PASHoM

Record of Meetings

2000-01 2001-02 2003-04 2004-05 2005-06 2006-07 2007-08

Pre-history

November 25, 2000, William Dunham of Muhlenberg College, at West Chester University, organized by Paul Wolfson
December 7, 2000, Jim Stasheff, Life as a Graduate Student at Princeton in the 1950's, Temple University, organized by David Zitarelli.

Spring 2001

January 18, 2001, Rüdiger Thiele, Universität Leipzig, Hilbert's twenty-fourth problem.
February 15, 2001, Fr. Frederick A. Homann, S.J., St. Joseph's University, "Mathematical History of Surveying"
March 15, 2001, Brief work-in-progress reports by members
April 26, 2001, Paul Wolfson, West Chester University, "How Relativity Changed Invariant Theory"

2001-2002

September 20, 2001, Alan Gluchoff, Villanova University, "Close-to-Convexity: An Episode in Function Theory, 1915-1952"
October 25, 2001, Tom Foley, St. Joseph's University, "The Golden Ratio in Physics -- Revisited"
November 30, 2001, Rob Bradley, Adelphi University, "The Euler d'Alembert Correspondence and Complex Logarithms"
January 22, 2002, Joel Goldstein, "A bridge over troubled waters: Evidences of Christianity courses at dissenting academies and the emergence of rational dissent, 1729-1798.”
February 24, 2002, George Rosenstein, Franklin and Marshall College, "Granville: The Man and His Book"
March 21, 2002, Alan Gluchoff, Villanova University, "Thomas Gronwall"
April 25, 2002, “Research-in-progress by four Temple graduate students”

2002-2003

September 19, 2002, William Dunham, Muhlenberg College, "Volterra and pathological functions from 19th Century analysis"
October 24, 2002, Robert Jantzen, Villanova University, "The Princeton Mathematics Community of the 1930's: An Oral History Project."
November 21, 2002, Paul Halpern, University of the Sciences in Philadelphia, "History of Dimensionality"
January 23, 2003, Eleanor Robson, All Souls College (Oxford University), "Mesopotamian Mathematics: Tablets at the University of Pennsylvania Museum"
February 26, 2003, John Dawson, Pennsylvania State University, York, "Twenty years of Gödel studies in retrospect"
March 20, 2003, Frederick A. Homann, S.J., St. Joseph's University, "Combinatorial Theory in Boscovich's Mathematics"
April 24, 2003 Thomas L. Bartlow, Villanova University, "Mathematics and Politics: The Apportionment Debate of 1920-1940"
May 22, 2003, Amy Shell-Gellasch, United States Military Academy - West Point, New York, "Descriptive Geometry in the New Nation: West Point 1817-1870"

2003-2004

September 18, 2003, Fritz Hartmann, Villanova University, "Apollonius’ Ellipse and Evolute Revisited"
Thursday, October 23, 2003, Amy K Ackerberg-Hastings, Anne Arundel Community College, "Francis Nichols: Philadelphian, Bookseller, Mathematical Critic"
Thursday, November 20, 2003, John McCleary, Vassar College, "Heinz Hopf and the early development of algebraic topology"
December 11, 2003
David Zitarelli, Temple University
"The Bicentennial of American Mathematics Journals"
The first journal devoted entirely to mathematics in the United States was founded 200 years ago, in 1804. This talk will present an overview of the contents of the Mathematical Correspondent and discuss its relative importance in the history of mathematics in the U.S. It will also provide biographical snippets of the founder, George Baron, and some of the major contributors.
January 15, 2004
Rüdiger Thiele, Universität Leipzig
"The Brachistochrone Problem and its Sequels."
To a large extent Hilbert's list of problems (Paris, 1900) steered the course of mathematics in the 20th century. However, posing problems is an old mathematical tradition and there are many famous problems from the 17th century, among them the most influential Brachistochrone Problem (Johann Bernoulli, 1696). As a consequence of this problem mathematical physics (in its true meaning) got its start by developing essential variational methods that resulted in a new branch of
mathematics. Moreover, the concept of an analytic function was formulated (Bernoulli, 1697) and extended (Euler, since 1727). This lecture gives a comprehensive overview on these cornerstones of mathematics.
February 19, 2004
V. Frederick Rickey, United States Military Academy
"Mathematics at West Point in the Early Twentieth Century (a very preliminary report) "
The United States Military Academy celebrated its centennial in 1902 but was it a vibrant intellectual center or a school with a hundred years of tradition unimpeded by progress? Since the study of mathematics occupied a substantial portion of the education of every graduate, this motivates us to look at all aspects of the department of mathematics: Who were the faculty? What was their education and experience? What was the curriculum? Which textbooks were used? How were the classes conducted? How did the department interact with the national mathematical community? How did world events impact the department?
March 18, 2004
Peggy Kidwell, Smithsonian Institution
"Geometric Models for the Twentieth Century American Classroom: Richard P. Baker and his Contemporaries."
April 15, 2004
Vicki Hill
A film on the life and work of Constantin Caratheodory
May 13, 2004
Alexander Soifer, Professor of Mathematics, Art & Film History, University of Colorado at Colorado Springs
"One Result -- Three Lives: Issai Schur, Bartel van der Waerden, Pierre Joseph Henry Baudet"
A talk on the history of the classic van der Waerden-proved theorem on monochromatic arithmetic progressions in finitely-colored integers.
June 25, 2004, 4:00 p.m.
Ioan James
'The Mind of the Mathematician'
An introduction to the literature on the psychology of mathematicians, and other scientists. For example, highly
intelligent people with mild forms of autism often love mathematics and tend to excel at it. This leads into a discussion of the nature of mathematical creativity and what has been learned about it since Poincare gave his famous lecture on the subject just a century ago.

