October 20, 2011. Patricia Allaire, Queensborough Community College, City University of New York
Title: “Yours truly, D. F. Gregory”
Abstract: Duncan F. Gregory (1813-1844) was a proponent of the Calculus of Operations and a founding editor of the Cambridge Mathematical Journal. Extant is a series of six letters that Gregory wrote to a friend in 1839. This correspondence provides a glimpse into life at early-Victorian Cambridge, reveals something of the character of Gregory and his dedication to the CMJ, and shows some of the mathematical problems he pondered. In this talk, we will look briefly at Cambridge, Gregory and the CMJ, and will examine several of the problems.
November 17, 2011. Chris Rorres, University of Pennsylvania
Title: "The Turn of the Screw: The History and Optimal Design of an Archimedes Screw"
Abstract: The Archimedes Screw is one of the oldest machines still in use today. It is now enjoying renewed popularity because of its proven trouble-free design, its ability to lift wastewater and debris-laden water effectively, and its gentle treatment of aquatic life. Within the last decade it has also found a new application in the generation of electricity by being run backwards. In this presentation I will give a history of this device from Archimedes' time (3rd century BC) to the present day and also discuss my past and proposed research on the design of the Screw that maximizes the amount of water lifted or lowered in each turn of the screw.
December 8, 2011. Brittany Shields, University of Pennsylvania
Title: “The Architecture of Mathematical Institutes: A Comparative Study of Göttingen and NYU’s Mathematical Institutes under the Leadership of Richard Courant”
Abstract: In this study of the cultural history of mathematics, I consider the architecture of mathematical institutes as historical artifacts. The buildings in which mathematical research and teaching take place offer incredible insight into the work practices, as well as social and cultural identities, of the mathematicians who inhabit these spaces. As a case study, I consider the career of the mathematician Richard Courant (1888-1972), who served as director during the construction of two world-class mathematical institutes – the first, in the late 1920s at the University of Göttingen (where he was exiled in 1933), and then in the 1960s at New York University. In both cases, I consider the buildings’ planning, development, construction, and habitation processes, examining blueprints, committee meeting minutes, and correspondence between the mathematicians, university administrators, government officials and philanthropy representatives. Ultimately, I hope to explore how the built environment mattered to those whose work required a certain type of private workspace, desk, and chalkboard –situated in the right relationship to shared workspaces, a mathematics library, classrooms, and other scientific departments. What can the physical environment of mathematical institutes tell the historian about the work practices and social identities of mathematicians?
January 19, 2012. Thomas L. Bartlow, Villanova University
Title: “A Tentative Look at American Postulate Theory”
Abstract: American postulate theory is the body of work of several American mathematicians in the first few decades of the twentieth century, concerned with studying the structure of established mathematical theories by examining fundamental assumptions. They examined alternative postulational formulations and considered desirable features of a postulate system: consistency, independence, completeness, categoricity, brevity. John Corcoran, “On Definitional Equivalence and Related Topics,” History of Symbolic Logic 1 (1980), 231—234, introduced the term “American postulate theory,” identified some of its practitioners and suggested a need for historical study of their work. Michael Scanlan “Who Were the American Postulate Theorists?,” The Journal of Symbolic Logic 56 (1991), 981—1002 and “American Postulate Theorists and Alfred Tarski,” History and Philosophy of Logic 24 (2003), 307-325 identified others, compared two American postulate theorists to European contemporaries, and analyzed their influence on mathematical logicians. I will undertake a broader review, attempting at least partial answers to the following questions: Who contributed to American Postulate Theory? What were the characteristics of their research? Who or what influenced them? Were there mutual influences or rivalries among them? What influence did they have on other lines of mathematical research? Did a theory of postulation develop?
February 16, 2012. Marina Vulis, Fordham University
Title: "Tales of Nineteenth Century Russian Mathematics"
Abstract: The Moscow Mathematical Society, which grew out of a math circle, had its first meeting on September 27, 1864. It was founded with the purpose of promoting mathematical sciences in Russia. In a few years, it started the publication of the "Mathematichekij Sbornik, " the first Russian Mathematics Journal. The Moscow Society reflected the philosophy of the Moscow School of Mathematics which rejected the importance of applied mathematics and emphasized mysticism and spirituality, whereas the St. Petersburg School of Mathematics, influenced by the French school, saw the importance of practical applications in development of mathematical ideas.
