David A Kazhdan

Quick Info

20 June 1946
Moscow, USSR (now Russia)

David Kazhdan is Russian/American/Israeli mathematician who has made outstanding contributions to representation theory and combinatorics. He has been awarded major prizes: the Rothschild Prize; the Israel Prize; the EMET Prize; and the Shaw Prize.


Let us note at the start that only since emigrating to the United States has the subject of this biography been known as David Kazhdan, for he was given the name Dmitry Aleksandrovich Kazhdan and was known by this name when growing up in the Soviet Union. His name was also transliterated as Kajdan on some of his early papers. We, however, will use the name David Kazhdan throughout this biography. David Kazhdan was the son of Alexander P Kazhdan (1922-1997) and Rimma A Ivjanskaja (born 18 October 1920). Alexander Kazhdan was born in Moscow on 3 September 1922 and educated at the Pedagogical College of Ufa before receiving his PhD in 1946 from the Institute of History at the Moscow Academy of Sciences. At this time, because of Stalinist persecution, it was almost impossible for Jews to obtain university positions. Alexander Kazhdan began teaching in teacher training institutes but was later exiled to posts in provincial colleges. Alexander and Rimma Kazhdan were married in 1944. Their only son, David Kazhdan, the subject of this biography, was born two months prematurely and was not expected to survive. But, against the odds, he did. He grew up, the only child in a Jewish but atheist family, with both parents academics. In the video [21] he explained how he became interested in mathematics because of a stunt to skip school when he was in the fifth grade of his local elementary school:-
When I was eleven, I decided that I didn't want to go to school every day. I asked my parents to give me permission to skip one day of school. They said, yes, if you do something reasonable. So I suggested to them that I'd learn chess. And for half a year I learned playing chess. And then they said it was not sufficient, choose something else. So I chose mathematics. This is how I started mathematics.
For a year, with his grandfather who had no secondary education, he quickly studied algebra, geometry and trigonometry. After this year in which he was self-taught, he joined a mathematics club run by two students who were studying mathematics at Moscow State University. This was a revelation; he quickly appreciated the beauty of the subject and also began to understand how different mathematical topics which at first sight looked totally unrelated, were in fact supporting each other. He became an avid reader of mathematics texts and in his frequent visits to book stores he would meet Naum Yakovlevich Vilenkin (1920-1991). Vilenkin had studied at Moscow State University where he had been a student of A G Kurosh. He was the author of many books, both monographs on representation theory, harmonic analysis and special functions, as well as books on recreational mathematics and high school texts. Vilenkin was attending Israil Moiseevic Gelfand's seminar at the time Kazhdan met up with him.

I M Gelfand had a son Sergei I Gelfand who was two years older that Kazhdan. Gelfand was about to start teaching his son advanced mathematics and was hoping to find another pupil to teach with him. Vilenkin told Kazhdan about this and gave him Gelfand's phone number. Although Kazhdan was only about thirteen years old at the time, he phoned Gelfand and said how keen he was to join Sergei in being tutored by Gelfand. After being invited for an interview, during which he showed his extraordinary potential, Kazhdan began going to Gelfand's home to learn advanced mathematics. He wrote [5]:-
Those meetings opened the world of mathematics to me. The fundamental lesson Gelfand imparted was the feeling that mathematics constitutes a unity, that even if in the apparent diversity of subjects falling within the discipline, such divisions should not be taken too seriously.
Kazhdan wrote his first paper with Sergei Gelfand when he was fourteen years old and Sergei was sixteen. The paper was An integral equation connected with a pulse motion around a circle (Russian) and the review of the paper in [42] states:-
The following problem is considered. An impulse is propagated along the circumference of a circle. The velocity of the propagation of the impulse depends on the position of the given point on the circumference which is given by the time τ\tau elapsed since the last previous passage of the impulse through the given point. The object is to prove that if we are given τ\tau on the circumference in any way, and after that induce on the circumference one or several impulses, than their velocity will tend to some constant which is independent of the initial state. If the number of impulses is greater than one, then their limiting velocity will be the same for all impulses and the distances between the impulses will become equal. This problem has been considered in an earlier work [I M Gelfand and M L Cetlin (1960)]. The proof is accomplished under the assumption that the velocity function υ(τ)\upsilon(\tau) is strictly monotone and differentiable.
This is a remarkable work by two high school pupils. Kazhdan continued to mix with top mathematicians through clubs and seminars while still at school and continued to be almost intoxicated by the beauty of mathematics when, at the age of seventeen, he began studying at Moscow State University.

