The Princeton Mathematics Community in the 1930s [before, during and after]:
Related Documents

[located at Princeton University in the Seeley G. Mudd Manuscript Library web at the URL: http://www.princeton.edu/mudd/math]

The Short Story

In the 1930s, a remarkable mathematical community was born in a building built specifically to house such an unusual community: Fine Hall at Princeton University (now Jones Hall, reverting to the donors' names with the construction of the new Fine Hall and Jadwin Physics complex in 1970). The Mathematics Department of Princeton University, then emerging as a world class center for mathematics, shared its new quarters with the Department of Mathematics of the Institute for Advanced Study for six years while the latter's facilities (Fuld Hall) were planned and constructed nearby. During this period, the beginning of which saw the arrival from Europe of Einstein and Gödel, Fine Hall served as a mathematical club in which graduate students, faculty, Institute members, and many visitors mingled together in an atmosphere of exchange, including close ties with the adjoining Palmer Hall and its physics community, including some joint members of both the math and physics departments.

The Princeton Mathematics Community story begins with Henry B. Fine, Princeton class of '80 (background in physics and mathematics) who started as an assistant professor of mathematics at Princeton (College of New Jersey until its name change in 1896) in 1885, becoming the senior member of the department by 1900 and then chairman (1904-28), dean of the faculty (1903-12), and dean of the science departments (1909-28), and even temporarily as acting president of the university (1911). A textbook writer and institution builder, he was a leading supporter of the plan to found the New York Mathematical Society in 1988, which became the American Mathematical Society (1893).  It was Fine who built the mathematics department into a strong research oriented department, including members Luther P. Eisenhart, Solomon Lefschetz, and Oscar Veblen.  Finally as a fundraiser he made an important connection that upon his accidental death in 1928 lead to the donation of funds to build a luxurious new mathematics building to facilitate research, completed in 1931 and dedicated in his honor as Fine Hall.

Luther Eisenhart took over in Fine's place during the key decade of the 1930s which brought Einstein to Princeton and saw the formation of the Institute for Advanced Study which was housed in Fine Hall during the 6 years (1933-1939) of the construction of its own Fuld Hall facility. Eisenhart was also a leader: chairman of the mathematics department (1929-45), Dean of the Faculty (1925-1933), and Dean of the Graduate School (1933-45).  As a specialist in differential geometry, he was also keenly interested in general relativity.

Through a happy coincidence of circumstances in which Solomon Lefshetz (department chair 1945-1953) met Abraham Flexner who was thinking of establishing some kind of academic institute in the East with money from Louis Bamberger and his sister Caroline Bamberger Fuld, the Institute for Advanced Study was founded with a mathematics department in Princeton precisely because of Princeton University's own renowned mathematics department, with Albert Einstein, Oscar Veblen, John von Neumann, and James Alexander (the latter three hired away from the university) as its first members. Veblen was instrumental both in envisioning the Institute before the circumstances led to its creation as well as in the design of Fine Hall and in the initial selection of members for the Institute. Awaiting the construction of its own building, the Institute shared Fine Hall with the university mathematics department from 1933 to 1939, during which a great deal of daily interaction took place among many leading mathematicians and physicists (Fine Hall was connected to the physics department building).

Fine, Eisenhart and Veblen were also past presidents of the American Mathematical Society.

This oral history project,  The Princeton Mathematics Community in the 1930s: An Oral History Project, grew out of the interest of Albert Tucker (1905-1995), who succeeded Lefschetz as department chair (1953-1963), in turn succeeded by a Princeton bred mathematician John Milnor (1963-1967??). After his retirement (1974), Tucker wanted someone to record the history of that remarkable mathematical community of the 1930s, but in the end, he had to take matters into his own hands. Together with historian of science William Aspray and the help of another Princetonian Charles Gillispie, editor of The Dictionary of Scientific Biography, The Oral History Project was launched with a series of interviews conducted with as many of the personalities of that decade who were still alive in 1984, and then edited with the help of graduate student Frederik Nebeker, reaching completion in 1985.

