Schedule of Talks for the 2018-2019 Academic Year

Date:	Wednesday, October 3, 2018
Speaker:	Prof. Joseph Dauben Department of History Lehman College/Graduate Center - CUNY Email: jdauben AT lehman DOT cuny DOT edu
Title:	The Jesuits' Failure to Transmit Western Mathematics, Astronomy, and Mathematical Perspective to China: Reflections on Matteo Ricci, Giuseppe Castiglione, Andreas Pozzo, and the Needham Question
Abstract:	In 1607 the Jesuit missionary Matteo Ricci (1552-1610), in collaboration with his colleague Xu Guangqi (1562f1633), translated the first six books of Euclid's Elements of Geometry into Chinese. Among those to take a serious interest in this work was the prominent mathematician Mei Wending (1632-1721), but his Jihe tongjie (General Explanation of (Euclid's) Geometry) eliminated most of the demonstrations and redrew many of the original diagrams. Most Chinese mathematicians at the time found the Chinese version of Euclid's Elements too difficult to understand, or too foreign to their interests as mathematicians to take this work seriously as a standard for their own work. Similarly, although the Jesuits' success at predicting astronomical phenomena was highly valued, and they became central figures in Chinese calendar reforms early in the Qing dynasty, they never succeeded in convincing the Chinese to adopt western models of the heavens. Likewise, when the Jesuit artist Giuseppe Castiglione (1688-1766) collaborated with Nian Yixiao (1671-1738), a high-ranking official of the Yongzheng reign, to produce a Chinese versions of Andrea Pozzo's Perspectiva Pictorum et Architectorum (1693-1698), Chinese artists found no reason to adopt the new realism that mathematical perspective made possible, despite its having revolutionized western art shortly after its discovery by Brunelleschi in the early Quattrocento. Despite the fascination of the Yongzheng emperor (r. 1723-1735) in the trompe l'oeil effects of illusionistic perspective paintings, this never became an interest of Chinese artists themselves. His successor, the Qianlong emperor (r. 1736-1795), commissioned many works that exploited western mathematical perspective, but imperial patronage did not result in popular success for the genre, and today only a handful of these Chinese perspective paintings, rarely seen, survive. Why were the basic elements of western mathematics, so essential for the Scientific Revolution, as well as the discovery of mathematical perspective that revolutionized western artistic vision (as exemplified by Pozzo's magnificent illusionistic frescoes in the Jesuit Church of St. Ignazio in Rome, for example, and imitated by Giovanni Gherardini for the Beitang or North Church of the French Jesuits in Beijing), not similarly appreciated by Chinese intellectuals and artists? Are the examples of the limited reception of Euclid's Elements by Chinese mathematicians and the general lack of interest in the principles of mathematical perspective in Chinese art in any way related? And does the answer to this question in turn shed any light on the Needham Question - the question Joseph Needham sought to answer through his monumental investigation of Science and Civilization in China - namely why was there never a Chinese scientific revolution?

Date:	Wednesday, November 7, 2018
Speaker:	Prof. Chris Rorres Department of Mathematics Drexel University Email: crorres AT comcast DOT net
Title:	The Count of the Cattle of the Sun: From Mesopotamia to Homer to Archimedes
Abstract:	One of the oldest and best known mathematical word problems is Archimedes' Cattle Problem, first presented by Archimedes as a challenge to his colleague Eratosthenes more than two thousand year ago. Its roots, however, can be traced back to Homer and eventually to Sumerian legends from some five thousand years ago. My talk will discuss how this problem influenced number theory and, in particular, the Pell Equation. Over the centuries the Pell Equation has engaged such mathematicians as Brahmagupta, Fermat, Pell, Euler, and Lagrange. From their analyses the number of Cattle of the Sun was finally computed (with the assistance of a computer) in 1965 and turned out to be an integer with 206,545 digits. I will also be presenting my own thoughts as to the authenticity of this problem and as to who may or may not have solved it.

Date:	Wednesday, March 6, 2019
Speaker:	Rob Bradley Department of Mathematics and Computer Science Adelphi University bradley AT adelphi DOT edu
Title:	Servois on Numerical Integration
Abstract:	In 1810s, the topic of numerical integration was hotly debated in the pages of the Annales de Gergonne. Christian Kramp (1760-1826) had published a paper in 1815 describing a novel method for estimating definite integrals, based on the Trapezoidal Rule and an ad hoc extrapolation technique. This sparked a debate among Kramp, the editor Joseph Gergonne (1771-1859) and Joseph Bérard (1763-1844?). François Joseph Servois (1767-1847) entered the fray in 1817 with his Mémoire sur les quadratures, in which he resolved most of the issues under dispute by the other authors. In this talk, we will examine the Kramp's first paper and Servois' memoir, which is at turns a showpiece of the calculus of operations, a feat of numerical prowess, and a collection of philosophical observations and opinions, including his forward-looking attitude towards the utility of divergent series.

Date:	Wednesday, April 3, 2019
Speaker:	Prof. Inna Tokar Department of Mathematics City College of NY, CUNY innatokar AT gmail DOT com
Title:	History of Mathematics Education for Gifted Students in the former Soviet Union
Abstract:	This presentation will examine programs for mathematically talented students in the former Soviet Union. Special emphases will be given to the boarding schools for gifted students at Moscow, Novosibirsk, St. Petersburg and Kiev Universities. The origins and history of education for gifted students in the former Soviet Union will be discussed. Specifically, the following questions will be considered: Role of Khrushchev's Polytechnic reform in the creation of special schools for mathematically gifted students. Why and how were these schools organized? What is the nature of and variations among special school curricula and student, faculty, and alumni bodies? To answer these questions, original literature from Russia and Ukraine was reviewed, including scientific publications, educational journals, government and university documents. Interviews were conducted with Soviet-born mathematicians and educators who created and taught at these schools.

Date:	Wednesday, May 1, 2019
Speaker:	Prof. Eisso Atzema Department of Mathematics University of Maine eisso DOT atzema AT maine DOT edu
Title:	Ferdinand Engel (1805-1866) and his Models of the Fresnel Wave Surface
Abstract:	Clearly, the turn of the 19th century was the golden age of the production of mathematical models and their use for educational purposes. The interest in mathematical models as a visualization aid, however, goes at least as far back as the first half of the 19th century. In this talk, I will discuss the early history of the visualization of mathematical surfaces and the manufacturing of physical models for such surfaces, culminating in a discussion of the work of Christian Gottlieb Ferdinand Engel (Magdeburg,1805-New York, 1866). In particular, I will discuss his prize-winning plaster models of the Fresnel Wave Surface still on display at the University of Mississippi. Along the way, I will talk about his work under Gustav Magnus at the University of Berlin and under Alexander Bache at the Coastal Survey in Washington DC.