2004-2005

September 23, 2004
Tom Archibald, Dibner Institute/Acadia University
"Aspects of the Reception of Fredholm's Work on Integral Equations"
In 1899, Ivar Fredholm (1866-1927) devised a method for solving a type of functional equation where the unknown function appears under the integral sign, a problem going back to Abel and which had already received some study at the hands of Vito Volterra and Picard's student J. Le Roux. This rather special-sounding problem had profound resonances. For one thing, it could be combined with methods of Carl Neumann and Henri Poincaré to prove the existence of solutions to many boundary-value problems, and indeed to find these solutions using Picard's successive approximation method. Still more far-reaching were the insights it provided to David Hilbert and his student Erhard Schmidt, who reinterpreted Fredholm's methods into the point of departure for what we now term operator theory on Hilbert spaces. In this paper, I examine the first of these threads, mostly concentrating on French and Italian work of the period from 1902 to 1910. This represents joint work with Rossana Tazzioli (Catania).
October 28, 2004
David Alan Grier, George Washington University
"When Computers were Human".
Before we had electronic devices to do scientific computation, lengthy calculations were done by large groups of human computers. These individuals were usually intelligent persons who were unable to pursue a career in science because of their social or economic standing. They are best characterized as "blue collar mathematicians." Several of the human computers, notably the staff at the U. S. Nautical Almanac, the workers at George Snedecor's Statistical Laboratory and the members of the WPA Mathematical Tables Project,
made many small contributions to the development of numerical analysis. The Mathematical Tables Project, which was probably the largest computing group of modern time with over 450 computers at its prime, became the basis for the Institute for Numerical Analysis at UCLA and the Applied Mathematics Laboratory at the National Bureau of Standards. This talk is based on a new book, which is being published by Princeton University Press.
November 18, 2004
Paul Pasles, Villanova University
"The Most Magically Magical Dr. Franklin."
In a parallel universe, the Philadelphia Area Seminar on the History of Mathematics celebrated its semiquincentennial in 2001. There, our alternate selves reflected on the founding members, local scholars who managed to do a little mathematics in the isolated colonial backwater called Philadelphia. Most prominent of these early mathematicians was Benjamin Franklin, master of the magic square.
Until recently it appeared that only two of Franklin's magic squares were still extant. In fact these were really two instances of the same example, extended to different orders. Now, however, it is clear that more than a half-dozen squares survive. How do these
compare with their predecessors? How exactly did Franklin effect his numerical oddities? What is the state of the art today? We consider these questions as well as some other mathematics of the day.
December 16, 2004
George Rosenstein, Franklin and Marshall College
"Calculators for a New Century"
One of the unusual features of the 1904 edition of Granville's calculus, a book I have described as the first 20th century calculus text, is a final chapter called "Integraph. Table of Integrals." In this chapter, Granville describes the theory and operation of a machine that draws integral curves by tracing a given curve. Later editions describe not only the Integraph, but also polar planimeters. By the 1941 edition, this material had disappeared. I will examine the operation of the relatively simple Integraph and speculate on the reasons for its inclusion in the text.
February 17, 2005
Paul Halpern, University of the Sciences in Philadelphia
"The Rise and Decline of the Goettingen Mathematical Institute (1929-1945)"
In 1929, a new Mathematical Institute opened just outside the old city walls of Goettingen, with Richard Courant assuming its prestigious directorship. This modern facility offered the venerable department a spacious library, comfortable offices, housing facilities for visitors, and prominent exhibit space for its valuable collection of mathematical models and instruments. Only four years later, however, the ascendancy of the Nazi party forced the faculty to emigrate to the United States. Their hastily chosen replacements needed to steer an impossible course between the department's hallowed tradition and the odious dictates of the regime.