The original  protagonists of the decade of the thirties, including the generation of students which contributed to the Oral History Project, had an enormous influence on American mathematics  in the decades which followed.

The Web Version

This web version grew out of several random events in 1999, including a Fine Hall librarian's remark about Charles Gillispie's then current presence at Princeton. Gillispie had been crucial in getting funding for the original project, again through a chance meeting much earlier with Tucker, and helped make the present web project possible through Princeton University. Gillispie's advice to me was the same as what I later learned he had given to Tucker: "Do it yourself," and he made that possible again. [details]

Background Materials

An article describing The Princeton Mathematics Community in the 1930s: An Oral History Project  appeared in the Princeton Weekly Bulletin while it was in progress in 1984:

Savani, Jackie
"Tucker recounts math in the 1930s," Princeton Weekly Bulletin, Princeton University, Dec 10, 1984.

Albert Tucker (responsible for the Prisoner's Dilemma in game theory) was a former chairman (1953-1963) of the Mathematics Department (following Eisenhart and Lefschetz, and succeeded by John Milnor), whose interest led to the Oral History Project during his retirement. This article briefly describes his background and how the project got started. William Aspray of the Charles Babbage Institute of the University of Minnesota did most of the recorded interviews and a History of Science graduate student Rick Nebeker was editing the transcripts at the time of the article. A few anecdotes about the contents are given, and a brief reference to John Nash, Tucker's most famous graduate student (Ph.D. 1950, Princeton instructor 1950-51, IAS 1957-58, "the phantom of Fine Hall" in later years during his illness) who did work in game theory (initiated by von Neumann and Morgenstern) that later earned him the Nobel Prize in Economics (1994); see his biography  A Beautiful Mind : A Biography of John Forbes Nash, Jr., by Sylvia Nasar [June 1998, Simon & Schuster; ISBN: 0684819066]. Nash also solved a classic problem in differential geometry, "the embedding problem," in part motivated by general relativity. Curiously enough, Tucker does not say a single thing about Nash in his many transcripts, only mentioning his name once in a list with some other students, unable really to talk about him still in 1984, before Nash's recovery. [Ironically this is a perfect example contradicting the point made by Nebeker in this article about Tucker being a superb interviewee after noting that Church had nothing to say about his own most famous student Alan Turing as a person, but in fact in both cases the circumstances were troubling. See Alan Turing: the Enigma by Andrew Hodges, Walker and Company, New York; ISBN: 0-8027-7580-2.]

A short review of this story linking it to more recent personalities in the Math Department appeared in the Princeton Alumni Weekly:

Merrel Noden '78
"Math Mecca (Once Again These are Heady Times in Fine Hall)," Princeton Alumni Weekly, November 7, 2007
[Errata: 1) the shape of the tiles in the game John Nash invented is hexagonal rather than octagonal, 2) in the parenthetical mention of Pythagoras: Fermat's marginal note said that he believed he had shown that there were no triplets of positive integers that satisfied xn + yn = zn for any n larger than 2].
Summarized in "From the Editor."

A short essay by an undergraduate math major 1960–1964 about the math department he experienced, recounted nearly a half century later:

Carl L. Heimowitz '64
"Lessons learned at Princeton: Reflections of a failed mathematician," Princeton Alumni Weekly on-line PawPlus extra, November 7, 2007. Summarized as: Math lessons - What Carl L. Heimowitz ’64 remembers about his days in the math department are the people - “alternately crazy and great” - doing work that changed the world.

The background and context for The Princeton Mathematics Community in the 1930s: An Oral History Project are well described in the following documents.

Chaplin, Virginia
"Princeton and Mathematics: a Notable Record," Princeton Alumni Weekly, May 9, 1958, pp.6-15 [Princeton University Fine Hall Library, Pamphlet Collection].

