EPADEL:A Semisesquicentennial History, 1926-2000

We end the chapter with an analysis of the mathematical classification of the invited lectures presented at the annual EPADEL fall meetings from 1979 to 2000. Keeping in mind that strict classification is impossible, interested readers are urged to consult the list of titles of all talks in the appendix, or abstracts provided in sectional newsletters.

This period was witness to one dramatic development: talks in analysis no longer dominated the programs, as they had done in every period heretofore. In fact, the EPADEL period showed an almost even distribution among speakers in the three main areas of mathematics: algebra/number theory (11.5), topology/geometry (10.5), and analysis (9). The fractional part comes from David Harbater’s 1996 talk, “Symmetry in algebra and geometry”. This period also reflects three other noteworthy changes. For one, there were a dozen talks related primarily to educational themes, continuing the section’s involvement with the central concern that manifested itself in the 1950s. Second, 10 lectures were devoted to topics in the history of mathematics, the most ever. Third, eight lectures discussed computer science. On a related note, the EPADEL period bore witness to six talks on applications.

The talks in the algebra/number theory category were almost evenly divided between the two subjects. The second lecture in the present period, presented in 1979 by local algebraist Willard Baxter, was titled “Rings with involution - An overview”. The two lectures on algebra presented four years later were both notable, one because of a local connection, with topologist/analyst Albert Wilansky describing “What matrices can do”. Wilansky followed Yale’s Walter Feit, who discussed the history and future prospects for completing the classification of the finite simple groups. The next lecture on algebra did not occur until 1996, when two more were given, including EPADEL member Gary Gordon’s “Using symmetry in teaching group theory”.

Although none of the six speakers on number theory is a member of our section, two have strong local ties. George Andrews, a Ph.D. student of Emil Grosswald and Hans Rademacher at Penn, presented his recent research in a lecture titled, “An old algorithm in a new era: Major MacMahon, you were born too soon!” Andrews was one of only four invited speakers to take the podium at Penn’s Centennial Celebration in 1999. It is not surprising that David Bressoud, the other EPADEL speaker on number theory, would lecture on this subject because he earned his Ph.D. at Temple under sectional governor Emil Grosswald after having matriculated at Swarthmore. Bressoud’s 1988 talk “Factorization and primality testing” was followed five years later by one of the country’s leading experts in this field, Carl Pomerance. The three other speakers on topics in number theory were internationally known Donald Zagier (1984), MAA president Kenneth Ross (1997), and acclaimed great teacher Arthur Benjamin (1999).

Of the 10.5 lectures in geometry/topology, seven were on topology proper, four by EPADEL members: Kenneth A. Brakke of Susquehanna (1993), “Soap films and covering spaces”, Herman Gluck of Penn (1989), “How can a drum change shape while sounding the same?”, Judy Kennedy of Delaware (1990), “Exotic topology in dynamical systems”, and James P. Fink of Gettysburg (1994), “Bifurcation, catastrophe, singularity, and all that”. Chapter 6 described Gluck’s invited lecture on topology in 1974.

Robert L. Devaney of Boston University delivered a particularly memorable lecture in 1987 titled “Computer graphics experiments in complex dynamical systems”. A pioneer in the use of computer graphics to demonstrate dynamical systems, Devaney’s lecture included an impressive array of color graphics at a time when such presentations attracted throngs of curious viewers.

We categorized David Harbater’s 1996 lecture as half algebra – half geometry. Three of the lectures given in the present period were devoted to purely geometrical subjects. Harbater’s Penn colleague Stephen S. Shatz gave an invited lecture 12 years earlier entitled, “Mordell’s conjecture: Ideas and the confluence of arithmetic and geometry”, which seems to suggest an intersection with algebra as well. However, the remaining two talks in topology/geometry were strictly geometric. In 1982 Peter Hilton (SUNY at Binghamton) gave a lecture titled “Descartes, Euler, and polyhedra”. Ten years later Princeton’s John Conway lectured on “Polyhedra and their symmetries” in his inimitable style, replete with physical models to enhance the presentation.

We have seen that members of the Penn School of Analysis dominated the invited lectures in the category of analysis until 1961, but Penn analysts gave only three of the 14 talks from 1956 to 1978. This trend almost reached a limit of zero in the present period, when the only talk on analysis given by someone associated with Penn was “Strange attractors and chaotic motion”, by Jerry P. Golub, who held a joint appointment in physics at Haverford and Penn in 1985. Two Temple analysts accepted invitations to speak on analysis during this period but only famed problem-solver Donald J. Newman (1985) was able to deliver his, “Addition chains when multiplications are free”. Shiferaw Berhanu (1991) was prevented by illness from presenting, “A nonlinear Fourier transform and its applications to complex vector fields”.