March 24, 2005
Nathan L. Ensmenger, University of Pennsylvania
``Chess Players, Music Lovers, and Mathematicians: Towards a Psychological Profile of the Ideal Computer Scientist''
In the early 1950s, the academic discipline that we know today as computer science existed only as a loose association of institutions, individuals, and techniques. Although computers were widely used in this period as instruments of scientific production, their status as legitimate objects of scientific scrutiny had not yet been established. Computer programming in particular was considered by many to be a "black art, a private arcane matter." General programming principles were largely nonexistent "and the success of a program depended primarily on the programmer's private techniques and inventions." Those scientists and mathematicians who left "respectable" disciplines for the uncharted waters of computer science faced ridicule, self-doubt, and professional uncertainty. As the commercial computer industry expanded at the end of the decade, however, corporate interest in the science of computing increased significantly. Faced with a serious shortage of experienced, capable software developers, corporate employers turned to the universities as a source of qualified programmers. Academic researchers, unsure of
what skills and knowledge were associated with computing expertise, began to develop a detailed psychological profile of the "ideal" computer scientist. Their profile included not only an aptitude for chess, music, and mathematics, but also specific personality characteristics ("uninterested in people," "highly detail oriented," etc.). Many of these early empirical studies turned out to be of questionable validity and were of almost no use to potential employers; nevertheless, many of the characteristics identified in
these early personality profiles survived in the cultural lore of the industry and are still believed to be indicators of computer science
ability. My paper explores the development of computer science as an academic discipline from the perspective of the corporate employers who encouraged it as a means of producing capable programming personnel. I explore the uneasy symbiotic relationship that existed between academic researchers and their more industrial-oriented colleagues. I focus on the use of psychological profiles and aptitudes as a means of identifying "scientific" and mathematical abilities and expertise.
April 21, 2005.
David L. Roberts, Prince George's Community College.
"Mathematicians in the Schools: The 'New Math' as an Arena of Professional Struggle, 1950-1970"
What is sometimes casually described as the "mathematics community" in the United States already by the late 19th century was displaying divisions, which became more distinct and variegated through the course of the 20th century. The aim of this talk is to use the arena of mathematics education during the 1950s and 1960s, which encompassed most of the so-called "new math" educational reforms, to illuminate fine distinctions between and within professional groups involved with mathematics, notably the American Mathematics Society, the Mathematical Association of America, and the National Council of Teachers of Mathematics. Simple dichotomies such as researchers versus teachers, pure mathematicians versus applied mathematicians, mathematicians versus mathematics educators, or progressive versus traditional educators offer only limited utility in understanding the complex jurisdictional struggle that in fact occurred. By close analysis of the career trajectories of several representative figures from the period, a more nuanced categorization will be proposed, yielding a better understanding of the outcome of the reforms. Special attention will be given to individuals associated with two of the most prominent curriculum reform projects: the University of Illinois Committee on School Mathematics (UICSM), and the School Mathematics Study Group (SMSG), originally headquartered at Yale and later at Stanford.

