gloomier by the fact that the Polish government has not granted the President of the IMU, Lennart Carleson, the assurances that he has requested.

Our committee does not believe that a successful Congress can be held under martial law ...

We understand fully the earnest desire of the Polish mathematicians to hold the Congress in Warsaw. We believe that they, as well as we, would like the Congress to be successful. Accordingly, we would welcome the postponement of the Congress for one year, in hopes that it might be held in Warsaw with complete success a year later.
...
Our apprehension about convening the 1982 Congress in Warsaw does not apply to the General Assembly. Indeed, the U.S. delegation would be delighted at the prospect of contact with Polish mathematicians.
A General Assembly of the National Committees that make up the IMU is held before each ICM to approve the location of the next IMU, elect their next Executive Committee, and vote on proposed resolutions. The Executive Committee decided to hold a General Assembly in Warsaw in 1982, and if possible, hold the ICM in 1983.

Dan arrived at the Assembly with a list of 156 scientists who had been reported detained or imprisoned. He had received his list from the National Academy of Sciences Committee for Human Rights, which was led by his old friend, Lipman Bers.

Dan met with Polish officials to discover the status of the 156 scientists. He was told that most were free, but there was no way to check the numbers. A letter-writing campaign was organised to urge release of the remainder. Not long after this, the Bers Committee received and forwarded a letter from a Polish mathematician that described the current brutal treatment of prisoners.
Nonetheless, the IMU Executive Committee decided to go forward with the ICM in August, 1983.

The Miraculous Polish Pope.

The Polish Pope, John Paul II, visited Warsaw in June, 1983, and met with leader General Wojciech Jaruzelski for two hours.

Pope Paul pressed Jaruzelski to end martial law and restore the Solidarity Union - and to allow him (the Pope) to meet with Lech Walesa. Permission was given. The Pope met with Walesa and persuaded him to halt demonstrations. At a huge outdoor mass, the Pope urged restraint from his countrymen and an end to demonstrations. The result was that Jaruzelski set 22 July 1983 as the date for the end of martial law, and angry demonstrations ceased.

Before the ICM convened, almost all Polish mathematicians were released from prison and internment. The International Congress of Mathematicians proceeded in complete safety from August 16 to 24 and was a success.

A final assessment of the Polish ICM was done by Dan Mostow in an article entitled The 1983 Warsaw Congress published in the Notices of the AMS in October, 1983. He stated that the physical and scientific arrangements had been very well organised, the level of the invited speakers was excellent, mathematical topics were well covered, and there were good opportunities for mathematicians to meet informally. He reported that several of the very best Soviet mathematicians were able to attend a Congress for the very first time.

Ludwig Faddeev, the 1986 General Assembly, and A Resolution.

Ludwig Faddeev was a leading Russian Mathematical Physicist, publishing in both fields. Faddeev was the director of the mathematics division of the Steklov Institute in Leningrad. (The main Steklov Institute, in Moscow, housed researchers and the Russian Academy of Sciences.) In 1982, Faddeev had been elected to be one of the two Vice Presidents of the IMU Executive Committee.

In March, 1985, the Soviet National Committee proposed that Ludwig Faddeev should be elected President of the IMU. The Executive Committee, which now included Dan, met in May and discussed Faddeev's candidacy. A large majority was in favour, but a minority, including Dan, was opposed.

Dan summarised the pros and cons in a letter he sent to the members of the U.S. National Committee for Mathematics. It stated that, in Faddeev's favour, there never had been a Russian President, and Faddeev was a mathematician of high standing who had excellent personal qualities. Against, in Leningrad, Faddeev might be incommunicado, and the official Soviet bureaucracy might constrain him. Dan also cited the Russian discrimination against Jewish mathematicians, and their substantial violations of the norms of scientific merit in the selection of Soviet mathematics faculties.

Dan was firm in his opposition, but he was under a great deal of pressure to drop it. At the 1986 Assembly in California, the pressure on Mostow continued, but instead of relenting, Dan thought of a solution. The IMU was pledged to the Principle of Universality of Science, which already called for international collaboration and opposed "discrimination based on such factors as ethnic origin, religion, citizenship, language, political or other opinion, sex, gender identity, sexual orientation, disability, or age."

