[located at Princeton University in the Seeley G. Mudd Manuscript Library web at the URL: http://www.princeton.edu/mudd/math]
In 1999 while using the Princeton University Fine Hall math-physics library in trying to uncover the connection between the Italian mathematician Luigi Bianchi's 1898 work on homogeneous 3-spaces and their introduction into relativistic cosmology at the end of the 1940s by Kurt Gödel and then Abraham Taub [General Relativity and Gravitation, Golden Oldies, vol 32, 1398-1427, 2000; vol 35, 2003], I discovered a very interesting story about the Princeton mathematics community in which these events occurred. The surprising thing about it was that it was completely unknown to me even though I had been a Princeton undergraduate in math and physics from 1970 to 1974, and had had one of the protagonists of this story, Abe Taub, as my physics Ph.D. advisor at UC Berkeley just before his retirement in 1978 when I received my degree. This in part motivated me to try to make this story more accessible to many that already might have some interest in this story as well as those future undergraduates like myself who might pass through the Princeton mathematics environment without knowing its past.
My own life has been indirectly shaped by the events of this story. Born in 1952, I came from a small village in lower New York State (Florida, known for its black dirt onion production, not academics) but my parents sacrificed to send me and my three brothers to a larger public school in the adjoining district of Goshen where one of the guidance counselors liked to point good students towards Princeton. One of my friends (David Coon, '74) and I, coincidentally the only two college bound students to take keyboarding (then called typing, probably my single most useful high school course) with the female secretarial skills crowd, then wound up at Princeton together, where I intended to major in mathematics, but my freshman physics instructor detoured me into physics. Having encountered Einstein's relativity early in high school long before calculus through the Lillian and Hugh Lieber book The Einstein Theory of Relativity (1945), it was not a great leap for me to fall into relativity in my sophomore year, with John Wheeler as my modern physics professor and his black hole collaborator Remo Ruffini offering a student (Jim Isenberg, '73) initiated seminar in differential geometry for relativity that spring. This was the golden age of relativity at Princeton not long after the term "black hole" had been coined by Wheeler, and I was caught up in the excitement.
As a project for the relativity seminar I volunteered to translate into English a long 1898 article by an early Italian geometer Luigi Bianchi on the isometry classes of Riemannian 3-manifolds with Ruffini, but ended up doing it mostly on my own based on three semesters of college Spanish and some introductory Italian books and a dictionary in the summer of 1972. A Jadwin Hall secretary typed it up under some NSF grant, and I pasted in the formulas cut from a photocopy, but it never found a route to widespread distribution. I did a junior independent paper and my senior thesis on Bianchi cosmology, spatially homogeneous but anisotropic cosmological models whose space sections are one of the Bianchi symmetry types, encountering Eisenhart's Continuous Groups of Transformations and Riemannian Geometry, both of which I studied and photocopied for later reference (this was the time in which "Xeroxing" came of age), but I never really knew who Eisenhart was or how he was connected to Princeton, other than a vague notion that he had been a professor there. I did meet Gödel at his office at the Institute for Advanced Study in 1973 to ask him about rotating universes, and he was surprisingly familiar with the then current literature (several decades after his own brief work on the topic) and pointed me in the right direction to do a decent senior thesis. Why the tall relatively math tower was called Fine Hall, or that it was connected to the physics building Jadwin Hall by a partially underground floor containing the joint math-physics library never occurred to me. They just were.
In 1974 Ruffini channeled me to UC Berkeley for graduate school in physics to work with Abe Taub in the math department. Taub was known for bringing Bianchi's complete work to application in relativistic cosmology just before I was born. This immediately followed Gödel's startling revelations about rotating cosmologies which were based on some special Bianchi geometries. Later I learned that Abe had gotten his Ph.D. at Princeton working under H.P. Robertson of the Friedmann-Robertson-Walker cosmological models, but I was never that interested in history to think to ask him about how he himself learned about the background leading to his Bianchi cosmology work or to connect him with Eisenhart (an expert on Bianchi's work and the associated mathematics), or how he happened to begin that study in the same period Gödel was working with the Bianchi geometries in solitude at the Institute, during which Taub had been a year-long visitor.
My dad used to say that when I got older, I would find an interest in historical connections, but I couldn't imagine it at the time. Eisenhart, Gödel, Robertson, and Taub had all been a part of that magic decade of the 1930s when the Institute for Advanced Studies was formed but initially remained seamlessly a part of the special Fine Hall mathematics community (1933-1939) that blossomed out of the mathematics department in those years and welcoming its most famous member Einstein in 1933. This community had close ties to the physics department in the adjacent Palmer Laboratory to which Fine Hall was connected by a corridor and Fine Hall housed their joint math-physics library and some joint appointments, including initially von Neumann and Wigner, and Robertson.
Some 27 years after my original Bianchi translation work, during which time I spent a year as a postdoc with Ruffini at the University of Rome "La Sapienza" 1979-1980 initiating some 20 years of regular visits to Rome, I was asked by the journal General Relativity and Cosmology to translate that very same Bianchi article, which I explained I had already worked on so many years before. But new technology was now available and my improved command of Italian could polish up the original job and my LaTeX computer typesetting expertise would help me set the complicated mathematics, after a rough scanning process of the poor photocopy of the original. It took over a year and a half to complete, during which I finally began to think about the historical context of the article's application to relativistic cosmology for the editorial note. Although through a series of trips to the Bay area in the 1990s associated with the 1994 Marcel Grossmann Meeting on General Relativity at Stanford, and some International Center for Relativistic Astrophysics (Ruffini, again) annual meetings there, I had seen Abe Taub and his wife Cece regularly, and listened to many stories about the old days, but I was a passive listener and again did not think to actively seek out historical information that I would later be interested in. But by the time I was interested, Abe was quickly going downhill and in no condition to be asked such questions.