2005-2006

September 15, 2005.
Ed Sandifer. Western Connecticut State University.
"A Series of Extraordinary Events: How Some Lesser Euler Fits Together."
Leonhard Euler (1707-1783) published more than 800 books and articles, many of which are among the most important mathematics ever discovered. Over 80 of his papers are about series, and two of his books deal primarily with series. Some of his results appear in "blockbuster" papers that make a huge contribution in just a single paper. Examples include the Basel Problem paper in which he evaluates zeta(2), Philip Naudé's problem in which he solves many problems of partition numbers, his paper on the Sum-Product formula for the zeta function and his paper on the foundations of continued fractions. There are other ideas, though, where the results are spread out over several papers, like the Euler-Mascheroni constant and Euler-Maclaurin series, were developed over several papers and several years. We will follow some of these lesser threads and trace a few of these longer stories, and connect them to the mathematical and scientific life in the 18th century.
October 13 – 15, 2005.
THE MIDDLE ATLANTIC SYMPOSIUM ON THE HISTORY OF MATHEMATICS.
An intensive study of Euler's “Introductio in Analysin Infinitorum, Book 1” by participants who have read the “Introductio,” either in Latin or in its English translation Introduction to Analysis of the Infinite, Book 1, Springer, 1988 and prepared a short paper for presentation and discussion.
November 17, 2005.
Prof.Dr.Reinhard Siegmund-Schultze
Agder University College
Realfag, Serviceboks 422
4604 Kristiansand S
Norway
"Richard von Mises - a non-conformist between mathematics, engineering, philosophy and politics"
The main focus of the talk is von Mises’s “outsider-position” or “non-conformism” in scientific, philosophical, and - to a lesser degree - political respects and the implications for the reception of his theory of probability, the one achievement he is still most known for today. Not unexpectedly, a considerable part of von Mises’ “non-conformism” was related to his “betweenness” with respect to mathematics and its applications, which can be related to his education as an engineer and mathematician and to his practical work.
Von Mises gave in 1919 a definition for the then rather new discipline “theory of probability” and tried to relate and connect it to existing “pure mathematics” on the one hand and to applications in statistics and physics on the other. This attempt was, indeed, very influential, if perhaps even more in a “critical” than in a constructive meaning, “critical” including both von Mises’s criticism of existing notions and applications of probability and ensuing criticism of von Mises’s proposals by others such as A.N.Kolmogorov and A.Ya.Khinchin.
Literature: Siegmund-Schultze, R.: A non-conformist longing for unity in the fractures of modernity: towards a scientific biography of Richard von Mises (1883-1953); Science in Context 17 (2004), 333-370.
December 8, 2005.
Alan Gluchoff, Villanova University.
"The Contributions of Four 'Mathematical People' to the Mathematical Ballistics of the World War I Era in America."
By 1917 the American mathematical community was quite diverse and stratified, comprising, among others, word class researchers, university and college instructors, some applied mathematicians, and students with Masters and Bachelors degrees who found various uses for their talents. This work focus on four such "mathematical people," Gilbert Ames Bliss, Forest Ray Moulton, Roger Sherman Hoar, and Philip Schwartz, to the "New Ballistics" of the World War I era. Their efforts included a revision of the approach to calculating trajectories by the introduction of numerical integration, a tying of the new methods to the newly emerging research area of functional analysis, an organization of this mass of material into a coherent, presentable form with some physical motivation of required formulae, and a critical and experimental look at the resulting work. These efforts were characterized by an unusual emphasis on mathematical rigor which is in some ways analogous to the movement in sophistication from calculus to advanced calculus, but also included instructional activities geared to making the new methods accessible to its users.
January 19, 2006.
Chris Rorres, University of Pennsylvania
"If Archimedes Had a Computer: Continuing his Work on Floating Bodies"
According to legend, Archimedes ran naked through the streets of ancient Syracuse shouting ³Eureka!² after discovering his famous Law of Buoyancy‹the basic law that determines how things float. He illustrated this law in his work "On Floating Bodies" by computing various floating positions of a solid paraboloid. With the geometric tools of his day Archimedes could only consider those cases when the flat base of the paraboloid is not cut by the water. However, as I show using modern computing power, the most interesting things happen when the base is cut by the water. For example, an iceberg that is slowly melting can suddenly overturn, or an obelisk originally sitting on solid ground can come crashing down when the soil under it liquefies during an earthquake. Such drastic phenomena are now studied in Catastrophe Theory, a field that Archimedes could have begun if he had had the computational tools to investigate all the possible cases of his floating paraboloids.
February 16, 2006. Bill Ewald, University of Pennsylvania.
"Hilbert's Papers."
An informal presentation on the state of Hilbert's papers and progress on a forthcoming volume of Hilbert's papers and notebooks on logic in the 1920s.
March 16, 2006. David Zitarelli, Temple University.
"J. B. Reynolds and the research mission at Lehigh University"
Joseph B. Reynolds (1881-1975) was a student and professor at Lehigh University from 1903 to 1948. We examine his major accomplishments in terms of Lehigh's change to a research mission in the 1920s. Reynolds's exploits include contributions to engineering as well as pure and applied mathematics. He is also viewed as an amateur historian, departmental administrator at Lehigh, and founder of our local EPADEL section.
April 20, 2006. Peter Freyd, University of Pennsylvania. "Saunders Mac Lane, an oral history."
May 18, 2006. Shelley Costa, Independent scholar. "Making a name for oneself in professional mathematics: Women’s lives and “women’s work” in the 19th century."
The concept of the professional mathematician came relatively late to European history. (This truism is expressed in history of mathematics code as “Fermat was a lawyer.”) After the ingenious dabblers had had their due, an array of institutions, titles, degrees, prizes and professorships secured mathematics as a professional endeavor. Among its other consequences, the rise of professional mathematics created a new set of formal barriers to women. I will summarize the experiences of three who succeeded in the new atmosphere: Sophie Germain, Sofia Kovalevskaia, and Alicia Boole Stott. These 19th-century mathematicians came from different countries, were of three distinct generations and hailed from contrasting economic backgrounds. I am uniting them here not merely to pay homage to exceptional talent, luck, and resources, but to highlight commonalities in their experiences as women. I wish to pose an important and difficult question: What do these women’s experiences tell us about the construction of mathematical knowledge?

