EPADEL:A Semisesquicentennial History, 1926-2000

The Philadelphia Section sponsored 56 presentations involving 58 speakers at the 14 annual meetings held from 1942 to 1955. The 1954 meeting included a discussion by three people that accounts for the disparity in the two numbers. After discussing the presenters and their affiliations, we take a chronological tour of the meetings to analyze sectional activity from this perspective, after which we discuss the lectures in terms of mathematical classification. Unlike previous chapters, however, we do not list a separate table of the presentations. The interested reader is referred to the appendix for the complete list in this period.

Altogether 50 different individuals account for the 58 presenters, a number that clearly indicates a wide span of invited speakers. Nobody spoke more than two times over the 14-year period, with eight different people appearing twice: Bernard Epstein (1950, 1951), Nathan Fine (1947, 1952), Ralph Fox (1945, 1953), Herman Goldstine (1949, 1954), Marguerite Lehr (1944, 1954), Francis Murnaghan (1944, 1947), John Oxtoby (1943, 1949), and Isaac Schoenberg (1942, 1949). Epstein, Fine, and Schoenberg were at Penn at the time of their presentations, Lehr and Oxtoby at Bryn Mawr, Fox at Princeton, Goldstine at the Institute for Advanced Study, and Murnaghan at Johns Hopkins. Epstein’s talks in consecutive years mark the only time that has happened in the history of the section.

Institutional affiliations are as diverse as the range of speakers, with 18 different institutions accounting for the 58 presenters. Once again the University of Pennsylvania led the way, with 10 speakers, followed by Bryn Mawr College and Princeton University (7 each), Lehigh University and the University of Delaware (5 each), Haverford College and the Institute for Advanced Study (4 each), and Swarthmore College (3). The preceding chapter noted that only once in the section’s 75-year history were there lectures by two individuals from the same institution at the same fall meeting. That happened in 1952 when the University of Delaware’s Russell Remage and E. V. Lewis spoke. At the opposite end of the spectrum, Penn’s 10 lectures in the present period were delivered in 10 different years. It is relevant to point out that a total of 13 speakers came from institutions located in New Jersey because that state formed its own section in 1956, the last year of the period under discussion.

F. D. Murnaghan was one of the few speakers who were invited from outside the area at that time. Others who came from beyond the section’s boundaries were Colonel R. C. Yates (U. S. Military Academy) in 1951 and Morris Kline (NYU) in 1955. Five other speakers were invited in the midst of their stays at institutions in the area, though their normal affiliations were elsewhere. Three of these positions were war related: Haskell Curry was on leave from Penn State at the Frankford Arsenal in 1942, and A. A. Bennett and D. H. Lehmer were at the Aberdeen Proving Ground, on leave from Brown in 1943 and Berkeley in 1945, respectively. We might also mention that in 1954 Ernst Snapper was a visiting professor at Princeton University from the University of Southern California and the famous A. S. Besicovitch was a visiting professor at the Institute for Advanced Study from Cambridge University in England.

Now we take a chronological tour of annual meetings from 1942 to 1955, highlighting some of the more notable events. We already observed, for instance, that three of the speakers worked at war-related institutions at the time they spoke to our section. At the first meeting held after the U.S. entered the war, the title of the talk by Lehigh’s G. E. Raynor was “Exterior ballistics”. This is the same meeting at which Haskell Curry spoke while assigned to the Frankford Arsenal in North Philadelphia, though his topic was Heaviside operators. Hilda Geiringer, an émigré who was teaching at Bryn Mawr at the time, spoke on numerical solutions of linear problems, but her talk concerned pure rather than applied mathematics.

Returning to the theme of war-related activities in the section, the 1943 meeting featured an invited talk by one of the section’s three founders, A. A. Bennett of the Aberdeen Proving Ground. The topic of Major Bennett’s talk was Euclidian geometry rather than the ballistics research he was involved with on a daily basis. Another speaker, J. B. Rosser from the National Defense Research Committee, chose to talk about a mathematical subject (many-valued logics) instead of a more bellicose topic. The minutes from the 1943 meeting also reflect the war in progress by setting a “tentative” date for the 1944 meeting, which actually was held on the date assigned a year later. Recall that national MAA meetings were cancelled in 1942 and 1945.