Dan drafted a non-discrimination Resolution that was stronger than the existing rule, and could be submitted to a vote at this General Assembly. He was willing to support Faddeev if Faddeev would support the Resolution. Dan wrote:
Thereafter I showed the draft to Faddeev; he replied that the proper person with whom to discuss the draft was the Chairman of the Soviet delegation to the General Assembly. When I did so, the Chairman listened attentively and asked if he might take the draft and meet me a few hours later at noon. When we met at noon, he returned my draft with a barely perceptible revision and pledged their support in the General Assembly.
This step of obtaining Russian support was crucial. At the Assembly session, there were 98 votes in favour of Mostow's Resolution (including all of the Russians), and 0 against. The result was that Faddeev was the only nominee for President, and the chairman suggested that the new President be elected by acclamation. The Assembly agreed, and so, for the first time, written ballots were dispensed with. The new President-elect grumbled, "An election like in my country."

Thus, the following Resolution had been adopted by the 1986 General Assembly, and, as shown, preceded the existing Article 5:
RESOLUTION I

One of the principal objectives of the IMU is to promote international cooperation for the advancement of mathematics. It is therefore of fundamental importance that adhering organizations support the basic policy of non-discrimination including freedom of access to higher education, publication in international journals, and participation in mathematical meetings, as expressed in the ICSU Statute, Article 5:

"Article 5. In pursuing these objectives, ICSU shall observe the basic policy of non-discrimination and affirm the rights of scientists throughout the world to adhere to or to associate with international scientific activity without regard to race, religion, political philosophy, ethnic origin, citizenship, language, or sex. ICSU shall recognize and respect the independence of the internal scientific planning of its national Members."

The General Assembly of the IMU supports the ICSU resolution in full and appeals to all adhering organizations to follow it.
Of course, there were no results for the immediate meeting. Although the general attendance at the 1986 Congress in Berkeley, California was large, almost half of the Russian speakers were not present and only 57 other Russian attendees appeared.

However, Russia had good participation at the 1990 Congress, which took place in Kyoto. Faddeev concluded his presidential address at the 1990 General Assembly with the statement:
It is traditional ... to reiterate our commitment to the principle of free circulation of scientists. The political issues in connection with this were sometimes a source of tension. Now due to changes in many countries this topic became self-evident, as it must be. This makes it possible for us to concentrate on our main professional duty - mathematics.
A Russian Revolution - and a Redemption.

Starting in 1985, immense changes occurred in the USSR under Gorbachev. By 1989, Soviet satellite states were breaking free. By the end of December, 1991, the USSR had dissolved.

Life in Russia was chaotic. There were serious economic problems. Many mathematicians fled to the West. Others were suffering hardship at home.
After the Berlin wall came down and the Cold War was over, the reaction in the U.S. scientific community was extraordinary.

The U.S. National Research Council of the U.S. National Academy of Sciences began collaborations with the Academy of Sciences of the USSR. After a meeting of their representatives, the Presidents of the two Academies confirmed their support for a five-year agreement for scientific cooperation and developed an ambitious program of joint activities that included four scientific workshops per year, with two held in the United states and two in the USSR.

The U.S. NSF offered funds for cooperation between American and Soviet scientists.

Vladimir Platonov had been Director of the Institute of Mathematics of the Academy of Sciences of Belarus in Minsk since 1977 and wished to host a joint USSR/US Symposium there. Mostow and Borel agreed to help. They developed a proposal, obtained approval from both the U.S. and the Russian National Academies, and gained financial support from the NSF.

The result was the 'Soviet-American Symposium on Algebraic Groups and Related Number Theory', 22-29 May 1991, at the Minsk Mathematics Institute. The Organizing Committee consisted of: Borel and Mostow from U.S, Platonov and Margulis from U.S.S.R.

In 1990, Margulis left Russia and came to the U.S., and in 1991, he accepted a professorship at Yale. A few years later became a U.S. citizen. He subsequently received a Wolf Prize, an Abel Prize, and other honours.

#### Chapter 3.

Human Rights.