This gives a brief overview of the entire period through the late 1950s, starting from the late 1800s, discussing Harry Fine and Luther Eisenhart, the arrival of Einstein, noting the "mathematical prodigy" John Milnor (undergraduate, graduate student and professor at Princeton), Solomon Lefschetz, and Albert Tucker, among many others.
Uncredited Article
"A Memorial to a Scholar-Teacher," Princeton Alumni Weekly, October 30, 1931, pp.1-3.

This tells the story of how the original Fine Hall came to be and describes its physical details and purpose, reproducing the complete text of the dedication address of Osvald Veblen in 1931.

The next four documents are longer articles on various aspects of this story taken from the three volume collection A Century of Mathematics in America edited by Peter Durren and published by the American Mathematical Society in 1989 as a part of their series History of Mathematics (plus an additional two documents not on-line about Veblen and Lefschetz). These three volumes are a valuable resource whose individual tables of contents [I, II, III] should be examined for other closely related articles.

Aspray, William
"The Emergence of Princeton as a World Center for Mathematical Research, 1896-1939," in History and Philosophy of Modern Mathematics (Minneapolis, MN, 1985), Minnesota Stud. Philos. Sci. Volume 11, pp.346-366, Univ. Minnesota Press, Mineapolis, MN, 1988 [MathSciNet 89f:01087 01A73(01A60)]; also in:
[MathSciNet 90k:01053 01A73] A Century of Mathematics in America, Part II, History of Mathematics, Volume 2, pp.195-215, Amer. Math. Soc., Providence, RI, 1989.

Lefschetz, Solomon
"Luther Phahler Eisenhart. January 13, 1876-October 28, 1965", in A Century of Mathematics in America, Part I, History of Mathematics, Volume 1, pp.56-78, Amer. Math. Soc., Providence, RI, 1988 [MathSciNet 91a:01043 01A70, Princeton University Fine Hall Library 8104.322.572] .

Borel, Armand
"The School of Mathematics at the Institute for Advanced Study," in A Century of Mathematics in America, Part III, History of Mathematics, Volume 3, pp.119-147, Amer. Mat. Soc., Providence, RI, 1989 [MathSciNet 91k:01016 (01A60)] .

Rota, Gian-Carlo
"Fine Hall in its Golden Age: Remembrances of Princeton in the Early
Fifties," A Century of Mathematics in America, Part II, History of Mathematics, Volume 2, P. Duren, Ed., pp.223-236, Amer. Math. Soc., 1989.

Gian-Carlo Rota, born in Italy in 1932, was an undergraduate at Princeton University (1950-1954) who went on to become a leading American mathematician at M.I.T. passing away in 1999, honored with a memorial article in the Notices of the American Mathematical Society, Vol. 47, No. 2, pp.203-216, February 2000, which curiously failed to mention his mathematical origins at Princeton. He talks about some of his professors, including Solomon Lefschetz.
 
Montgomery, Deane
"Oswald Veblen," in A Century of Mathematics in America, Part I, History of Mathematics, Volume 1, pp.118-130, Amer. Math. Soc., Providence, RI, 1988 [MathSciNet 91a:01043 01A70, Princeton University Fine Hall Library SM 8104.322.572] .

A biography of the man most responsible for catalyzing the establishment of the Institute for Advanced Study in Princeton as an academic think tank, once Flexner and the donors were ready to start something.
 
Lefschetz, Solomon
"Reminiscences of a Mathematical Immigrant in the United States," in A Century of Mathematics in America, Part I, History of Mathematics, Volume 1, pp.201-208, Amer. Math. Soc., Providence, RI, 1988 [MathSciNet 91a:01043 01A70, Princeton University Fine Hall Library SM 8104.322.572] .

The title says it all. Originally from Moscow, educated initially as an engineer in Paris, his own account of coming to Princeton and his years there after about a decade in the midwest following his graduate studies in Massachusetts.