The program in 1943 featured the section’s first talk on foundations when J. B. Rosser spoke “On the many-valued logics”. This was the first time the section heard a talk on foundations, which is rather surprising in light of the fact that Alonzo Church and Kurt Gödel had propelled Princeton into worldwide leadership in the field since the 1930s. However, neither of these stalwarts ever attended a sectional meeting. Theodore Hailperin in 1948 and C. D. Firestone in 1950 gave other talks on foundations during this period.

Interestingly, the 1944 meeting of the Philadelphia Section did not reflect the ongoing war. Even Marguerite Lehr’s talk, “Mapping problems in aerial photography,” dealt with a method employed by the Canadian Topographical Survey and not with a theme that the title might otherwise suggest. The only vestige of World War II at the 1945 meeting was that D. H. Lehmer’s affiliation was listed as Aberdeen. However, the title of his talk was “Some graphical methods in the theory of numbers”.

The 1945 meeting thus serves as a dividing line between wartime activities and the period that followed. Although only 27 people attended the meeting in 1944, 44 attended in 1945 and 51 in 1946. All were held at the University of Pennsylvania. The 1945 program consisted of only three lectures, but the presenters were all outstanding mathematicians. One was Ralph Fox of Princeton University, who spoke about homotopy groups. One was Antoni Zygmund, then at Penn but soon to be enticed to the University of Chicago by Marshall Stone; Zygmund spoke on his specialty, trigonometric series. The remaining speaker was Derrick H. Lehmer, who taught at Lehigh University from 1934 to 1940 and spoke to the section in 1939. For the record, D. H. Lehmer’s father was the mathematician Derrick N. Lehmer, a 1900 Ph.D. from the University of Chicago. Our Lehmer produced only two Ph.D. students, both at Berkeley, but his two students are household names today and both have been extremely active with the MAA – Tom Apostol and Ronald Graham.

By 1946 sectional meetings had returned to normal. Once again there were three lectures at the meeting. This was the first of the two years that T. A. Botts taught at the University of Delaware. He spoke on “Convex sets”. Next, Haverford’s C. B. Allendoerfer spoke on “Slope in solid analytical geometry,” the topic of a Monthly paper that appeared earlier that year. Edwin Hewitt delivered the third paper, “Generalizations of the Weierstrass approximation theorem”. Hewitt was at Bryn Mawr for only one year, 1946-1947, so the Program Committee is to be commended for its perspicacious invitation. Hewitt himself received his Harvard Ph.D. under Marshall Stone.

Three of the four talks at the 1947 meeting at Bryn Mawr were delivered by people who accepted multiple invitations to speak at the section’s annual meetings. The day began with the first of Nathan Fine’s three lectures, “On Walsh functions,” based on his 1946 dissertation with the same title written under the supervision of A. Zygmund. The afternoon session featured F. D. Murnaghan’s second lecture, on vector methods in teaching trigonometry and geometry. He had spoken three years earlier on an article published in the Monthly, “The uniform tension of an elastic cylinder”. The final presentation of the day was the third talk by the Princeton statistician S. S. Wilks, who accompanied his remarks on statistical inference “with material on slides”. This is the only mention of such technology in the history of the section.

Two of the three lectures at the 1948 meeting are deserving of special mention. Theodore Hailperin (Lehigh) began the day with a talk titled, “Recent advances in symbolic logic”. A. W. Tucker (Princeton) gave the other notable lecture that year on game theory, the second of his three invited lectures to the section. This one not only marked the first time the section heard about the theory of games, but it marked the first topic to reflect a post-WWII national trend.

A. W. Tucker’s talk on game theory was not the only time that sectional audiences could listen to a world renowned specialist speak about a topic that was then at the cutting-edge of research. Over the next five years, invited lectures were given by Herman Goldstine in 1949 and 1954 on computers, by H. W. Kuhn in 1953 linear programming, and by Ralph Fox in 1953 knot theory.

