Princeton Weekly Bulletin, December 10, 1984, Volume 74, Number 11

Tucker recounts math in the '30s

Oral history project preserves recollections of golden era in Princeton mathematics

By Jacquelyn Savani

Albert Tucker belongs to a legendary part of Princeton's past—the ascendancy of the Mathematics Department in the '30s and its intimate association with the mathematics group at the newly founded Institute for Advanced Study. The mathematicians at the University and at the Institute shared office space in the building that has since become Jones, but was then called Fine Hall. There the common room and its afternoon teas formed the hub of an extraordinary intellectual community that included such luminaries as James Alexander '10 *15, Alonzo Church '24 *27, Albert Einstein, Luther Eisenhart, Solomon Lefschetz, John von Neumann, Oswald Veblen, Hermann Weyl and Eugene Wigner.

Tucker arrived in 1929 to do graduate work in mathematics. He had a master's degree from the University of Toronto and intended to return there after completing a Princeton Ph.D. He never did go back.

When Tucker got his degree in 1932, the Depression was even worse in Canada than in the United States. Unable to get the position he had hoped for at Toronto, Tucker studied for a semester at Harvard, where he was then offered a job. He traveled "mostly by overnight boat" from Boston to Princeton to talk over the offer with Dean Eisenhart, and his dissertation advisor, Lefschetz, who then countered with an instructorship at Princeton.

Why was Tucker reluctant to accept the Harvard position? He had simply come to the conclusion that he didn't like to do math there as much as at Princeton. The Fine Hall common room exemplified the difference between the two environments. At Harvard, where the department's professors were scattered throughout campus buildings, Tucker had missed the easy conversation among mathematicians stimulated by the club-like atmosphere at Fine Hall.

Tucker's appointment came at a time when Nazism forced Einstein from the Kaiser Wilhelm Institute in Berlin, and Weyl from Göttingen. And the new Institute for Advanced Study was also siphoning off talent from the University's Mathematics Department, thereby creating departmental openings for newcomers. The departure of Veblen, Alexander and von Neumann made room for Tucker and four other young mathematicians. There wouldn't have been a place for Tucker at the University if the Institute hadn't recruited from the department. If Tucker hadn't gotten that appointment in 1933, the records of that extraordinary mathematics community centered in Fine Hall would be thinner. Recently, at the age of 79, the Albert Baldwin Dod Professor of Mathematics Emeritus, instigated an oral history project of that Princeton era.

After he got the idea for the project, Tucker consulted Princeton University Press Director Herb Bailey '42, who suggested a conversation with Professor of History of Science Charles Gillispie. When Tucker proposed his project to Gillispie at a cocktail party, Gillispie was taken with the idea. He agreed to submit a proposal for funding to the Sloan Foundation and to act as the project's supervisor. The resulting grant of $13,000 was small by the standards of most scientific research projects, but adequate for the oral history.

William Aspray of the Charles Babbage Institute of the University of Minnesota conducted most of the project's roughly three dozen interviews that take up more than 100 hours of tape. Aspray says that the questions he asked were designed to elicit descriptions of the general social and intellectual climate at Princeton in the '30s.

"We wanted to look at the background that enabled Princeton to develop the best mathematics department in the world, to look at the interaction between the Institute's and the University's mathematicians, to look at the effects of developments in Europe, the impact of the Depression and the personalities of the principals, and also to get comparisons between Princeton and other American mathematics centers."

Aspray, who has a master's degree in mathematics and a Ph.D. in the history of science, admits that oral history is "a sloppy probe." Of one interview with a mathematician who was a graduate student at Princeton in the early '30s, he says: "There were a large number of things he said I already knew, and four or five things he said I know are false. Those inaccuracies are not uncommon for a project like this," which entails people talking about events that occurred 40 or 50 years ago.

Tucker interrupts to say that the sloppiness of the probe in part maintains its vitality. "If I could write a history of that period, I would. But I put something down, and then I begin to rewrite to represent it more precisely, and by the time I'm done, I've written all the life out of it."

"In my experience," says Aspray, who's done many interviews of scientists and technologists, "mathematicians have not proved to be very good subjects for oral history. It's like pulling teeth."

Rick Nebeker, a graduate student in the Princeton Program in the History of Science, has been editing the transcriptions of the tapes. Both he and Aspray think the material is more valuable as a source for the history of mathematics than as a social document. In the 12 transcripts Nebeker has edited, he says the mathematicians focus on their work—the conflict between schools of topology or the struggle to make mathematical statistics a part of the Princeton enterprise.

Nebeker had high expectations of the interview with the famed logician Alonzo Church, who was asked about the personality of his equally famous Ph.D. student, Alan Turing. Church and Turing did thinking in mathematical logic that laid groundwork for theoretical computer science. Church supervised the dissertation of Turing, an enigmatic English mathematician who was instrumental in breaking the German code during World War II and who then worked on a prototypic computing machine at the University of Manchester. Turing's homosexual liaisons led to a trial in England; as a possible security risk he was forced to undergo hormone treatment and subsequently killed himself. An intriguing personality, one would think, but according to Nebeker, Church simply had nothing to say about Turing the person.

Aspray says that only three of his roughly three dozen interviewees for the project turned out to be really good subjects. "Tucker is one of them. He's just superb. In fact, I've never had a subject as good as he in any of my fields."

