249 Years of Mathematics at Penn

The Centenary of the Department of Mathematics

by Stephen S. Shatz and Frank W. Warner

Founding Fathers

On December 17, 1750 the trustees of the original Pennsylvania Academy made the following appointment: "Mr. Theophilus Grew having offered himself as a Master in the Academy to teach Writing, Arithmetick, Merchants Accounts, Algebra, Astronomy, Navigation, and all other branches of the Mathematicks; it is ordered that he be received as such at the rate of one hundred and twenty five pounds a year, his service to commence on the seventh day of January next." Thus began mathematics education at the University of Pennsylvania.

Five years later on June 10, the trustees received a charter creating the College and Theophilus Grew was appointed the first Professor of Mathematics. From that time on, the highest ranking faculty position in the College was that of professor. Except for a few brief gaps early in the period, there was always one professor of mathematics at Penn in the century and a half following Grew's appointment, but never more than one. Indeed, the total number of professors of mathematics from 1755 to 1899, a period of 144 years, was ten. In the 100 years since 1899, there have been sixty professors of mathematics at Penn.

In sharp contrast to the parochial state of mathematics in colonial America were the riches of the mathematics world of 19th century Europe. With physics came the gradual understanding of electrical and magnetic phenomena, subjects impossible to understand without more advanced knowledge than simply calculus. Advanced training was available only in Europe, and all who taught in America had spent some time studying and obtaining advanced degrees there.

This situation in the U.S. began to change when, in 1876, Johns Hopkins University founded the first Graduate School of Arts and Sciences. At Penn in 1881, the trustees approved the formation of a Faculty of Philosophy for instruction leading to the Doctor of Philosophy.

The first meeting of the newly formed Faculty of Philosophy on December 8, 1882 is regarded as the beginning of the graduate school at Penn. The first mathematics Ph.D. was Edwin S. Crawley in 1892. In 1899 mathematics achieved final independence from other disciplines such as astronomy, physics, and moral philosophy with which it had been associated in earlier years. Thus this date is regarded as the beginning of the Department of Mathematics whose centenary is being celebrated in 1999.

20th Century Changes

On the world stage, mathematics continued at an accelerating pace. This was the time of Henri Poincaré, who founded the subject of topology and did research of extreme profundity in celestial mechanics. David Hilbert made so many different contributions to mathematics that one cannot escape his name even today. Added to this was the gradual mathematization of physics, of chemistry, and the crisis of abstract thought caused by special relativity. Mathematics assumed its current essential role in Western thought by the beginning years of the 20th century.

Then, in the 1930s and 1940s, the political climate in Europe changed dramatically, causing a substantial portion of the scientific and artistic elite to emigrate to America. With this movement, the United States became the world's center of intellectual life, especially in mathematics.

Hans Rademacher left Germany in 1934 and came to Penn in part because of its situation in Quaker Philadelphia. A distinguished mathematician famous for his work in analytic number theory, the theory of functions of a real variable, quantum theory, and mathematical genetics, he was also a kind and charming person. In the mid-1960s, a group of mathematicians and scientists provided seed funding for The Hans A. Rademacher Instructorships at the University. The University also honored Rademacher at his retirement in 1962 by conferring on him an honorary Doctor of Science degree. The citation noted not only his scientific contributions, but also the "great charm and winsome tolerance of human frailties that endeared him to his students."

After World War II many universities took advantage of the general ferment of the time to strengthen their science faculties. In mathematics, Penn was slow to react. With the arrival of M. Gerstenhaber (1953), I.N. Herstein (1953), and C.T. Yang (1956), things began to change. The newcomers were resourceful and when the department had no funds for visiting speakers, Gerstenhaber and Herstein became contestants on a local radio quiz show. The $25 they won per show established a small visitors' fund. In 1954, Gerstenhaber and Herstein were awarded the first NSF grant in mathematics at the University. Gerstenhaber remains on the faculty to this day, while the late Herstein eventually wound up at Chicago.

   At the Math Centenary Celebration on October 30, University of Pennsylvania Medals for Distinguished Achievement were awarded to Dr. Freeman J. Dyson and Dr. Cathleen Synge Morawetz. Dr. Dyson and Dr. Morawetz were also presented with Department of Mathematics Centennial Awards, as were Dr. George E. Andrews, GR'64 and Bert Vogelstein, M.D., C'70. (See Almanac October 26, 1999.)

Modern Mathematicians

In 1960, Gerstenhaber and Yang were pushing hard for modernization and found an ally in the new provost, David Goddard. Goddard appointed the late Oscar Goldman as chairman of the department in 1962. Goldman's idea was to build in the three main areas of current mathematics: algebra, analysis, and geometry/topology.

Algebra was represented by Goldman and Gerstenhaber while Yang was a topologist, so Goldman attracted R.V. Kadison from Columbia (an analyst) and E. Calabi (a geometer) from Minnesota. Calabi was appointed to the Scott chair, while Provost Goddard resigned his own chair--the Gustave C. Kuemmerle Professorship--in favor of Kadison. Calabi was elected to the National Academy of Sciences in 1982; and Kadison, still an active member of the department, was elected Foreign Member of the Royal Danish Academy of Sciences and Letters (1974), Member of the Norwegian Academy of Sciences and Letters (1986), and Member of the National Academy of Sciences (1996).

With the appointments of Calabi and Kadison, Penn began its contemporary period of mathematics in which the department ranks very high on the national scene. In 1985, for example, Penn was the lead institution in the creation of the East Regional Geometry Festival, now a major annual event rotating among Penn, Courant Institute, Duke, University of Maryland, University of North Carolina, and SUNY, Stony Brook. In December, 1988, the department sponsored the first major US-USSR mathematics conference to be held in the United States in modern times. And during one recent six-year period, the number of Sloan Foundation Research Fellowships held by junior faculty in the department was the largest of any university in the country.

Over one hundred mathematicians per year from all over the world visit and speak in the department. Students from every part of the University, at all levels, take courses offered by the department and many earn dual degrees, or have double majors, with their second program in engineering, the Wharton School, or the other fields in arts and sciences. In the last 35 years, 187 Ph.D.s were awarded by the department compared with 133 Ph.D.s between 1892 and 1964. There is great activity, much research, and an attention to detail and quality in the important tasks of training and educating undergraduate and graduate students.

Dr. Shatz and Dr. Warner are professors of mathematics and former chairs of the department.

Almanac, Vol. 46, No. 14, December 7, 1999

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