Temple was not the only institution with two faculty members lecturing on analysis. In addition to Jerry Golub, Haverford’s chair Curtis Greene presented the very first lecture in the present period, “Problems and results in unimodal sequences”. The only other talk on analysis during this period by an EPADEL member was “Real, complex, and metaphysical ideas of Karl Weierstrass” by Jerry King (Lehigh) in 1997. Some prominent members of the American mathematical community who spoke on themes from analysis during this period include Richard Anderson of LSU (1980), Paul Halmos of Santa Clara (1987), and Mary Ellen Rudin of Wisconsin (1993). Rudin is yet another prize graduate of the famous R. L. Moore School of Topology to speak to our section.

This chapter has already described the section’s overwhelming preoccupation with various themes in education during the entire EPADEL period in various realms. To support the notion that educational themes presented the membership’s overarching concern, the section invited 12 speakers to address educational issues on a wide range of subjects, more than any other category.

EPADEL members delivered two of these talks. In 1984 Temple’s Raymond F. Coughlin, a pioneer in “short calculus” texts, gave a lecture about teaching what then was becoming an increasing problem at many institutions, students ill- prepared for university-level mathematics. The title of Coughlin’s talk, “Remediation: A waste or a gold mine?”, provides no clue to the speaker’s strong feeling that remediation presented a potential lucrative market for universities if they took it seriously. Lafayette’s James Crawford presented a talk about teaching a contrasting set of students. At the 1999 meeting commemorating the 100 th anniversary of Elizabethtown College, Crawford dealt with students who came to college well prepared for calculus courses in a talk titled “Teaching calculus: A personal, institutional, and historical perspective”.

Individuals with strong MAA ties delivered five of the remaining ten lectures that carried educational themes. In 1982 Alan C. Tucker, of SUNY at Stony Brook, whose father, Princeton’s Albert W. Tucker, lectured to the section in 1938, 1948, and 1957, described the “Mathematical sciences curricula”. His talk was immediately followed by an EPADEL panel discussion on a related topic, “CUPM recommendations”. Two years later, MAA president-elect Lynn A Steen (St. Olaf) made a plea for “Renewing undergraduate mathematics”. Two years after that, in 1988, Martha Siegel (Towson State) discussed “Freshman mathematics for the modern age”. The sectional newsletter for that meeting carried an MAA advertisement for the position of Executive Director. Thanks to the knowledge and foresight of sectional governor Gerald Porter, the person chosen to fill that position, Marsha Sward, gave her very first presentation to any MAA section at the meeting held the next year at Millersville. In a lecture titled “Everybody counts: From vision to reality”, Sward discussed timely work initiated by the National Council of Teachers of Mathematics. The very next year, Kenneth Hoffman, then Director of the Mathematical Sciences Education Board, continued this line of investigation in his lecture, “Mathematics education reform: Our critical role”.

There are three other categories in which numerous invited talks were presented, history (10), computer science (8), and applications (6). This was the very first period in the section’s history when talks dealing with the history of mathematics attracted such widespread interest. Local historians Paul Wolfson (West Chester) and William Dunham (Muhlenberg) accounted for three of the 10. Earlier in this chapter we noted Wolfson’s involvement with European tours covering various aspects of the history of mathematics. A book-review editor for the journal Historia Mathematica, he highlighted one of those aspects in his 1987 talk, “Newton: The calculus, the Principia”. The other local historian, the husband of present Executive Committee member Penelope Dunham of Muhlenberg College, presented two invited lectures during the 1990s. The clever title of his 1992 talk was “Constructing the regular heptadecagon: Ingenuity or just a lucky Gauss?” The topic of Dunham’s 1999 lecture, “Euler’s sums and Euler’s crumbs”, concerned the main theme from one of his best-selling books, Euler: The Master of Us All. (Recall from Chapter 5 that the Koehler family donated a set of Euler’s works to the library at Muhlenberg College.)

Distinguished historians delivered five of the remaining lectures on the history of mathematics. In 1985 Ann Hibner Koblitz (University of Washington) read the paper, “The mythification of Sofia Kovalevskaya”. The very next year V. Frederick Rickey (Bowling Green) answered many a question asked by calculus teachers everywhere in his talk, “The invention of calculus: Who, what, when, where, and why?” Just two years later Harold Edwards, of the Courant Institute at NYU, spoke about “Kronecker’s views of the foundations of mathematics”. In 1995 Marcia Ascher, recently retired from Ithaca College, presented “Tracings in the sand: An introduction to ethnomathematics”, while three years after that James Tattersall (Providence College) showed some “Mathematical vignettes from Cambridge University”.

In the remaining two talks on the history of mathematics, two prominent members of the international mathematical community reminisced about their involvement in the development of the subject in the 20 th century. In 1980 Mark Kac presented “Recollections and reflections on 50 years of probability theory” and three years later Stanislaw Ulam gave “Mathematical reminiscences and suggestions for the future”. The 1983 meeting was held at Bryn Mawr College, the home of John Oxtoby, our section’s former president and Ulam’s good friend.