In addition to Herman Goldstine’s talk on applications of numerical analysis to computing at the 1949 meeting, A. D. Hestenes of Philadelphia’s famous science institution, the Franklin Institute, spoke about industrial research and development organizations. The program also included the third lecture by Bryn Mawr’s John Oxtoby in the 1940s, matching the three talks that J. A. Shohat delivered in the 1930s and the three that Bernard Epstein would deliver in the 1950s.

The final lecture at the 1949 meeting was the second of four talks given by Penn’s Isaac Schoenberg. In a similar vein, Albert Wilansky’s talk to begin the 1950 meeting was the first of the record-number five talks he would give to the section, his others taking place in 1956, 1963, 1970, and 1983.

In the final address at the 1950 meeting at Lehigh, S. T. Hu of the Institute for Advanced Study spoke on “Topological properties of spaces of curves”. During this talk the speaker cited the work of our own Everett Pitcher in the field and included a proof of Pitcher’s theorem characterizing when certain sets of curves are metrizable.

All four talks at the 1951 meeting are deserving of mention. Two dealt with the increasing attention being paid to mathematical pedagogy. The first speaker, R. C. Yates of the U. S. Military Academy, described various topics that stimulated interest in mathematics courses taken during the first two college years. Yates had spoken to the section in 1938 when he was at the University of Maryland. The day’s final speaker, P. J. Kiernan of the Lawrenceville School, a private secondary school located near Princeton, discussed a theme that garnered increasing interest throughout the 1950s, “Articulation of secondary and college mathematics”. In between those two talks the famous algebraist Emil Artin spoke about “Constructions with ruler and divider” and Bernard Epstein gave the first of his three talks in the decade, titled “An infinite-product expansion for analytic functions”.

The 1952 meeting featured talks on probability (by Samuel Goldberg of Lehigh University) and statistics (by E. V. Lewis of the University of Delaware). Russell Remage opened the meeting with a lecture titled “Matrix inversion by partitioning”. Remage and Lewis continued the active Delaware involvement in the section begun in the 1940s by Rees and Webber. We will meet Remage in the next chapter as chairman of the section.

The next notable event to take place at an annual meeting was a presentation in 1954 titled “Mathematics through the television lens”. Not exactly a panel discussion, it featured three speakers who discussed various ways to teach mathematics via this relatively new medium. Although panel discussions per se did not start in the section for four more years, this program might be considered the prototype of a format that has been used successfully on numerous occasions since then. The 1954 meeting included three outstanding lectures in addition to this presentation. To open the program Ernst Snapper talked on “Coordinates of algebraic varieties”. The two lectures after lunch were “Area and volume” by A. S. Besicovitch and “Some remarks on numerical stability” by Herman Goldstine. Besicovitch’s topic was not surprising; 28 years earlier he had shown that there exist planar regions of arbitrarily small area in which a segment of fixed length could be rotated, thus solving the Kakeya needle problem. Goldstine demonstrated the electronic computer that had been developed at the Institute for Advanced Study. Goldstine, a 1936 Ph.D. from the University of Chicago, was appointed a permanent member of the Institute in 1952 and served as the associate director of the electronic computer project there from 1946 to 1955. Although born in 1913, hence approaching his 90 th birthday, Goldstine remains active with the American Philosophical Society, located on Independence Mall in Philadelphia.

The last meeting in this period began with a discussion by H. W. Brinkmann of work carried out under the auspices of the College Entrance Examination Board. As we saw in the preceding chapter, Brinkmann was one of the most active mathematicians in the section during the 1930s; he would speak to the section again in the 1960s! Brinkmann was followed on the program by another émigré, Hans Rademacher, who spoke on one of his favorite subjects, Dedekind sums. Two notable speakers ended the day. The renowned probabilist William Feller, yet another émigré, spoke about differential operators. In the final talk of this period NYU’s multifaceted Morris Kline spoke about material that he felt should be included in courses taught to college freshmen. Given Kline’s work in applied mathematics and his interest in the history, cultural, and pedagogical aspects of mathematics, it is not surprising that his talk carried the unusual title “Pea soup, tripe and mathematics”.