Almost alone among the surviving participants, Tucker had the consciousness then to take in and appreciate the remarkable scene. He remembers the details that bring that world back to life.

"Yes," says Tucker, "Einstein didn't wear socks. And James Alexander walked around in tennis shoes—shocking attire by '30s academic standards." The shoes enabled Alexander, a world-renowned mountain climber, to scale the exterior wall of Palmer Lab when that Physics Department building (adjacent to the old Fine Hall) was locked; Alexander left his second-floor office window unlatched to facilitate his unorthodox entrance.

Tucker remembers a verse sung in the common room:

Here's to Uncle Oswald V.,
Lover of England and her tea.
He is that mathematician of note
Who needs four buttons to fasten his coat.

Veblen, Tucker explains, was quite tall, so he had his jackets made with an extra button. And it was Veblen, taken with the English customs of his wife, who introduced the afternoon tea ceremony to Fine. He was dubbed "Uncle" by the satiric Lefschetz because he had a way of dropping the name of his famous uncle, Thorstein, into conversation.

Tucker's memories aren't confined to whimsy. His voice quavers and breaks when he recalls the special quality of devotion that characterized the relationship between Mrs. Lefschetz and her brash husband, who heckled even von Neumann mid-lecture and who told Einstein, harassed by autograph-seekers, to get his hair cut as a disguise.

According to Tucker, Lefschetz trained as an electrical engineer in France, immigrated to the United States in 1907 and worked at Westinghouse Labs, where an accident led to the amputation of his hands. With the accident compensation, he financed Ph.D. studies in mathematics at Clark University in Worchester, Mass. (then one of the three or four places in the United States for mathematics graduate study), and later married the one woman who was a fellow student there. "She did so much for him," Tucker says; "they were more devoted to each other than any couple I've known."

It was under Lefschetz's editorship that the Annals of Mathematics became the preeminent journal in the field. This year the Annals is celebrating its centenary. Founded in 1884 at the University of Virginia, the publication moved to Harvard in 1899 and to Princeton in 1911. Since 1933 it has been put out jointly by Princeton's Mathematics Department and the Institute's School of Mathematics. In the '30s Lefschetz edited for the University, and von Neumann for the Institute.

Tucker says that it was Lefschetz's mercurial mode of editing that made the publication great. Now, five editors—three from the University and two from the Institute—shepherd the journal. According to one of the present editors, Professor of Mathematics Joseph Kohn, and the publication's manager, Eleanor May, papers undergo a rigorous selection process through referees to determine their merit. But back in the '30s, as Tucker recalls, Lefschetz simply had an uncanny knack for quickly identifying seminal work, especially in his field of topology, so that key papers were published faster than they would have been if the selection process had been less intuitive. Though Lefschetz immediately accepted some papers, it fell to his assistant, Tucker, to get the rest through a more judicious refereeing.

As Tucker says, life was simpler then. As an example, he recalls the closing of Palmer Lab at 6:00 each evening and on weekends. The graduate students had to get keys if they wanted to use the reference books in its library after hours. Tucker was sent to a certain office to get his key. There, "a pleasant fellow" asked for a dollar deposit, put the dollar in a cigar box, checked off Tucker's name, and got a key for him from another cigar box. That person handling the library keys, says Tucker, "was Karl Taylor Compton, chairman of the Physics Department, who was the next year to become MIT's president."

As with the episode of the key, when Tucker makes a general observation about life back then, he backs it up with examples.

Insisting that the common room functioned like a club, he talks about the recreational activities there. One evening during the academic year 1931-32 when the old Fine Hall had just hummed the "St. James Infirmary Blues." A young Englishman, later a Fellow of the Royal Society, sang the ballad about Frankie and Johnny. The mathematicians also played "serious games like chess," and lighter ones like bridge and poker. Qualifying his assessment of poker as light entertainment, Tucker asserts, "von Neumann proved mathematically that bluffing is a good strategy, provided it's done in the right way."

After starting out as a geometer, Tucker shifted around 1948 to game theory and mathematical programming. "I'm better known now by people in operations research than in pure mathematics," he says of the legacy of his life's work. Game theory, mathematical programming and operations research hadn't really existed when Tucker wrote his dissertation in combinatorial topology.

It's not altogether surprising that the man who savored the human quality of that community of great mathematicians should turn to game theory.

In 1944 von Neumann and Oskar Morgenstern published the Theory of Games and Economic Behavior and founded game theory as a branch of mathematics. Von Neumann's minimax theorem states that every finite two-person zero-sum game has an equilibrium outcome in mixed strategies. Tucker's graduate student, John Nash, generalized this result in 1950 to prove that non-zero-sum games also have equilibria. But it was clear that non-zero-sum games could have strange properties.

In 1950 when Tucker was visiting at Stanford University, he was asked to address psychologists there on game theory. He decided to mention the difficulty of analyzing non-zero-sum games, but figured he'd better make the mathematical theory concrete with a story, so he concocted what has become known as the "prisoner's dilemma." In an article on it, Philip Straffin has written, "The example ... with its accompanying story, has played a major role in social thought in the last thirty years. It is an example of a simple idea, originating in mathematical analysis, which can be said to have changed the way we think about our social world."

It seems that Tucker is a mathematician who has a feeling for a good story.


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Albert Tucker

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Rick Nebeker in the faculty room that was used for formal occasions when the old Fine Hall housed the Mathematics Department.

The Princeton Mathematics Community in the 1930s