A later volume of this series:

Parshall, Karen Hunger and Rowe, David E.,
The Emergence of the American Mathematical Research Community 1876-1900: J.J. Sylvester, Felix Klein, and E.H. Moore, History of Mathematics, Volume 8, American Mathematical Society, London Mathematical Society, 1994.

This volume provides the background of the American mathematics and Princeton story beginning with its roots in Europe, including the often mentioned names of the influential mathematician Felix Klein and his Erlanger Programm and the European mathematical center of Göttingen University in Germany (the institution of Gauss and Riemann, later Klein, Hilbert, Minkowski and Weyl), where Fine had been one of numerous Americans attracted to study under Klein, who supervised his  1885 doctoral dissertation (Chapter 5). See especially chapter 10: Epilogue: Beyond the Threshhold: The American Mathematical Research Community, 1900-1933.

See also: Parshall, Karen Hunger,
Perspectives on American Mathematics, Bull. Amer. Math. Soc. 37 (2000), 381-405.

More background information is available in:

 
The following is a much later article in the same spirit as the Oral History Project by a mathematician mentioned in the 1950s PAW article above, and who succeeded Tucker as chairman of the department in 1963.
 
Milnor, John
"Growing Up in the Old Fine Hall," in Prospects in Mathematics: Invited Talks on the Occasion of the 250th Anniversary of Princeton University, March 17-21, 1996, pp.1-11, American Mathematical Society, Providence, R.I., 1999.

The author records personal and mathematical reminiscences, starting in 1948 when he first came to the mathematics department at Princeton University at the age of seventeen as an undergraduate, then becoming a graduate student and finally a professor. He concludes with a plea for mathematical tolerance.

Stasheff, Jim
"Reminiscences of a Graduate Student at Princeton in the Late 50s:
Temple-Villanova History of Math Seminar Dec 7, 2000 focusing on his graduate studies at Princeton in the late 1950s, but with earlier and later reminiscences as well, including some interactions with Milnor.

Some books which cover the period:

Regis, Ed
Who Got Einstein's Office?, Addison-Wesley, New York, 1987.

A book devoted to the history of the founding of the Institute for Advanced Study and its early days, focusing on Einstein, Gödel, and von Neumann from this period , and a number of other later notable members (including John Milnor) up to the time of its publication:
 
Wheeler, John Archibald
Geons, Black Holes & Quantum Foam (with Kenneth Ford), Princeton University Press, Princeton, 1998. [Princeton Alumni Weekly Review][90th birthday symposium in 2001]

John Wheeler was a short term visitor at the Institute for Advanced Study (1936-37), settling in Princeton a few years later in the University Department of Physics where he later became enthused about general relativity and became a close friend of Einstein. Chapter 7 describes this early period, Eisenhart, the connection between math and physics at the former Fine and Palmer Halls and other interesting details.
 
The Princeton Physics Dept newsletter (Princeton Physics News, Winter 2006) provides an update on John Wheeler at 94 and the 2005 Centennial of Einstein's Annus Mirabilis.
Halpern, Paul
The Great Beyond: Higher Dimensions, Parallel Universes and the Extraordinary Search for a Theory of Everything, John Wiley, New York, 2004 [Amazon reader reviews]

A terrific accounting of the people involved in the geometry and physics of relativity and higher dimensions which played an important role in the most public face of this mathematics community of the 1930s.
About Einstein and Godel
Palle Yourgrau, A World Without Time: The Forgotten Legacy Of Godel And Einstein  [Amazon reader reviews]
Rebecca Goldstein, Incompleteness: The Proof and Paradox of Kurt Godel (Great Discoveries) [Amazon reader reviews]

For the 40's and postwar period:

Veblen, Osvald
opening address in International Congress of Mathematicians (Cambridge, MA 1950), American Mathematical Society, Providence, RI, 1952. See also the secretary's report.

This addresses the missing decade of the 1940s interrupted by World War II and its aftermath, including the start of the cold war and its effect on the international mathematics community.
 

