Luther Pfahler Eisenhart

January 13, 1876 October 28, 1965

L. P. EISENHART OF PRINCETON

Mathematician and Humanist 1876-1965

BY ISAAC L. BATTIN, SR.

Trenton State College

Luther Pfahler Eisenhart—Albert Baldwin Dod Professor of Mathematics, and Chairman of the Mathematics Department at Princeton University from 1929 until 1945; Dean of the Faculty from 1925 until 1933; and Dean of the Graduate School from 1933 until 1945—was both a great mathematician and a great humanist. It was his interest in other human beings that spurred him to work much harder, and accomplish much more, than most men ever attempt.

Dean Eisenhart made very effective use of his time—even of its smallest portions. In the Dean's Office in Nassau Hall, as in the office of the Chairman of the Mathematics Department in Fine Hall, there was a large table covered with materials for the books, articles, and reports on which he was always at work—while holding down what ordinary men would consider two full-time jobs. For Mr. Eisenhart never used the fact that he was a Dean as an excuse to eliminate teaching.

In Nassau Hall, as in Fine Hall, if Dean Eisenhart had a five-minute break between appointments, instead of resting, he would go to his work table and a batch of material where a five-minute task waited. Another paragraph would be revised; another problem would be properly worded; another theorem would be roughed out; a few more cards would be added to an index.

It was effective use of time which enabled the Dean to produce his COORDINATE GEOMETRY and AN INTRODUCTION TO DIFFERENTIAL GEOMETRY. These books are landmarks of his interest in students. His COORDINATE GEOMETRY was years ahead of the times. For example, it placed great emphasis on linear algebra. But only today is the importance of linear algebra fully recognized.1

The Dean wrote AN INTRODUCTION TO DIFFERENTIAL GEOMETRY because he wanted to introduce the tensor notation to undergraduates. He believed that in order for society to prosper, it was necessary to get young men and women to the frontiers of knowledge quickly. He felt that if anyone's creative potential was not developed to the fullest extent, society as a whole was the loser.

The importance which he attached to the development of each individual's creative ability is attested by the Princeton Program of Independent Study for Upperclassmen know to generations of students since 1923 as "the four-course plan." It differs from most honors plans in this: At Princeton, every upperclassman in liberal arts takes only four courses, instead of the usual five courses. Thus, he is able to devote one-fifth of his time to independent study, writing a thesis, and preparation for a comprehensive examination. He is automatically a candidate for honors.2

On the Dean's retirement in 1945, the Trustees of the University paid tribute to Luther Pfahler Eisenhart as "the guiding genius in the origination of the four-course plan ... and its later development." In the Dean's own words, the plan was designed "to teach the student how to educate himself." In their tribute to the Dean, the Trustees stated that accomplishments of Princeton graduates had shown that the plan was "the greatest advance since the adoption of the preceptorial system ... under Woodrow Wilson."

Dean Eisenhart was aware of the problems of the underprivileged. He knew that our society suffered because many bright youngsters had no chance whatever of going to kindergarten, and were forced to learn their A, B, C's in overcrowded classrooms. But — his academic positions being what they were—he felt that he could do most to improve things by working for high standards in college mathematics. He was confident that this would, in turn, result in higher standards in the secondary schools, and right on down to the kindergarten level. His interest in the teaching of mathematics led him to be one of the founding members of the AMTNJ.

After retiring as Professor and Dean in 1945, Mr. Eisenhart went to his office in Fine Hall regularly, and kept abreast of the latest developments in mathematics, science, and other fields. At the same time, he continued to serve as Executive Officer of the American Philosophical Society, a position which he had held since 1942. In this capacity he commuted to Philadelphia three or more times a week, until his retirement in 1959. But he continued to be active in the Society until 1962.

In spite of his many duties, Dean Eisenhart always had time to help others. No matter who came to his office—and no matter how many pressing tasks were waiting he was always "delighted to see you"—as he would say. And everyone came away from a conference with him refreshed and inspired. He never wasted time in trivial talk. Bur he had a fine sense of humor and enjoyed a good joke.

With students, Dean Eisenhart often used the Socratic method. Sometimes he would have to ask many, many questions before a student would finally get the point. But then, his "That's it! That's the way to do it!" would always make the student feel that he had made the discovery. Thus he created an environment in which his students thrived intellectually.3

He enjoyed the artistic side of mathematics, and often stressed the difference between an elegant proof and "just a proof." He believed that each student would learn more about how mathematicians think and work by facing and solving problems geared to his level, than by reading volumes about mathematics.

The aim of Dean Eisenhart's COORDINATE GEOMETRY was "to encourage the reader to think mathematically." He believed that to think mathematically was the only way to think. In other words: Look at the data, face the facts, decide what consequences are likely to follow what actions, and then—think precisely.

Luther Pfahler Eisenhart believed that if everyone could learn to think mathematically, the world would be a better place for all of US.4

Footnotes

1As the flood of recent texts on the subject shows. Dean Eisenhart's COORDINATE GEOMETRY was published in 1939 by Gina and Company, New York. AN INTRODUCTION TO DIFFERENTIAL GEOMETRY was published in 1940 by Princeton University Press, Princeton, New Jersey.

Other publications by L. P. Eisenhart include:

A TREATISE ON THE DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES, Ginn and Company, Boston, New York, etc., 1909

TRANSFORMATIONS OF SURFACES, Princeton University Press, Princeton, N. J., 1923 and (second edition) Chelsea Publishing Company, New York, 1962

RIEMANNIAN GEOMETRY, Princeton University Press, Princeton, N. J., 1926, and (second printing with new appendices and additional bibliography), 1949

NON-RIEMANNIAN GEOMETRY, American Mathematical Society,, New York, 1927

CONTINUOUS GROUPS OF TRANSFORMATIONS, Princeton University Princeton, N. J., 1933

THE EDUCATIONAL PROCESS, Princeton University Press, Princeon, N. J., 1945

Besides the preceding books, Dean Eisenhart published numerous research papers during the years 1947-1960. Some of these are collected in a volume SELECTED PAPERS Presented to Dean Eisenhart as a Token of Esteem by the Graduate Students of Mathematics at a Dinner Honoring Him at Proctor Hall of the Graduate College, Princeton University, March 8, 1961. A duplicate of the original volume is available in the Fine Hall Library.

In addition, Dean Eisenhart supervised many Ph.D. theses.

2 About forty percent of the graduates achieve honors.

3 With his collegues, Dean Eisenhart often used a similar phrase. When someone had summed up a situation and concensus was about to be reached, his face would light up with a smile, and he would ask: "Isn't that it? Isn't that it?" This pleasant way of ending a conference was also an effective time-saver.

4 I am indebted to Miss Julia Noonan of the American Philosophical Society for supplying various dates. And I am very indebted to Mrs. Eisenhart, and to Mr. Alexander Leitch, Secretary of Princeton University, for reading the manuscript critically, making many helpful suggestions, and supplying many details of information.

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The Princeton Mathematics Community in the 1930s