As a professor in the Department of Mathematical Sciences of Villanova University in the suburbs just west of Philadelphia, I was living only an hour drive from the Princeton University Fine Hall Math-Physics Library. In the spring of 1999 I visited this familiar place to find background biographical material in Bianchi's collected works, discovering that the final signature on the borrowing slip of volume 9 was still that of Remo Ruffini in 1972. I also asked the library staff for help in finding background materials that they might have on Abe Taub and Eisenhart and the mathematics department history. They were very helpful, turning up an interview with Taub in "The Princeton Mathematical Community: An Oral History Project", a rich document whose existence I was unaware of, and some old mimeographed course notes of H.P. Robertson taken by Taub and Givens, in the style spoken of repeatedly in the Oral History Transcripts, and some things about Eisenhart and Fine and the development of Princeton mathematics. I was also unsure where to start for biographical information about Bianchi, so after a few false starts, the librarian on duty remembered Charles Gillispie's Dictionary of Scientific Biography, a monumental encyclopedia of famous scientists that I had never known about, given my prior lack of interest in the history of science. And she remarked that every now and then Gillispie himself would be in the library and that he was very niceI should make contact with him...
So I began reading these resources, which are now on-line here, and my interest increased by the fascinating stories unfolding to me. I became aware that Abe Taub had been right in the middle of that exciting decade of mathematics at Princeton, but he was no longer really coherent and died at age 88 on August 9, 1999 after several years of decline. Ironically only a few years earlier I could have learned directly from him the answers to many questions coming into my mind. Taub had been a graduate student in the mathematics department at Princeton during 1931-1935, taking comprehensive exams in both mathematics and physics, working with H.P. "Bob" Robertson on relativistic cosmology. He was an instructor in mathematics at Princeton 1934-35 and an assistant to Oscar Veblen at the Institute for Advanced Study 1935-36, and a later member of the Institute 1940-41 and 1947-48, the latter period when Kurt Gödel was studying spatially homogeneous cosmological models using the work of Luigi Bianchi that was well known to Eisenhart, and which Taub must have learned about during those years at Princeton in the 1930s. Taub made a general study of his own on this problem. Gödel had been there during 1933-35 and returned in 1940 to stay for the rest of his life. Both Gödel and Abe presented their results at the 1950 International Congress of Mathematicians in Cambridge, MA, sponsored by the American Mathematical Society and organized by Veblen. This was the first such international mathematics meeting held after the war. Taub's finished work using Eisenhart's techniques was published in 1951, crediting useful discussion with von Neumann, with whom he had also close ties [he later edited the collected works of von Neumann]. However, the details of how Gödel and Taub learned of Bianchi's work and how it involved Eisenhart will have to be left to the imagination.
I eventually arranged to meet Charles Gillispie to inquire about what he might know about these matters, then a professor emeritus in the history of science at the university. We had lunch together in the Princeton University Prospect Faculty Club in the fall of 1999, and I suggested that when the Oral History Project had been completed in 1985, the world wide web did not exist, but that now it was the logical place to put these materials to make them accessible to the world rather than existing only in a few paper copies in several library archives where they were difficult to know about or use. He agreed, but the question was, who would do this? It seemed clear that I was going to have to do it myself or it would not be done, so he offered to get the permission of the University for me to proceed with its copyrighted materials. In January 2000 I had lunch there again with John Wheeler to ask him what he remembered, having found an Oral History Project remark by Eisenhart's son that his father and Wheeler might have been working together on a book of differential geometry for relativity before Eisenhart's death. But by this time, Wheeler was in his late eighties and could not really recall anything helpful about the period.
The complete photocopy of the Oral History Project had arrived in the fall of 1999 after my meeting with Gillispie and I began test scanning it for optical character recognition to convert the typewritten document into partially formatted text and then to HTML coded text. The bulk of the scanning was then done by the generous assistance of Joan Lesovitch's Villanova University Multimedia Service students, but the glitch fixing and HTML editing was a long and arduous task, including the final proofreading of every page of the roughly 700 page document. The finishing touch was the conversion of the page references in the name index to links to bookmarks at the original paper version page breaks in the web transcripts, accomplished with the Unix Perl script written by my friend Najib Nadi of the Computer Sciences Department of Villanova University.
The proofreading stage enabled me to finally read all the contents, which was a
wonderful experience. All these famous names came alive with down-to-earth stories
of real people, told by participants from the making of the story. I hope others enjoy
some of these as much as I did.
Robert T. Jantzen
Professor of Mathematical Sciences
A.B. in Physics, Princeton University, 1974
Ph.D. in Physics, University of California at Berkeley, 1978
[thesis advisor: Abraham Taub (PMC14),
Ph.D. in mathematics, Princeton University, 1935,
editor of John von Neumann: Collected Works,
Oxford University Press, 1963]
The Princeton Mathematics Community in the 1930s