Dan's actions at the 1982 Warsaw Assembly, and his efforts to bring about adherence to IMU non-discrimination standards have appeared in Chapter 2.

He also was a regular correspondent for the National Academy of Sciences Committee on Human Rights (led by his friend Lipman Bers), and in response to their notices, wrote in defence of scientists who were prisoners of conscience in countries that included Cuba, Chile, China, Egypt, Ethiopia, Poland, Russia, Turkey, and Yugoslavia.

Some of his activity was more personal.

Ilya Piatetsi-Shapiro.

Ilya Piatetsi-Shapiro was an extremely gifted Russian mathematician.
Dan first met Ilya in 1970, at a conference in Budapest organised by K Malyuscz, a student of Gelfand. As described in a Dan's memorial article about Ilya in the November, 2010 Notices of the AMS:
The conference was designed to bring together, for the ﬁrst time, leading mathematicians from the USSR with their counterparts from the West. Such meetings had not occurred since World War II. ...

I first met Ilya at this conference. One evening, Ilya invited as many of his countrymen and westerners as could ﬁt into his small room. We shared the bottle of amber-coloured old Vodka that he had brought from Moscow. I still get a high when I recall the conviviality of that get-together - a far cry from the discriminatory anti-Jewish policies of the USSR National Committee for Mathematics at that time.
In 1970, Ilya had two jobs, but that changed. He lost his part-time position at the mathematics department of Moscow State University in 1973 after he signed a letter asking Soviet authorities to release a dissident mathematician from a mental institution.

In 1974, he applied for an exit visa and was refused - becoming a Refusenik. He lost his other job (at the Moscow Institute of Applied Mathematics), was followed around by a KGB car, and his apartment was under electronic surveillance. In his apartment, he communicated with visiting friends and colleagues by writing on a plastic board.

In 1976 Mostow joined with Ahlfors and Tate to ask the U.S. National Academy to intervene on behalf of Ilya, and to also recommended action by the U.S. State Department. The Council of the U.S. National Academy of Science exerted pressure, and later that year, Ilya obtained an exit visa. From then on, Ilya divided his time between positions at Yale University and Tel Aviv University in Israel.

Ilya and the Brailovsky Seminar.

A series of bold Moscow mathematicians brought some relief to Refuseniks by hosting seminars in their apartments. In 1977, Victor Brailovsky became the seminar's host. He was arrested in November, 1980. U.S. alumni of the Moscow Seminars decided to bring attention to the situation by holding seminars in the United States. Each seminar was held in a different city, and minutes of each meeting were mailed to Moscow contacts for distribution.

On 21 December 1980, a seminar organized by Piatetsky-Shapiro, Mostow, and Prof D E Prober was held at Ilya Piatetsky-Shapiro's apartment in New Haven. The goal was to bring attention to the closing down of the Moscow Refusenik seminars and the jailing of Viktor Brailovsky. They made sure that the event was well covered by the press.

1999, A Shared Retirement.

In 1999, Dan and Ilya shared 3-day conference in honour of their concurrent Yale retirements. Speakers included Cogdell, Deligne, Margulis, Rallis, Sarnak, Selberg, Siu, and Zimmer, and there were many attendees.

Defending Mathematical Research in the U.S.

In the U.S., the 1970s and 1980s were times of economic instability, with periods of recession, industrial contraction, and unemployment. Many in the U.S. government - and among the public - blamed this on a failure of U.S science and technology, even though the U.S. led the world in both. The frequent cry was "The Cold War is over, and everything is changed!"

Most of the problems actually stemmed from poor industrial management. But the public wanted scientists to be recruited to team up with industry and produce technology that would solve all of industry's troubles. The recruitment effort was to be implemented by targeting government research money to support collaborations with industry.

Most people had a image of mathematics that was static, consisting of what they had learned in school. The usefulness of mathematical research and the environment in which it flourished were not understood.

Dan was a passionate promoter and defender of mathematical research, and worked hard to gain financial support and create homes for research. In 1982, he was a leader in the effort to create research centres at UC Berkeley 'Mathematical Sciences Research Institute' (MSRI) and the 'Institute for Mathematics and its Applications' (IMA) at the University of Minnesota.