Friday, February 17, 2012. Dr. Jesse Frey, Villanova University
Title: "Data-Driven Nonparametric Prediction Intervals"
Abstract: Prediction involves using one sample to make inference on some aspect of a future sample. In this talk, I’ll consider the problem of using a simple random sample of size n to create a prediction interval for an independent future observation from the same distribution. Prediction intervals may be parametric or nonparametric, but I’ll focus on nonparametric intervals. I’ll describe the standard nonparametric prediction intervals, and I’ll also describe new data-driven prediction intervals that outperform the standard intervals. Specifically, the new intervals are much shorter than the standard intervals when the distribution is skewed, and they are only slightly longer than the standard intervals when the distribution is symmetric. Coverage probabilities for the new intervals are determined by using a combination of new theoretical results, Monte Carlo simulations, and known results about Brownian motion and Brownian bridges. All needed background material will be provided.
Friday, March 16, 2012. Dr. Martha Yip, University of Pennsylvania
Title: "Counting Upper-Triangular Nilpotent Matrices of a Given Jordan Type"
Abstract: The Jordan forms of upper triangular nilpotent matrices are indexed by paritions. Over a finite field of q elements, the number of matrices with Jordan form corresponding to a given parition is a polynomial in q. In this talk, I will explain how these polynomials can be calculated recursively. These polynomials are connected to certain q-rook polynomials, and I will show how the recursive formula gives a refinement of q-rook polynomials.
March 22, 2012. Robert E. Bradley, Adelphi University
Title: “The Origins and Contents of de l’Hôpital’s Analyse”
Abstract: Guillaume François Antoine de l’Hôpital’s Analyse des infiniment petits (1696) was the first ever calculus textbook. It was also something of an enigma. For one thing, it was published anonymously, although de L’Hôpital’s authorship was no secret. Also, it made no mention of the integral calculus: instead, its introduction to the differential calculus was followed by what can only be described as an advanced text on differential geometry, motivated by what were then cutting-edge problems in mechanics and optics.
However, the oddest aspect of this book is its genesis. The introductory chapters were based on Johann Bernoulli’s Lectiones de calculo differentialium, lessons that only ever existed in manuscript form and were unknown to the scholarly community until 1921. De l’Hôpital received his copy when he hired Bernoulli to tutor him in 1691-92. Subsequently, he “purchased” the advanced material of the later chapters, in an arrangement under which he supported Bernoulli with a stipend in 1694-95.
In this talk, we will consider both the mathematics that was presented in the Analyse and the process by which in came into being. We will compare de l’Hôpital’s exposition of the elements of the differential calculus with that of Bernoulli and examine some of the more advanced results presented in the Analyse.
April 13, 2012. Dr. Mohammed Yahdi, Ursinus College
Title: “Mathematical modeling, transmission dynamics and control of antibiotic-resistant infections”
Abstract: The emergence and spread of antibiotic-resistant bacteria is considered to be one of the biggest threats to human health in the 21st century. In the last decade, mathematical models have been increasingly used as tools to identify factors responsible for observed patterns of antimicrobial resistance, to predict the effect of various factors on the prevalence of antimicrobial resistance, and to help design effective control and intervention programs. This talk focuses on the emergence of Vancomycin-Resistant Enterococci (VRE) infections that have been linked to increased mortality and costs in intensive care units (ICU). A new mathematical model is introduced, key factors are determined and simulations are produced. Optimal Control Theory is used to determine efficient and economically favorable strategies to prevent outbreaks and to control the emergence of VRE. Key controls included combinations of the levels of special preventive care, healthcare workers' complicance rates, and health and economical costs.
April 19, 2012. Francine F. Abeles, Kean University
Title: "Hypotheticals, Conditionals, and Implication in Nineteenth Century Britain"
Abstract. Modern logicians ordinarily do not distinguish between the terms hypothetical and conditional. Yet in the late nineteenth century their meanings were quite different.and their tie to implication unclear. In this paper, I will explore the views of four prominent British logicians of the period, W. E. Johnson, J.N. Keynes, H. MacColl, and J. Venn on these issues.
