History of Science, History of Mathematics

My research illuminates the interconnections between mathematics and its social and cultural setting by telling the history of the field from a novel perspective – that of popular stories told about mathematics and mathematicians. Such stories are cultural productions, shaped by the traditions of their time and place, but they also play a crucial role in shaping the actual practices of mathematics. As a result they serve as bridges, linking abstract mathematical techniques with broader historical circumstances.

My first book, Geometrical Landscapes (2002), demonstrates how early modern geometers came to view their field as a hazardous voyage of exploration on the seas of mathematics. This new vision of the field in turn made possible the emergence of the new infinitesimal mathematics, leading to the development of the calculus. My most recent book, Duel at Dawn: Heroes, Martyrs, and the Rise of Modern Mathematics (2010), focuses on the role of stories in the emergence of the modern practice of mathematics in the 19th century. It demonstrates how higher mathematics as it is practiced today is inseparable from the enduring figure of the mathematician as a tragic romantic hero.

I am currently working on a new book, provisionally entitled Infinitely Small, which examines the interconnections between mathematics and political and social order. Mathematics, at its most abstract, is the science of order, and it follows that different conceptions of mathematics have been associated with different views of proper social arrangements. In particular, the book will examine a sequence of historical instances in which mathematical infinitesimals acquired political significance, showing that even the purest mathematics can at times serve to buttress or undermine a political order.

Education

Stanford University
1996 Ph.D. in History of Science
1990 M.A. in History of Science

The Hebrew University in Jerusalem
1988 B.S. in Mathematics and History


Selected Professional Activities

Member of Advisory board of Isis, 2008-2010.

Course Co-Director of "Mathematics and Narrative" summer course, Central European University, Budapest, Hungary, July 2009.

Member of Advisory Board for Thales & Friends, an international organization for the cultural study of mathematics.

Co-organizer, International Conference on Narrative and Mathematics, Mykonos, Greece, 2005.

Member of Organizing Committee of Society for Literature and Science Annual Meeting, Pasadena, 2002.

Member of Organizing Committee of Humanities Consortium Conference, “The Two Cultures Reconsidered,” UCLA, 1998.

Books

Infinitely Small, (New York: Farrar, Strauss, and Giroux, 2012), forthcoming.

Duel at Dawn: Heroes, Martyrs, and the Rise of Modern Mathematics, (Cambridge MA: Harvard University Press, 2010).

Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical Practice (Stanford: Stanford University Press, 2002). Recipient of the Outstanding Academic Title Award for 2003 by Choice magazine.


Selected Publications

“The Skeleton in the Closet: Should Historians of Science Care about the History of Mathematics?” introduction to a focus section on the history of science and the history of mathematics, Isis, vol. 102, no. 3, September 2011.

“From Voyagers to Martyrs: Towards a Storied History of Mathematics,” in Apostolos Doxiadis and Barry Mazur eds., Circles Disturbed (Princeton: Princeton University Press, 2011), forthcoming.

"Introduction" to focus section on mathematical stories, Isis, vol. 97, no. 4, December 2006.

“Tragic Mathematics: Romantic Imagery and the Refounding of Mathematics,” Isis, vol. 97, no. 4, December 2006.

"Through the Mathematical Looking Glass," in Siegfried Zielinsky and David Link eds., Variantology 2: On Deep Time Relations of Arts, Sciences, and Technologies (Cologne: Walther König, 2006).

“Hariot and Dee on Geographical Exploration and Mathematics: Did Scientific Imagery Make for New Scientific Practice?” in Brett D. Steele and Tamera Dorland eds., The Heirs of Archimedes: Science and the Art of War Through the Age of Enlightenment, (Cambridge: MIT Press, 2005).

“Stories and Numbers: How a Romantic Tale of Geographical Exploration Transformed Mathematics,” Historically Speaking: The Bulletin of the Historical Society, January 2004.

“Mathematics,” in Jonathan Dewald ed., From Gutenberg to the Bastille: The Emergence of the Modern World, (New York: Scribner, 2003).

"Exploration Mathematics: The Rhetoric of Discovery and the Rise of Infinitesimal Methods," Configurations, vol. 9, no. 1, Winter 2001.

"The Scientific Revolution," in Arne Hessenbruch ed., A Reader's Guide to the History of Science, (Chicago: Fitzroy Dearborn Publishers, 2000).

"Lunar Maps and Coastal Outlines: Thomas Hariot's Mapping of the Moon," Studies in the History and Philosophy of Science, vol. 29, No. 3, September 1998.

"The Imperialist Space of Elizabethan Mathematics," Studies in the History and Philosophy of Science, vol. 26, No. 4, December 1995.

"Israeli Television and the Problem of the Modern Subject," Zeitschrift fur Literaturwissenschaft und Linguistik, vol. 98, June 1995.