Some obituaries:
Obituary of Luther P. Eisenhart
"L.P Eisenhart of Princeton: Mathematician and Humanist 1876-1965", by Isaac L. Battin Sr., Obituary in New Jersey Mathematics Teacher, vol 23, no. 3, March, 1966, pp.15-16.
 
Obituary of Henry Burchard Fine
"Henry Burchard Fine—In Memoriam", by Oswald Veblen, Obituary in Bulletin of the American Mathematical Society 35, 726–730 (1929)
 
Obituary of H.P. Robertson
"H.P Robertson, Obituary" by A.H. Taub in Nature, December 21, 1961, pp.797-8.

"Bob" Robertson was a mathematical physicist (joint appointment in math and physics) at Princeton University from 1929 to 1947, working on general relativity (the middle name in "Friedmann-Robertson-Walker" cosmologies), and Ph.D. (1935) thesis advisor of Abraham Taub, who also worked in general relativity and participated in the oral history project: PMC14. Robertson later moved to Cal Tech, where he died in 1961 in a tragic auto accident, and his lecture notes were then put into book form by Thomas Noonan as Relativity and Cosmology, by Robertson and Noonan. This obituary by his former student describes his life and contributions. Like Fine, Robertson also studied a year at Göttingen in Germany, one of the leading centers of mathematics in Europe where Gauss, Riemann, and Klein in succession held positions.
 
Obituary of Abraham Taub
Originally written by Bahram Mashoon to accompany a reprint of Taub's most famous relativity article in the journal General Relativity and Gravitation, which instead appeared in SIAM NEWS, volume 34, Number 7, September 2001.
 
Obituary of Albert Tucker
Princeton University Press Release, 1995.
 
Obituaries of John Tukey
Princeton Alumni Weekly Obituary, Princeton University Press Release, NY Times Obituary, 2000;
David Brillinger, Notices of the AMS, Feb 2002, pp.193-201: John Wilder Tukey (1915–2000)
 
Obituary of Peter Bergman
NY Times obituary, 2002: obituary of Einstein's assistant and collaborator at the IAS during this decade.
 
Obituary of Herman Goldstine
Philadelphia Inquirer obituary, 2004: computer pioneer worked with von Neumann and helped build the first computer, the ENIAC.
 
Obituaries of John Archibald Wheeler
Princeton Archive obituary, NY Times obituary, 2008.

Some biographies:

Wigner, Eugene P. and Szanton, Andrew
The Recollections of Eugene P. Wigner As Told to Andrew Szanton, Perseus Publishing, 1992 ISBN: 0306443260

Autobiography, including the period described in his transcript and his friendship with John von Neumann.
 
Heims, Steve J.
John Von Neumann & Norbert Wiener: From Mathematics to the Technologies of Life & Death, MIT Press, 1985 ISBN: 026258056X

Biography.

Web Links

Some interesting related web articles.

The first group of documents are from A Princeton Companion by Alexander Leitch, Princeton University Press (1978), now reproduced in its entirety on-line at http://meca.princeton.edu/CampusWWW/Companion/index.html:

Eisenhart, Luther Pfahler
Biography of Eisenhart.
 
Fine, Henry Burchard
Biography of Fine.
 
Veblen, Oswald
Biography of Veblen.
 
Lefschetz, Solomon
Biography of Lefschetz.
 
von Neumann, John
Biography of von Neumann.
 
Einstein, Albert
Biography of Einstein.
 
Mathematics, [by Gunning, Robert C.]
A brief history of the Princeton University mathematics department:

Mathematics has been prominent in the Princeton curriculum since
the founding of the College. The state of mathematics in Princeton changed
dramatically after 1905; the beginning of the development of Princeton as one of
the world's great centers of math ...
 
Physics, The Department of [by Shenstone, Allen G.]
A brief history of the Princeton University physics department.
 