He also served on the U.S. National Academy 'Ad Hoc Committee on Resources for the Mathematical Sciences' to review the health and support of U.S. mathematical research. Their report, Renewing U.S. Mathematics: Critical Resource for the Future, published in 1984, (referred to as the "David Report" after the capable committee leader, Edward David Jr.) stated that:
Unless corrective action is taken, the health of the nation's mathematical research effort, now still the strongest in the world, will be seriously weakened.
For many years, the National Science Foundation (NSF) had been a major source of funds for University mathematical research and support for graduate students and post-docs. But allocations decreased steeply through the 1970s and 80s. The problems persisted into the 1990s. The prevailing attitude towards mathematicians was hostile. An article in the March 19, 1992 article in The Scientist newspaper reflected this. Its headline read:
Mathematicians: Real-World Applications
Are Keys to Increasing the Field's Appeal
Mathematicians: Industry Ties are Vital
On 31 March 1992 Robert Zimmer, Chairman of the University of Chicago mathematics department, wrote to peers at other universities (including Dan Mostow), and formed a Committee to take action. In April, member Dan Mostow drafted a resolution to be considered in the Mathematics and Applied Mathematical Sciences Sections of the National Academy of Science:
Resolution: Among Federal Agencies, the NSF more than any other carries the mission of nurturing the broad culture of the physical sciences, from which future science, technology, and the nation's well-being will flow in ways that we cannot now anticipate or program. The NSF therefore has a special responsibility for sheltering basic science by keeping its needs in proper balance with its legitimate short term economic and technological objectives. The recent NSF budgets suggest that this responsibility is at risk.
As the months passed, Members of the Zimmer Committee communicated with NSF administrators and with their own University officers. On behalf of his Committee, Robert Zimmer wrote to the recently formed Special Commission on the future of the NSF to raise the issue. Dan was chosen to speak to the oversight National Science Board. Part of Dan's colourful argument was:
To sum up with a metaphor, mathematics can be compared to a mine which has been in operation for a long time. Most of the ore that has been mined in the past has been shipped all over the world; some lies stockpiled near the mine entrance, ignored for long periods. The mine is very deep; what is visible above ground is only a small part of the intricate system below.

To pursue this metaphor, the mines are currently encountering more and more gold. One cannot find the gold on the stockpile. Rather the expert miners have to go down to the depths and dig deeper. Our core mathematicians correspond to those miners. And the minerals they seek are not the obvious ones like gold alone. Industrial needs keep changing and the mathematical algorithms they require correspond to novel ores that are not stockpiled but can be found only after much exploration and additional digging. To divert mathematicians from their deep digging is counterproductive.
Finally, in its 20 November 1992 final report, the Special Commission affirmed the continuance of the responsibility of the NSF to support research and education, and conditions gradually improved.

American Mathematical Society (AMS).

Dan gave many years of service to the American Mathematical Society (AMS). Between 1959 and 1993, Dan served as a member or chair of eighteen AMS committees.

1988 was the 100-year anniversary of the AMS, and there was a wish to celebrate it in grand style. It was probably with this in mind that Dan was elected to be President of the AMS for the 1987-1988 term. A very ambitious program was planned, with meetings in Atlanta GA, Boston MA, Washington D.C., Irvine CA, Hempstead NY, and Minneapolis, MN, climaxing in a very large assembly in Providence RI.

The overall program was designed with the goal of making mathematical topics more accessible to students, teachers, and academics. In his speech at the start of the Providence meeting, Dan said:
... Revelations, resting on both the invention of new concepts and discoveries of interrelations among pre-existing concepts, occur repeatedly throughout the development of mathematics, in our times as of old. The scientific program this week will describe revelations in the major mathematical areas, which opened new roads to attack old problems, to create new syntheses, and which lead the way to rich uncharted territory. ...

Dan became a member of the National Academy of Sciences (NAS) in 1994.
However, long before he was a member, Dan served on a number of committees of the National Academy of Sciences and the National Research Council, which conducts studies and publishes reports.