An important event occurred in 1966 when the International Congress of Mathematicians took place in Moscow. The congress opened on 16 August 1966 when the president of the Academy of Sciences of the Soviet Union, Mstislav Vsevolodovich Keldysh, welcomed over 4200 mathematicians. Ivan Georgievich Petrovsky, the rector of Moscow State University, was president of the Congress. It was an important event for Soviet mathematicians, particularly for Kazhdan, since contact with mathematicians outside the Soviet Union had been non-existent for many years but now they had the opportunity to have discussions with over 2000 mathematicians from the West. Particularly significant for Kazhdan was his contacts with Michael Atiyah and Harish-Chandra. He wrote [5]:-
Despite the hermetically closed borders of the communist state, for young Soviet students such interactions offered access to cutting edge developments in the various realms of mathematics on an international scale.
He produced an amazing result while an undergraduate and published it in the paper On the connection of the dual space of a group with the structure of its closed subgroups (Russian) (1967). This paper introduces what today is called Kazhdan Property (T). In the video [21] Alex Lubotsky said that Kazhdan:-
... proved to be a prodigy. Let me illustrate this by an early example. When he was still a kid, I am not sure exactly what age but maybe about 18 or 19, he had already become internationally famous for something which nowadays is called Kazhdan Property (T). What is amazing about this Kazhdan Property (T) is that so many applications in so many different areas have been found, some of then by Kazhdan himself, but also by so many other people, and the most interesting thing is that they've even found application of the Property (T) in down-to-earth applied mathematics, or more precisely in computer science. There are nowadays some network communications which are built by the so called expander graphs and expander graphs were constructed for the first time using Kazhdan Property (T).
Gregori Aleksandrovic Margulis was a student at Moscow State University at the same time as Kazhdan and the two collaborated in solving an important open question. They published the joint paper A proof of Selberg's hypothesis in 1968. In this paper they solved several outstanding problems, including proving a conjecture of Selberg on the existence of unipotent elements in non-uniform lattices. In fact the paper proves two results which had been conjectured by Selberg and proved by him and others in some special cases. In a review, Armand Borel describes these results by Margulis and Kazhdan as "basically elementary, but very ingenious."

Kazhdan received his diploma (equivalent to a B.Sc.) from Moscow State University in 1967. He then undertook research advised by Alexandre Aleksandrovich Kirillov and was awarded a Kandidat Degree (equivalent to a Ph.D.) from Moscow State University in 1969. While a research student at Moscow State University, Kazhdan married fellow mathematics student Helena Slobodkin (born 18 September 1946). Between 1969 and 1974 three of their children, Eli, Dina and Misha, were born in Moscow. We note here that Misha Kazhdan received his bachelor's degree in mathematics from Harvard University in 1997. He then earned a master's degree and Ph.D. in computer science from Princeton University in 2001 and 2004, respectively. His Ph.D. thesis was Shape Representations and Algorithms for 3D Model Retrieval. He then joined the Whiting School of Engineering at Johns Hopkins University.

David Kazhdan had grown up in an atheist family, and in his early years felt that religion was irrelevant and something left over from the middle ages. When in his early twenties a close friend converted to Christianity and Kazhdan became very aware of his Jewish roots and taught himself Hebrew and studied Aramaic Jewish texts. On the Sabbath he would attend the central synagogue in Moscow on Archipova Street and between the two morning prayer sessions he would deliver a talk on what he had learned. He was occasionally approached by KGB agents who attended the synagogue and tried to encourage him to join the KGB. Trying to bring up a family in the Jewish religion was not going to be easy with the restrictions against organised religion that the Soviet authorities imposed and this was a major factor in his desire to emigrate. Another factor must have been the fact that, despite his amazing achievements from a very young age, he worked as a researcher in the Laboratory of Mathematical Methods in Biology at Moscow State University from 1969.