Chapter 6 noted the section’s interest in computers as early as 1970, when it sponsored a panel discussion on their place in the mathematics curriculum. This interest intensified in the present period, which featured eight lectures on topics related directly to computer science. Two of these talks were given by individuals with ties to Temple University. In 1987 Elaine Jacobson, a Ph.D. graduate of Temple then employed by Control Data Corporation, spoke about “Parallel processing architectures”. Twelve years later, Temple faculty member Doron Zeilberger spoke about the role of computing in the future in a lecture that carried the unusual title, “Synopses of two textbooks: Levi Ben Gerson’s Ma’asei Khoshev (ca. 1320) and Shalosh B. Ekhad’s Plane Geometry (ca. 2050).”

Three of the remaining talks on computer science were presented by distinguished personalities in the field. In 1985 Frank Thomson (Tom) Leighton of the Department of Mathematics and the Lab for Computer Science at MIT spoke on “Networks, parallel computation and VLSI”. At the Sunday meeting the following year Thomas Kurtz (Dartmouth) presented a talk called “Computing in the classroom”. Kurtz is one of the inventors of the language BASIC, which was taught to all undergraduate students at Dartmouth since the late 1950s. The final speaker from this New England troika was recent MAA president-elect Thomas Banchoff (Brown), who in 1991 presented the invited address titled, “Computer graphics and surfaces in four-space: Visualizing characteristic classes”.

Although the section sponsored six talks on traditional applications of mathematics during the present period, the types of applications varied considerably. The two lectures by EPADEL members concentrated on economics. In 1994, J. Michael Steele, of the Wharton School at Penn, spoke on “Ruin and riches from Bachelier to Black-Scholes”. Four years later Lehigh’s Vladimir Dobric lectured on a similar theme in his presentation, “A fundamental model in mathematical finance”. The other four speakers described a range of applications whose content can be inferred from their titles – Ward Whitt (1980; AT&T Bell Laboratories), “Approximation for networks of queues (description of complex systems adequate for engineering purposes)”, Daniel Gottlieb (1988; Purdue), “Topology and the robot arm”, John D. Grace (1990; Atlantic Richfield Corp.), “Oil and uncertainty”, and Joseph A. Gallian (1993; Minnesota), “The mathematics of identification numbers”.

Chapter 6 noted that Penn’s Herbert S. Wilf presented the very first lecture in the category combinatorics/graph theory in 1967. He gave two more talks on this topic during the present period: “Some bijective proofs in combinatorics” (1982) and “Finding and proving identities with your computer” (1995). Wilf’s stranglehold was broken in 1997 when Rodica Simion (George Washington) lectured on “The many lives of set partitions”. The same could be said about a 1998 talk by Wilf’s partner in proving identities, Doron Zeilberger, but we categorized the latter talk under computer science.

Three lectures were devoted to probability/statistics in this period, although one of them was a hybrid. As the title “Probability and the approximation of continuous functions” suggests, the lecture delivered by former EPADEL governor Jerry King of Lehigh in 1981 contained as much analysis as probability. The invited lecture by Mary Gray (American University) carried the fetching title, “Justice by lot: Olympic gold medals, Rwandan prisoners and employment discrimination”. Gray had been one of the founders of the Association for Women in Mathematics. The remaining talk in this category was special too. Recall that Shif Berhanu had to cancel his talk due to illness. On almost no notice, Alan J. Rossman (Dickinson) prepared a lecture with another alluring title, “Bayesian statistics in the courtroom”. The section chair at the time, Walter Stromquist, has called Rossman a hero for his duty beyond the call of service.

There was only one talk on mathematical logic during this period, and someone with nonacademic credentials delivered it. In 1994 Karvel Thornber, of the NEC Research Institute, presented a paper with the title, “Inference beyond logic”.

Seven lectures seem to defy exact classification yet are worthy of mention. Penn professors delivered three of them. In a perspicacious presentation in 1980 sectional governor Gerald Porter spoke about “The future of the MAA”. In 1991 his colleague Dennis DeTurck answered the question, “What problems are we trying to solve?” DeTurck described several problems in which powerful theories were developed to deal with generalized problems while the original “simple” problem remained unresolved. Four years later Sampath Kannan spoke on “Tractable algorithms for phylogeny reconstruction”.

Two of the remaining lectures in the “miscellaneous” category were concerned with the mathematics involved in juggling, by Ronald Graham of AT&T Bell Laboratories, in 1991 and 1998. Ten years before Graham’s first lecture/demonstration the renowned author Paul R. Halmos asked “Does mathematics have elements?” Immediately after lunch Kenneth Appel lectured on his celebrated – and controversial – computer-aided proof (with Wolfgang Haken) of the four-color problem, which had been completed in 1976.

Overall, this chapter has indicated that the greatest number of activities at annual meetings during the period 1979-2000 was concerned with educational issues, as reflected principally by panel discussions and invited lectures. Among the invited lectures, there was almost a dead heat among the three major categories of mathematics. Close on the heels of the “big three” were the history of mathematics, computer science, and applications.