May 1, 2012. John Hessler; Library of Congress, Geography and Map division
Title: "Complexity and Chaos in Medieval Cartography"
Abstract: The source of the peculiar accuracy of certain medieval maps known as Portolan charts has been a mystery that has stumped scholars for hundreds of years. In this presentation I will describe the surprising accuracy of these maps, produced from 1250-1550, using mathematical models based on stochastic processes, like Brownian bridges, and transformational geometry. I will also show how the geometry of these charts develops out of the non-systematic nature of early navigational measurements and the chaotic shifting of the secular part of the earth's geomagnetic field, hints of which are encoded in the data used to make the charts themselves.
- October 15, 2009. Frank Swetz. "Glimpses of Chinese Mathematics."
Abstract: The history of mathematics in traditional China is often clouded by myth and uncertainty. For the Chinese Empire, mathematics was not a priority. Mathematicians were not highly honored nor recognized for their work. They worked in isolation. Social and political upheavals within the Kingdom were frequent, resulting in the destruction of books and libraries. In such a climate of turmoil, efforts at preservation focused on Confucian and philosophical classics. Scientific works, including those about mathematics were frequently destroyed and lost. Later mathematicians were forced to rediscover techniques and concepts established by their predecessors. Thus, in examining the state and content of traditional mathematics in China, one must rely on "glimpses. " This talk will survey some of the accomplishments of traditional Chinese mathematics and discuss the interaction of societal pressures on the development of mathematical thinking.
- October 8, 2009. Danny Otero, Xavier University. "Determining the determinant."
Abstract: Nearly every undergraduate student of mathematics learns how to solve linear systems with the help of determinants, so it may come as a surprise that the history of the development of the determinant is not better known than it is. In fact, there may be a good reason for this: befitting the complexity of the idea, its history is also quite complicated. The story of its genesis and evolution involves the interplay of a number of different problems, perspectives and approaches, and contributions were made by dozens of people over centuries. We plan to survey a key period of this history, for the time of Leibniz at the end of the 17th century, up to the watershed day of November 30, 1812, when Binet and Cauchy both presented papers on the determinant at the same meeting in Paris.
- September 17, 2009. Craig P. Bauer, York College. "Cryptology on campus during World War II."
Abstract: Over 30 colleges and universities offered cryptology courses during World War II. There was great diversity in who delivered the classes. Mathematicians were represented, as were the departments of astronomy, biology, classics, English, geology, Greek, philosophy, and psychology. Even a dean managed to make himself useful... Some classes were secret, run for the benefit of the military, while others were open to all. The lecture surveys these courses, along with biosketches of the professors and, in some cases, describes original research contributions they made to the field of cryptology.
- November 19, 2009. Shelly Costa, Independent Scholar. "Throwing the book at mathematical talent."
Abstract: In this talk, I will contrast the careers of the late seventeenth-/mid-eighteenth-century mathematical authors Guillaume de I'Hôpital (1661-1704), Emilie du Châtelet (1706-1749), and Maria Gaetana Agnesi (1718-1799). My basic aim is to assess the impact of social factors such as class, gender, and economic status on contemporary perceptions of mathematical talent and originality. I will recount my recent attempts to do so through a material approach--that is, through a close inspection of the physical features of relevant primary sources.
- December 10, 2009. John W. Dawson. "The development of the notion of compactness in topology and logic."
Abstract: During the early decades of the twentieth century the notion of a compact topological space arose as a generalization of results obtained in studies of the topology of the real line (in particular, the Heine-Borel theorem). Somewhat later, what is now called the compactness Theorem for first-order logic was proved by Godel as a lemma in his proof that every first-order axiom system is semantically complete. But for years thereafter connections between the two notions of compactness lay unrecognized and applications of compactness in logical contexts were not pursued. This talk will survey how the Compactness Theorem eventually came to be regarded as a fundamental tool in model theory and algebra, and will explore why recognition of it's usefulness was so long delayed.
- January 21, 2010. Bud Bowman. "Ghosts of Departed Errors: A look at Bishop Berkeley's The Analyst and the scientific community's initial response to it."