Jones Hall [The Old Fine Hall]
The history of the old Fine Hall, now renamed for its donors after its replacement by the new Fine Hall.

Jones Hall, designed by Charles Z. Klauder, was built in 1930 as the
first home of the mathematics department. When the new Fine Hall was
completed in 1969, the old one was renamed in honor of its donors, Thomas D.
Jones and his niece Gwethalyn Jones ...
 
Fine Hall
Description of the new Fine Hall.

Fine Hall, home of the Department of Mathematics and the Department of
Statistics, was dedicated in 1970 as a memorial to Henry Burchard Fine, the central
figure in the early development of the mathematics faculty of the University...
 
Jadwin Hall
Description of Jadwin Hall, attached to the new Fine Hall by the math-physics library, in the tradition of the original Fine Hall and Palmer physics building.
 
The Institute for Advanced Study [by Brown, J. Douglas]
Brief history of the Institute for Advanced Study.

The remaining links are from various sources:

Ackerberg-Hastings, Amy
"Toward the Unification of Mathematics: The Evolution of Topology in Its Twentieth-Century Cultural Context", Mathematical Connections [website], 6 (1998): 3-27, Augusta State University.
Article describing the influence of Alexander, Lefschetz, and Veblen on topology.
 
DePauli-Schimanovich, Werner
"Kurt Gödel and his Impact on A.I." [artificial intelligence]
Interesting background on Gödel, including that fact that he first learned about relativistic rotating universes from Hans Thirring in Vienna where he studied physics; this was an obsessive hobby that he carried with him till the end of his life.
 
Kurt Gödel and his rotating universe hobby
Gödel information: collected works, biography, and the connection with relativity
 
Rheingold,  Howard
Chapter Four: "Johnny Builds bombs and Johnny Builds Brains," from Howard Rheingold's Tomorrow [website]: Tools for Thought.
Long article about John von Neumann and his influence on Turing, Gödel, the Manhattan project, computers, etc.
 
J. Petard Spoof
e-mail exchange about a joke wedding certificate mentioned by John Tukey in PMC41.
 
Anthony T. Grafton
Precepting: Myth and reality of a Princetonian institution, Princeton Alumni Weekly, March 12, 2003, pp.16-19. Princeton professor Grafton (Henry Putnam Professor of History and chairman of the Council of the Humanities) writes on the birth of Woodrow Wilson's preceptorial system, and the effort to create a new kind of man, a story in which Henry Fine plays a role.

For biographies of the famous mathematicians of this story:

Gillispie, Charles C. (editor)
Dictionary of Scientific Biography, Scribner's Sons, New York, 1970.
Excellent biographies of all of the famous figures in this story.
[Fine, Eisenhart, Veblen, Lefschetz, von Neumann, Alexander, Einstein, Gödel, Weyl, ...]

MacTutor History of Mathematics Archive on-line biographies:

Treasure Trove of Scientific Biography: Einstein, Godel, Weyl, Wigner.

Wikipedia is also worth consulting.

The actual tapes of the oral histories of the Princeton Mathematics Community are available through the Charles Babbage Institute (Center for the History of Computing) at the University of Minnesota. Only the Tucker interviews are explicitly listed. Searching the university catalog on the string "Princeton Mathematics Community" leads to a description of the project and the archival materials available there. A paper copy of the transcripts may be consulted at the Princeton University Fine Hall library, at the Babbage Institute, and at the American Philosophical Society in Philadelphia.

Suggestions for additional background material to be linked or described here are welcomed by:

Robert Jantzen
Dept of Mathematical Sciences
Villanova University
Villanova, PA 19085
robert.jantzen@villanova.edu

I am not a historian of science. Building this site was something I stumbled into by accident, and people with more experience and knowledge can contribute to improving its usefulness. Please help if you can, especially in updating the Princeton Math Department history for the second half of the twentieth century.

 

robert jantzen: 5-aug-2008

The Princeton Mathematics Community in the 1930s