In 1970 the International Congress of Mathematicians was held in Nice, France. Kazhdan attended this Congress and delivered the invited lecture Arithmetic varieties and their fields of quasi-definition in Section C5 - Groupes algébriques fonctions automorphes et groupes semi-simples. The 1974 Congress was held in Vancouver, Canada and Kazhdan was again an invited speaker. The Russian authorities, however, did not allow him to attend the congress.

Kazhdan and his family went to the United States in 1975 and Harvard University offered Kazhdan a visiting professorship in the Mathematics Department. He writes [4]:-
Harvard was a remarkably friendly and stimulating place. The Department integrated many different mathematical minds and offered a unique platform for interactions and collaborations between the faculty and the graduate student community. And more broadly, the world of Boston academia provided an auspicious environment for my work. I collaborated with various colleagues at Harvard and was exceptionally lucky to become a friend and collaborator of Romanian-born George Lusztig. And beyond the academic satisfactions of my tenure at Harvard, my family quickly made Boston our "home". Relationships were built and long-lasting friendships forged.
After two years as a visiting professor at Harvard, in 1977 he was appointed as a full professor there. Daniel Kazhdan, the youngest of David and Helena's four children, was born in Boston in November 1980.

Let us note that Kazhdan's parents, Alexander and Rimma Kazhdan, emigrated to the United States in 1979 to reunite with their son. Alexander Kazhdan became a senior research associate at the Center for Byzantine Studies in Washington. From 1983 until 1991 he was editor-in-chief of the Oxford Dictionary of Byzantium.

In 1990 David Kazhdan was awarded a MacArthur Fellowship, known colloquially as the "Genius Grant," which he held until 1995. The MacArthur Foundation states that:-
... the fellowship is not a reward for past accomplishment, but rather an investment in a person's originality, insight, and potential but the award is based on a track record of significant accomplishments.
In [18] the MacArthur Foundation gives details of Kazhdan's most important contributions:-
David Kazhdan is a mathematician known for his contributions to geometry, number theory, and mathematical physics. Kazhdan is concerned with the different ways symmetry occurs in nature and mathematics and his research focuses on algebraic aspects of analysis and geometric, representation theory.  His ideas have influenced work in the areas of automorphic representations, differential geometry, differential equations, representations of finite groups, and number theory.  His most celebrated result, the Kazhdan-Lusztig conjecture, showed that most of the fundamental invariants of representation theory are really invariants of intersection cohomology. He is co-editor of 'Quantum Fields and Strings: A Course for Mathematicians' (1999), and serves on the editorial board of the 'Journal of the American Mathematical Society'.
American Academy of Arts & Sciences adds [13]:-
He also discovered Kazhdan's property and jointly, with Margulis, proved Selberg's conjecture, fundamental in the theory of discrete groups. Kazhdan made important contributions to the theory of infinite-dimensional Lie algebras, quantum groups, representation theory of Hecke algebras, Langlands program, differential geometry, and model theory.
Perhaps the most famous of the students that Kazhdan advised for a Ph.D. at Harvard was Vladimir Voevodsky who was awarded a Ph.D. in 1992 for his thesis Homology of Schemes and Covariant Motives. The ideas in this thesis eventually led to work which saw Voevodsky awarded a Fields Medal in 2002.

But mathematics was not the only topic in which Kazhdan is a leading scholar. Itzhak David Goldberg explains in [23] that in 1976 he met David Kazhdan at Rabbi Joseph Soloveitchik's Sunday morning Talmud class at the Maimonides School in Brookline, Massachusetts:-
I had just started my postdoctoral work in vascular biology at Harvard Medical School. I was immersed in a world of cutting-edge science, of empiricism. But on the weekends I left that world behind to engage with the preeminent rabbi and legendary philosophical scholar who promoted building bridges between traditional Orthodox Judaism and the modern world. And it was in Soloveitchik's class that I met David.