Abstract: In 1734 Bishop Berkeley criticized the logical foundations of the Calculus in The Analyst and set off a small 'pamphlet war.' Jame Jurin and John Walton replied immediately and angrily. Berkeley then responded to each of them. Shortly after this exchange Jurin and Benjamin Robins engaged in a lengthy and eventually acrimonious public debate on the same topic. Somewhat later Benjamin Robins, Collin Maclaurin, Thomas Simpson and others wrote treatises on The Method of Fluxions which were at least in part intended as responses to The Analyst. These exchanges offer a window onto the scientific community's view of Calculus in its earliest stages. I will attempt to peer through that window.
- February 18, 2010. Steven H. Weintraub. "On Legendre's Work on the Law of Quadratic Reciprocity."
Abstract: As is well-known, Legendre was the first to state the Law of Quadratic Reciprocity in the form that we now know it (though an equivalent result had earlier been conjectured by Euler), and he was able to prove it in some but not all cases, with the first complete proof being given by Gauss. In this talk we trace the evolution of Legendre's work on quadratic reciprocity in his four great works on on number theory, from 1785, 1797, 1808, and 1830.
- March 18, 2010. Eisso Atzema. "Beyond the Compass: On the Mechanical Construction of the Conic Sections."
Abstract: As is well known, there was little concern in Apollonius' Conics about the actual "mechanical" construction of the conic sections. In fact, it is not entirely clear whether there ever was an interest in Classical Antiquity in any tool that would draw a given conic section in the same way one can draw a circle with the help of a compass. There certainly was an interest in such a tool among Muslim mathematicians. In Renaissance Europe, a number of mathematicians suggested various mechanical ways to construct the conic sections as well-although no actual drawing devices seem to have been built. In this talk I will outline the most important proposals for the mechanical construction of the conic sections and sketch their historical context. I will discuss one particular construction in more detail and pursue it history from the early 17th century to the mid-20th century.
- April 15. 2010. Alan Gluchoff. "The Introduction and Spread of Nomography in American, 1900-1950."
Abstract: Nomography can be roughly defined as the theory and methods by which numerical evaluation of ordinary functional relations can be accomplished geometrically. (The slide rule is a simple example of one such method.) It was established as a mathematical discipline in 1899 by Maurice d'Ocagne (1862-1938), an accomplished French engineer who synthesized earlier work on this subject. His 1899 volume "Traite de Nomographie" is a systematic development of the construction and use of what came to be called nomograms (variously called charts, alignment diagrams, intersection diagrams, or abaques) for use in computations in diverse engineering disciplines. While the use of nomograms to aid in calculation became widespread in Europe in the following years, the mathematics associated with their construction received attention as well. This resulted in articles in mathematical journals and a mention of the field by Hilbert in connection with problem 13 of his list of 23 problems of 1900. Nomograms have been described by one writer as the "fractals of their day" due to their relation to mathematical law and visual appeal.
This talk attempts to survey how nomography was introduced into the United States in the years following the publication of d'Ocagne's book, looking at its debut in the various communities of mechanical, civil, and electrical engineers, scientists, and mathematicians, with special focus on the latter. During the period from 1900 to 1950 mathematicians such as Frank Morley, E. H. Moore, T. H. Gronwall, O. D. Kellogg, Lester Ford and Edward Kasner concerned themselves with popularizing, extending, and using the ideas of nomography. The subject was taught in colleges and technical institutes, often out of textbooks written by the instructors. It appealed to all types of mathematical people: pure researchers, college professors and high school teachers, and had its enthusiasts among algebraists, geometers and analysts. Nomograms became particularly popular as a graphical method for solving polynomial equations of degree five or less, and found a place in the changing nature of college algebra during this time. We also will mention some mathematical obstacles which occurred as they came into wider use in scientific, engineering and industrial settings.
- September 18, 2008. Patricia Kenschaft, Montclair State University, "Minority Mathematicians", Abstract: A summary of some of the known facts about minority participation in the mathematical community, including some biographies, some statistical information, and a report of a survey of black mathematicians of New Jersey twenty years ago.
- October 16, 2008. Steven Weintraub, Lehigh University.
"Cayley Documents in Lehigh's Possession."
Abstract: The Lehigh University Library has acquired a set of letters and an unpublished manuscript by Arthur Cayley. I will report on this collection and its background, both mathematical and historical.