For example, the National Research Council appointed him to be the first Chairman of the new 'Office of Mathematical Sciences, Assembly of Mathematical and Physical Sciences', and he served from 1975 to 1978. Later, from 1983 to 1989, he was Chair of the 'Office of Mathematical Sciences'. From 1982 to 1985, he was Chairman of an NAS committee that supervised the balloting for new mathematics members, and prepared a report used to help select the list of new mathematics nominees to the Academy.

Also, from 1990 to 1994, he was a Member of the IMU Turn of the Century Committee, to plan events and publications for the World Mathematical Year 2000 (WMY) Celebration.

Dan was known to be an astute and honest reviewer. On several occasions, he was recruited to review a mathematics department over a period of years. In the U.S., his appointments ranged from Harvard (1975-1981) and MIT (1981-1996) to visiting the Military Academy at West Point for a few days in 1978.

At various times, he was appointed to advisory positions for the mathematics departments of four Israeli universities. He also was used as a reviewer of Fullbright and NSF applicants.

He was an able meeting organiser. Examples include the 1965 AMS Summer Institute, the Mathematical Heritage of Hermann Weyl, held at Duke University in 1986, the 1989 Gibbs Symposium at Yale, and a 1993 meeting in honour of Gelfand at Rutgers, Functional Analysis on the Eve of the Twenty-First Century.

Editor.

Dan usually could read and assimilate a research paper in his field quite quickly. He was offered many editorships, and accumulated a mountain of manuscripts.

Over the years he edited for the Princeton/IAS Annals of Math, the Hopkins American Journal of Mathematics, American Scientist, Geometriae Dedicata (Netherlands), and the Journal D'Analyse Mathématique, (Hebrew U) .
He also edited some Proceedings of meetings, including:

1. In 1965-66, with Borel, he edited: Algebraic groups and Discontinuous Subgroups, Proceedings of Symposia in Pure Mathematics, Boulder, Colorado.

2. In 1977, with Borel, he edited: Several Complex Variables - Proceedings of Symposia in Pure Mathematics, Volume XXX, Part 2, American Mathematical Society.

3. In 1989, with physicist D G Caldi, he edited: Proceedings of the Gibbs Symposium, Yale University.
[NOTE: When Dan was an editor of the American Journal of Mathematics, in 1964 he received a manuscript with the following covering letter:
Dear Sir,
The enclosed manuscript is submitted for publication in the American Journal. I believe you will find it easier to handle this business if you refrain from involving my collaborator in the considerations pertinent to the publication of this material.

Sincerely yours, G Hochschild.
Hochschild's collaborator was, of course, Mostow.]

Rigidity and the Steele Prize.

In 1973, Dan's most important work was published in his book, Strong Rigidity of Locally Symmetric Spaces. This work led to many later results including important work by Margulis, Thurston, Perelman, Siu, Corlette, Gromov, and Schoen.

It resulted in Dan's 1993 award - the American Mathematical Society's 'Leroy P Steele Prize for Seminal Contribution to Research'. His Citation stated, in part:
To George Daniel Mostow for his monograph on Strong Rigidity. The Strong Rigidity Theorems of Mostow proven in his Annals of Math. Studies Vol. 78 (1973) are central and landmark achievements in modern mathematics. ...

Mostow's Annals Study (and his paper in I.H.E.S. Publications 1967) changed the subject by proving the first global results. First in the I.H.E.S. paper he showed that if $G$ is the isometry group of hyperbolic $n$-space $n ≥ 3$, $\Gamma _{1}$ and $\Gamma _{2}$ lattices in $G$ and $\theta: \Gamma _{1} \rightarrow \Gamma _{2}$ is a group isomorphism of $\Gamma _{1}$ to $\Gamma _{2}$, then they are conjugate in $G$. In this paper Mostow introduces the crucial idea of extending equivariant maps (which are defined via $\theta$) to the boundary of hyperbolic space. He then uses and develops creatively the theory of quasi-conformal maps and ergodic theory to construct the conjugation. In his Annals of Math Study, Mostow proves the strong rigidity theorem for all semi-simple groups $G$ (not $SL_{2}(\mathbb{R})$.
...
It is clear that the subject initiated by Mostow is still very much alive and exciting. To quote M Gromov (see his paper "Asymptotic invariants of infinite groups", p. 11) "The hyperbolic geometry took a new turn in 1968 when G D Mostow discovered his amazing asymptotic proof of the rigidity of lattices in $O(n,1)$". These papers of Mostow merit this award both in their own right as foundational achievements and as the fountainhead of this great stream of mathematics.
The following is a brief extract from Mostow's response:
... The idea was to exploit the ergodic action of the group of homotheties in the space of all lattices in this group. Thereby one could show for the case of real hyperbolic space that the boundary map was not only smooth but even Moebius. Over the ensuing few years, in combination with other ideas, a corresponding result was obtained for every group except $SL_{2}(\mathbb{R})$, in which the rigidity phenomenon does not occur.