By the time we met, he had vast knowledge of both Hebrew and Aramaic Jewish texts. Soloveitchik enjoyed conversing with him and was amazed by his brilliance and his dedication to Jewish studies.

On a Sunday morning in 1977, following Soloveitchik's Talmud class, David approached me. "Do you want to learn together?" he asked, in a pronounced Russian accent. I said yes, and we set up a daily schedule and started studying "in friendship", as partners.

Over the following decades, we covered various topics and texts. Bible, tractates of Talmud, the writings of Maimonides and of Nachmanides, other philosophical texts. Initially, these daily sessions took place in the early mornings at the Tolner synagogue in Brookline ...
Kazhdan made many short visits to the Institute for Advanced Study, Princeton: April-May 1976; May-June 1986; January 1988; and June 1988. From September 1996 to June 1997 he was a Distinguished Visiting Professor at the School of Natural Sciences and the School of Mathematics during the 'Special Year in Quantum Field Theory' held at the Institute for Advanced Study in Princeton. He gave the course Introduction to QFT which was published in the two volume work Quantum Fields and Strings: A Course for Mathematicians (American Mathematical Society, 1999). In a review of the book William Faris writes:-
Kazhdan's lectures in Part 1 treat the axiomatic approach to quantum field theory. This is an attempt to prove general theorems about quantum fields that can be used in navigating the maze of specific examples.
In 2002 Kazhdan was made Professor Emeritus at Harvard and emigrated to Israel to become a professor at the Einstein Institute of Mathematics, part of the Hebrew University of Jerusalem. His son, Eli Kazhdan was already working in Israel. He had graduated with a B.A. from Harvard University with honours in Government and International Relations. Eli had served in senior economic positions in the Israeli Government from 1996 to 2002. He was the Chief of Staff in the Ministry of Industry & Trade, and then the Chief of Staff in the Ministry of Interior. He then became CEO of the economic development corporation, StartUp Jerusalem, which aimed at bringing investments to Jerusalem. Later he became CEO of CityBook Services.

Although David Kazhdan had spent two sabbatical leaves in Israel, moving there on a permanent basis was not without its difficulties. Kazhdan was a native Russian speaker who had learnt English as a second language but now had to learn Modern Hebrew at the age of 55. He was, however, given excellent support from the Department of Mathematics and his teaching was arranged making every possible allowance for his less than fluent Modern Hebrew. He took on a hectic life style getting up each morning at 5 a.m., spending two hours on religious studies, then cycling on his bicycle to the Einstein Institute of Mathematics to teach and undertake research. David Kazhdan and his son Eli would go for long, 40 to 50 mile, cycle runs. In 2011 David Kazhdan [22]:-
... climbed Mount Kilimanjaro, the highest mountain in Africa. The mountain juts 20,000 feet into the air is mountain climber's dream, and Kazhdan - his age notwithstanding - chose to climb Kilimanjaro to the summit on his own. After that, climbing Machu Picchu in Peru the following year was a breeze.
On 6 October 2013, David Kazhdan was hit by a truck when riding his bicycle in Jerusalem. He was near the end of a 44-mile cycle run with his son Eli. You can read details of this tragic accident at THIS LINK.

Three factors combined to see Kazhdan recover from this near fatal accident. As we have seen, he was extraordinarily fit, but also he was fortunate to be attended by an extremely skilled physician, and his absolute determination to succeed against the odds; these factors combined to bring him through.

Kazhdan has received many honours for his outstanding mathematical achievements. He was elected to the National Academy of Sciences (Washington) (1990), the Israel Academy of Sciences and Humanities (2006), the American Academy of Arts & Sciences (2008), and the Academia Europaea (2020). He has received a number of major awards for his outstanding contributions to mathematics. These include: the Rothschild Prize (2010); the Israel Prize (2012); the EMET Prize (2016); and the Shaw Prize (2020). He received the EMET Prize:-
... for his work in design of representation theory and its uses in algebra, algebraic geometry and number theory.
The award of the Shaw Prize 2020 was made in equal shares to Alexander Beilinson and David Kazhdan:-
... for their huge influence on and profound contributions to representation theory, as well as many other areas of mathematics.
For more information about these awards to Kazhdan, see THIS LINK.