2006-2007

September 21, 2006. Alexander Soifer, Princeton University, Department of Mathematics, Rutgers University, Center for Discrete Mathematics (DIMACS), University of Colorado.
"In Search of Van der Waerden."
In 1926 Bartel L. van der Waerden proved, and in 1927 published, a magnificent theorem: For any k, l, there is such that the set of whole rational numbers 1, 2, ..., N, partitioned into k classes, contains an arithmetic progression of length l in one of the classes. This result, which I call (in honor of the authors of the conjecture and the author of the first proof) Baudet-Schur-Van der Waerden Theorem, belongs to a few revolutionary, classic results which form “Ramsey Theory before Ramsey”, and it has awakened my interest in the life of Van der Waerden. I found the literature about his life surprisingly contradictory. On the one hand, in the writings of Günther Frei, Yvonne Dold-Samplonius, W. Peremans, and most recently Rüdiger Thiele, I found the highest praise of Van der Waerden as a man of utmost integrity, a hero of the opposition to the Third Reich. On the other hand, Queen Wilhelmina of the Netherlands refused to sign off on Van der Waerden’s appointment to a chair at the University of Amsterdam in 1946, and Miles Reid in his 1988 book wrote that “a number of mathematicians of the immediate post-war period, including some of the leading algebraic geometers, considered him a Nazi collaborator.” As a trained problem-solver, I commenced the search for the real Van der Waerden. Now, 12+ years and many hundreds of documents later, I can grant my predecessors one thing: it is hard to understand B. L. van der Waerden. And while a complete insight is impossible, my research has produced, I believe for the first time, a comprehensive portrait of Van der Waerden the man. We will visit Van der Waerden during his early years, although my main interest will be the two turbulent decades of his life: 1931-1951.
October 12, 2006. Ed Sandifer, Western Connecticut State University.
"Some Number Theory that Gauss Learned from Euler."

November 16, 2006. Adrian Rice, Randolph-Macon College, 
"The Life and Legacy of Augustus De Morgan (1806-1871)"
De Morgan's Laws are familiar to any mathematician who has taken an undergraduate course in set theory.  
Yet it is ironic that the man after whom they were named is remembered almost exclusively for a set of rules 
he did not invent in a subject he would never have known.  But the mathematical legacy of Augustus De Morgan 
spreads far wider than his limited fame of today would suggest.  In the last few decades, historical research has shed 
light on forgotten aspects of De Morgan's work to give us a more complete picture of the range and diversity of
his mathematical activities.  To mark the 200th anniversary of De Morgan's birth, this talk will examine the influence of these
contributions and thus re-evaluate the impact of his work on the mathematical landscape of both his time and ours.