The pleasurable excitement of working that out was its own reward. The subsequent contributions to rigidity of Prasad, Margulis, Sullivan, Zimmer, Siu, Mok, Pansu, Corlette, Gromov-Schoen added to the pleasure. The topological results of Thurston and Farrell-Jones added even more. Your award today makes my cup run over.
The Wolf Prize.

In 2013, Dan was awarded the Wolf Prize in Mathematics "for his fundamental and pioneering contribution to geometry and Lie group theory." His Wolf Citation stated:
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 led 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.
In an interview at Yale, Dan said that the solution to the problem came to him while waiting at a red light in New Haven, Connecticut, where he had resided since the 1960s. "Earlier, in my office, I had been thinking intensively about the problem. I did not think about it while I was driving, but at the light, at that moment, I suddenly thought: 'Use ergodicity!' When I got home, I immediately sketched out a path to the theorem. In fact, I only had to add eight pages to what I already had done to complete the proof."
I get a high every time I pass that intersection.
Dan spent most of his Wolf Prize money bringing his large American family to Israel, and they attended the ceremony and banquet at the Knesset, along with members of his large Israeli family. Dan had close ties to many Israeli universities, and was greeted warmly when he went to deliver Wolf lectures at Bar Ilan and Ben Gurion Universities.

Mostowfest.

On 23 October 2013, Dan was honoured by a meeting at Yale to celebrate his 90th birthday and his Wolf Prize: 'Mostowfest: Geometry, Analysis, and Wolf Prize'.

His daughter Carol spoke for the family, and the guest lecturers were Pierre Deligne, Robert Langlands, Curtis McMullen, and Yum-Tong Siu. The following quote is from the beginning of Yum-Tong Siu's lecture:
I remember when I came here to Yale it was 1970 and I was in my twenties and after I came here Dan was chairman and he took care of me in every way - in the settling in and in all aspects of department life and social life.

And also more important, he changed the direction of my research. Before I came, I was working on something else and then afterwards I went into to this whole area of rigidity.

I was a graduate student and I also remember Dan's office on the 4th floor more or less at the end and at one time I was on the second floor and after I moved up and I was told that he now was the chair.

And then Dan told me about his work - about reflections of subgroups to try to produce an arithmetic lattice. He was using a lot of computers in those days and at one point he did not quite yet get the discrete subgroups - almost discrete subgroups -and he wondered what could be done with it. And that is the point when I was introduced to his great work.

So we were trying to compute various things - volumes Chern classes and so forth.

One thing that really of shocked me was that Dan was 20 years my senior - and I think that he still is 20 years my senior - but when we were trying to compute things - in hyperbolic geometry with all these hyperbolic signs and when you really want to compute things with all these hyperbolic signs and so forth, you have to do everything arithmetically.

He could do it at tremendous speed. And I was 20 years his junior and I was very slowly writing down and he could zoom just write it and I was extremely shocked - this guy's intellectual power is just fantastic.

So I thought one day - timidly I asked him how could you compute so fast? He was very modest - he told me that he spent four years doing this during the war. He was teaching people how to fire cannons. And the cannons had such a big range that the curvature of earth had to be taken into account.

So he was using spherical functions not the hyperbolic ones, but you had to change the sign and if you changed the sign you could do it without a mistake quickly. You could do it with tremendous speed. And so this thing I distinctly remember.

So after that I studied his work and I saw this wonderful treasure so I went into it and tried to understand it. And of course his contribution changed my direction and it changed the direction of many, many people, I think.

Last Updated September 2021