The 6th European Congress of Mathematics was held in Kraków, Poland, and the Congress began on Monday 2 July 2012. It was organised by members of the Polish Mathematical Society and staff from the Jagiellonian University in Krakow. Around 1000 mathematicians attended. Kazhdan was a plenary lecturer, delivering the lecture Representations of affine Kac-Moody groups over local and global fields. Kazhdan was also a plenary speaker at the International Congress of Mathematicians in 2022 giving the talk On the Langlands correspondence for curves over local fields. Because of COVID-19, this Congress was a virtual event.

Let us end this biography with comments on the Bible Code. The Bible Code, also known as the Torah Code, claims that predictions of events are coded into the text of the Torah. The claimed codes are typically: for some nn, take characters nn apart, either forwards, backwards, diagonally etc. David Reagan claims in [36] amazing things are found in the Book of Genesis using these codes. He also states:-
The research was checked and confirmed by Dr David Kazhdan, chairman of the Harvard mathematics department and by Harold Gans, a senior code specialist with the U.S. Army. Both concluded that the Torah Code actually exists and that it could not have occurred by chance or by human design.
The nn used to find certain words is actually very large, often around 5000. Barry Simon asked Kazhdan if he had really claimed that "the Torah Code actually exists and that it could not have occurred by chance or by human design." Simon writes in [38]:-
Some presentations have made much of a letter of approbation signed by four distinguished mathematicians (Joseph Bernstein, then of Harvard, now of Tel Aviv University; Hillel Furstenberg of Hebrew University; David Kazhdan of Harvard and Ilya Piatetski-Shapiro of Tel Aviv University and Yale). Three of these are Orthodox and I'd be hard pressed to find a more distinguished group of Orthodox mathematicians.

But their letter is very carefully worded to state nothing more than that they find the Famous Rabbis experiment interesting and worthy of further study. Professor Rips himself [who undertook the Bible Code research] told me that he didn't think any of them were convinced of its validity and that is certainly true of the two of them I know and consulted. Indeed, Kazhdan's response to the presentation of his position on the above web site (Kazhdan was the chairman of the Harvard Mathematics Department at the time the page was prepared) was that "I am sorry to see my position in such a distorted form."

References (show)