 December 14, 2006  Paul Wolfson, West Chester University. 
“Topology Visits Algebraic Invariant Theory”.  
Abstract: During the 1930’s and 40’s, several mathematicians—notably Stiefel, Whitney, Pontrjagin, and Chern—developed 
the basic ideas of  characteristic classes.  These cohomology classes of a bundle over a manifold measure how far that 
bundle is from being a product. The existence of non-zero classes proved the impossibility of certain embeddings of manifolds.  
While these results were being found, other results connected the characteristic classes to the curvature of the base manifold.  
Then, André Weil systematized that connection via classical invariant theory.  His unification led to new developments in topology 
and geometry.

January 18, 2007. Jeff Suzuki, Brooklyn College. 
"The Fundamental Theorem of Algebra, or Why Did Gauss Title His Dissertation A "New" Proof?"
 Abstract: Gauss is usually credited with being the first to prove the fundamental theorem of 
algebra, but his dissertation is actually titled a "new" proof of the fundamental theorem.  
We will examine a few pre-Gaussian proofs, and make an argument that Lagrange, not Gauss, was 
the first to make a truly rigorous proof of the Fundamental Theorem.

February 15, 2007. Lawrence D’Antonio, Ramapo College of New Jersey
"Euler’s Contributions to Diophantine Analysis"
Abstract: In 2007 we celebrate the 300th anniversary of Euler’s birth. Many aspects of Euler’s vast 
output will be examined during this year. In this talk we will focus on Euler’s research in the field 
of Diophantine problems. Such problems were a long-term interest of Euler and are still of interest 
today.
We will consider particular highlights from Euler’s work on Diophantine equations, such as Euler’s 
landmark text Vollständige Anleitung zur Algebra, his work on Fermat’s Last Theorem and the Euler 
conjecture. This conjecture is related to Fermat’s Last Theorem. Euler had proven the special case  
that the sum of two cubes is never a cube. He then conjectured that the sum of three fourth-powers 
is never a fourth-power, the sum of four fifth-powers never a fifth power and so on. 
Many of the problems considered by Euler fall under the heading of what are now called Euler sums. 
These are Diophantine equations equating sums of like powers. For example, in a paper from 1754 we 
see Euler discussing the problem of when the sum of three cubics will equal a cubic. We will examine 
the subsequent history of research on Euler sums.

March 15, 2007. Dave Richeson, Dickenson 
College.
"Euler's polyhedron formula: a prehistory of topology"
A polyhedron with V vertices, E edges, and F faces satisfies the relation V-E+F=2. 
This relationship was first noticed by Euler in 1750 (although a related formula was known to Descartes in 1630). 
Euler's proof turned out to be flawed. From 1750 to 1850 mathematicians tried to come to grips with this formula. 
Legendre, Cauchy, Staudt, and others presented new proofs and generalizations. Meahwhile, Lhuilier, Hessel, and 
Poinsot unveiled exotic "counterexamples." In this talk we present the history of this beloved formula up to the middle 
of the nineteenth century, while it was still a theorem about polyhedra and before it was recognized as a topological 
theorem.

April 19, 2007. D. Florence Fasanelli, AAAS.
"Portraits of Euler: the provenance of those made when Euler sat for artists and other images."
Abstract: Two portraits of Euler which were done from life still exist. The 1778 oils apparently utilized a technique which made it possible for a realistic image. These portraits will be compared with other images in sculpture, coin, oil and reproductive prints giving a broader understanding of the world in which Euler lived.