- November 20, 2008. George M. Rosenstein, Emeritus Professor of Mathematics, Franklin & Marshall College.
"How Did Gibbs Discover the Gibbs Phenomena? A Speculation."
Abstract: Although it is very easy with computers to demonstrate the Gibb's Phenomena to today's students of Fourier Series, it was not a simple matter in 1899. I will trace the interesting history leading up to Gibb's announcement, and then speculate on his discovery.
- December 11, 2008. Thomas L. Bartlow, Villanova University.
"Edward V. Huntington and Engineering Education."
Abstract: Edward V. Huntington is best known as a prototypical American postulate theorist (Michael Scanlan, Who were the American Postulate Theorists?,
The Journal of Symbolic Logic 56:3 (Sep 1991), 981--1002) and as the mathematician behind the method of apportioning Representatives among the states
(Thomas L. Bartlow, Mathematics and Politics: Edward V. Huntington and the Apportionment of the United States Congress, Proceedings of the Canadian Society
for History and Philosophy of Mathematics 19 (2006), 29--54). However, much of his teaching was in the Lawrence Scientific School at Harvard and, in 1907, he
became chairman of the Committee on the Teaching of Mathematics to Students of Engineering, a joint committee of the AMS and the AAAS. This led him to become
involved in the Society for the Promotion of Engineering Education and to write several papers on mathematics and mechanics in the training of engineers.
- January 15, 2009. Yibao Xu, Borough of Manhattan Community College, City University of New York "Mathematicians and Mathematics in China during the Cultural Revolution."
Abstract: The Cultural Revolution (1966-1976) was the most destructive political movement in modern China. During that tumultuous ten-year period millions died as a direct consequence of political struggles and tens of millions were dislocated. Higher education was abandoned for the first five years. Leading experts in virtually all academic areas were deprived their rights of conducting research of their own interest. The promise of mathematical research during the first fifteen years of the newly created Communist China came to a halt, and then faded away. After briefly describing the status of mathematical research in Communist China before 1966, the speaker will provide a setting for the Cultural Revolution by showing a 10-minute documentary film. He will then take two leading Chinese mathematicians, Wu Wenjun, better known in the West as Wen- tsun Wu, and Gong Sheng, as examples, to discuss how the Cultural Revolution affected mathematicians’ personal lives and research. In order to show how politics and Marxist ideology determined mathematical research in mainland China during this period, the talk will also discuss Chinese translations of Karl Marx’s Mathematical Manuscripts and the nation-wide discussion of the Manuscripts.
- February 19, 2009. Paul Wolfson, West Chester University. "After Galois, What?"
Abstract. Many accounts of the nineteenth century theory of equations emphasize the contributions of Abel and Galois and the resulting shift towards abstract algebra. Nevertheless, some followed other lines of research. Mathematicians had originally introduced a resolvent equation as a step towards solving a given equation by radicals. After Galois' theory became known, mathematicians still studied resolvent equations, but now with new aims. This talk is the outgrowth of my attempt understand the background to one of the late manuscripts of Arthur Cayley that were previously discussed by Dr. Weintraub.
- March 19, 2009. Marina Vulis, Independent Scholar. "Russian Mathematics Textbooks."
Abstract: In 1703, Leonty Magnitsky, a mathematics teacher at a Moscow school, published the book "Arithmetika, i.e. the Science of Numbers". This was the first Russian mathematics textbook written by a Russian author. This presentation will discuss the contents of "Arifmetika" and the story of its publication.
- April 16, 2009. John Bukowski, Juniata College, "Christiaan Huygens and the Hanging Chain."
Abstract: In the mid-seventeenth century, it was generally thought that the shape of a hanging chain was a parabola. In a series of letters with Marin Mersenne, the 17-year-old Christiaan Huygens showed that the hanging chain did not in fact take the form of a parabola. We will investigate some of Huygens's geometrical arguments in detail, and we will discuss some of the general history of the problem.
- 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.
- 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.
- 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.
Agder University College
Realfag, Serviceboks 422
4604 Kristiansand S
"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.
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?
- 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.
- 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
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.
'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.
- 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"
- 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”
- 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.
- 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"