  1. 2012 Israel Prize for Mathematics and Computer Science goes to Hebrew University's Prof David Kazhdan, The Hebrew University of Jerusalem (25 January 2012).
  2. Alexander P Kazhdan, The Boston Globe from Boston, Massachusetts (Sunday 1 June 1997).
  3. Alexander Kazhdan, The Daily Telegraph, London (Wednesday 11 June 1997).
  4. Alexander Kazhdan, The Daily Telegraph, London (Wednesday 11 June 1997).
  5. Autobiography of David Kazhdan, The Shaw Prize.
  6. Beilinson and Kazhdan awarded 2020 Shaw Prize, Notices of the American Mathematical Society 67 (8) (2020), 1252-1253.
  7. R Bezrukavnikov, A Braverman, M Finkelberg, D Gaitsgory, A Goncharov and Y Varshavsky, A tribute to David Kazhdan, Advances in Mathematics 327 (2018), 1-3.
  8. S-J Cheng, W Wang, M-K Chuah, Interview with Prof David Vogan, Institute of Mathematics, Academia Sinica (20 December 2010).
  9. Contribution of Alexander Beilinson & David Kazhdan, The Shaw Prize (21 May 2020).
  10. David Kazhdan, Notices of the International Consortium of Chinese Mathematicians 7 (1) (2019), 65-66.
  11. David Kazhdan, The Hebrew University of Jerusalem.
  12. David Kazhdan, Academia Europaea.
  13. David Kazhdan, American Academy of Arts & Sciences.
  14. David Kazhdan, National Academy of Sciences.
  15. David Kazhdan, Institute for Advanced Study.
  16. David Kazhdan, nLab (8 January 2021).
  17. David Kazhdan, Research.com.
  18. David Kazhdan: Class of 1990, MacArthur Foundation.
  19. David Kazhdan awarded the Shaw Prize, Department of Mathematics, Harvard University.
  20. Y Dov, Chareidi Hebrew University Mathematician Wins Prestigious Shaw Prize, VIN News (26 May 2020).
  21. Feature Story - Prof David Kazhdan, Shaw Laureate in Mathematical Sciences 2020, facebook.com.
  22. S Gil, One step ahead, Mishpacha (30 September 2014).
  23. I D Goldberg, My Chevruta, Tablet Magazine (30 November 2016).
  24. Hebrew University Researchers Awarded 3 Of The 8 EMET Prizes for 2016, Australian Friends of the Hebrew University (5 December 2016).
  25. Hebrew University Professor Wins Prestigious Prize, United with Israel (23 January 2017).
  26. S Ho, Israel Prize laureate badly injured in hit-and-run, The Times of Israel (7 October 2013).
  27. C Jean, HU's Prof David Kazhdan becomes first Israeli to win the Shaw Prize, The Jerusalem Post (25 May 2020).
  28. C Jean, Prof David Kazhdan becomes first Israeli to win the Shaw Prize, The Jerusalem Post (25 May 2020).
  29. Kazhdan, David, Professor Emeritus, Department of Mathematics, Harvard University.
  30. Leading Byzantine Researcher Alexander Kazhdan Dies, The Washington Post (31 May 1997).
  31. Y K Leong, Art And Practice Of Mathematics, The: Interviews At The Institute For Mathematical Sciences, National University Of Singapore, 2010-2020 (World Scientific, 2021).
  32. Press Release. The Shaw Prize in Mathematical Sciences 2020, The Shaw Prize.
  33. Prof David Kazhdan, Einstein Institute of Mathematics, The Hebrew University of Jerusalem.
  34. Prof David Kazhdan, The Israel Academy of Sciences and Humanities.
  35. Y Rabinovitz, Professor David Kazhdan is first Israeli to win prestigious Shaw Prize, Israel National News (26 May 2020).
  36. D R Reagan, The Bible Code, Lamb and Lion Ministries.
  37. A Ross, Prof David Kazdhan Seriously Hurt in Hit and Run, Israel National News (7 October 2013).
  38. B Simon, A Skeptical Look at The Torah Codes, Jewish Action (Spring 1998).
  39. T P S, Israeli Mathematician Awarded Prestigious 2020 Shaw Prize, United with Israel (2020).
  40. The 2020 Prize in Mathematical Sciences: Alexander Beilinson, David Kazhdan, The Shaw Prize (May 2020).
  41. The 2020 Prize in Mathematical Sciences is awarded in equal shares to Alexander Beilinson and David Kazhdan, Hong Hong Laureate Forum (21 May 2020).
  42. H P Thielman, Review: An integral equation connected with a pulse motion around a circle (Russian), by S I Gelfand and D A Kazhdan, Mathematical Reviews MR0132978 (24 #A2814).
  43. Three Hebrew U Researchers Awarded EMET Prize, NoCamels (4 December 2016).
  44. World-Renowned Mathematician Survives Collision with Truck Thanks to Treatment at Hadassah, Hadassah Medical Center (5 February 2014).
  45. World-Renowned Mathematician, Near Death, Saved at Hadassah's Trauma Unit, Hadassah Medical Center (31 July 2014).
  46. D K Eisenbud, Police: Driver accused of hit-and-run of Israel Prize winner arrested in capital, The Jerusalem Post (10 October 2013).

Additional Resources (show)

Other pages about David Kazhdan:

  1. David Kazhdan Awards
  2. David Kazhdan's Accident

Honours (show)

Cross-references (show)

Written by J J O'Connor and E F Robertson
Last Update March 2024