2007-2008

September 20, 2007. Thomas L. Bartlow, Villanova University, and David E. Zitarelli, Temple University.
"Who was Miss Mullikin?"
R. L. Moore's first two doctoral students at the University of Pennsylvania, J. R. Kline and G. H. Hallett, are fairly well known, but "Who was Miss Mullikin," his third student? Our paper provides an answer by discussing her mathematical research, her influence on later investigations in point set theory, her career, and her life outside mathematics.
October 18, 2007. Edward Hogan, East Stroudsburg University, "Benjamin Peirce as Head of the Coast Survey."
            Under Alexander Dallas Bache the United States Coast Survey grew into an important, perhaps the most important, institution for American science. With little graduate work available in the United States, it served as an essential training ground as well as a source of employment for American scientists. When Peirce took over the Coast Survey after Bache’s death, he had no administrative experience.
            Yet he was able to garner even better congressional support for the Survey than had the politically savvy Bache.
            Peirce continued to support a broad spectrum of scientific activity. He was also successful in expanding the Survey my making a geodetic link between the existing surveys on the east and west coasts. This was not only a political triumph, but a scientific one. It was the longest arc of a parallel ever surveyed by one country. The extended scope of the Survey led to it being renamed the United States Coast and Geodetic Survey.
            During his tenure as superintendent of the Coast Survey, Peirce maintained his professorship at Harvard and his residence in Cambridge. He also wrote his Linear Associate Algebra, his most important mathematical work, during this period.
November 15, 2007. Marina Vulis. "Life and Work of Luca Pacioli."
We will examine Luca Pacioli’s contributions to mathematics. The Italian mathematician
Luca Pacioli discussed mathematics with Leonardo Da Vinci, wrote books on arithmetic, and worked
on chess problems. His long-lost manuscript on chess was recently discovered in Italy. Pacioli’s
system of double-entry bookkeeping has a group structure and can be viewed as error-detecting code.
We will also discuss some of the controversy surrounding his work and publications.
January 17, 2008. Alan Gluchoff, Villanova University. "Philip Schwartz, Probable Error, and the Variability of the Ballistic Trajectory"
At the close of World War I those who studied ballistics began to turn their attention to the "second order effects" - how such factors as wind, density of air, and small changes in initial velocity affected the range of a projectile. Related to these questions is the matter of the dispersion of a series of shots fired under as nearly identical conditions as possible, and how one measures this dispersion. In the United States efforts were made to introduce standard tools of elementary probability: mean, standard deviation (actually "probable error") , and normal distribution of errors, into this milieu, with mixed results. The talk highlights the attempt of Philip Schwartz, a young artillery officer with some mathematical background and an associate of Oswald Veblen, to analyze these concepts as they were used in dealing with the data of artillery firing. Emphasis is given on how difficult men found it to understand, defend, and apply these concepts by viewing a controversy played out in the pages of the Coast Artillery Journal during the years 1924-1930. No knowledge other than that of elementary probability and the normal distribution is required.
February 21, 2008. Paul Pasles, Villanova University. "Benjamin Franklin's Numbers."
Abstract: Quantitative literacy is a necessity for good citizenship, so it is appropriate that the "first American" was numerate in the extreme. That's not to say that Ben Franklin ever proved a novel theorem, but he was willing to apply basic mathematics to situations where only qualitative arguments had been admitted previously. This talk will explore the various mathematical aspects of Franklin’s life.
March 13, 2008. Amy K. Ackerberg-Hastings, University of Maryland University College. " 'The Acknowledged National Standard': Charles Davies, A. S. Barnes, and Textbooks as Teaching Tools"
Book historians have added a number of dimensions to our understanding of texts in the history of science and mathematics, including how readers and publishers participate alongside authors in the transmission of knowledge, how patterns of use indicate intellectual reception, and how textbooks communicate scientific ideas to popular audiences. However, promotion has been at least as important a factor as pedagogical and intellectual superiority in determining which objects have become widely established instruments for teaching mathematics and science. This talk explores the evolution of the textbook into a commercialized teaching tool by concentrating on how the partnership of Charles Davies (1798-1876) and Alfred Smith Barnes (1817-1888) shaped mathematics instruction in the United States. Davies parlayed his reputation as a professor at the United States Military Academy at West Point into a successful career of defining himself primarily as a producer of textbooks. Barnes, his publisher, organized the books into graded series and utilized aggressive marketing techniques. Together, the men sought to enlarge their audience of American students and laid claim to national status as the standard for the nascent mathematics textbook industry. This talk is based upon the first chapter of Material to Learn: Tools of American Mathematics Teaching, 1800-2000, a forthcoming book prepared jointly with Peggy Aldrich Kidwell and David Lindsay Roberts, and will include a few highlights from the entire volume.
April 10, 2008. Babak Ashrafi, Executive Director, Philadelphia Area Center for History of Science.
"Using the Ether to Save Quantum Mechanics."
As Max Born fled Germany in 1933, he started a research project in which he used concepts and methods from ether theory to reformulate classical electrodynamics in order to produce a quantum electrodynamics. In this talk, I will describe the circumstances that led Born to leap backwards in order to try and leap forwards, what he and his collaborators achieved, and what this episode tells us about the history of the development of quantum mechanics.

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