Introduction to the Special Issue on the use of History of Mathematics to Enhance Undergraduate Mathematics Instruction

PRIMUS ◽  
2014 ◽  
Vol 24 (8) ◽  
pp. 663-668 ◽  
Author(s):  
Kathleen M. Clark ◽  
J. B. Thoo
2007 ◽  
Vol 12 (8) ◽  
pp. 422-428
Author(s):  
Syamala Chenulu

One goal of the NCTM's connections Standard is that mathematics instruction pre- K–12 should “enable all students to recognize and apply mathematics in contexts outside of mathematics” (NCTM 2000, p. 64). Art of all kinds provides opportunities to address this goal. Moreover, many mathematics educators, including myself, believe that it is important and beneficial to provide a multicultural perspective in our classrooms. “Knowledge of the ideas of others can enlarge our view of what is mathematical and, in particular, add a more humanistic and global perspective to the history of mathematics. This enlarged view, in which mathematical ideas are seen to play a vital role in diverse human endeavors, provides us with a richer and fuller picture of mathematics” (Ascher 2002, p. 200).


2015 ◽  
Vol 9 (1) ◽  
pp. 59-87 ◽  
Author(s):  
Martin Calamari

In recent years, the ideas of the mathematician Bernhard Riemann (1826–66) have come to the fore as one of Deleuze's principal sources of inspiration in regard to his engagements with mathematics, and the history of mathematics. Nevertheless, some relevant aspects and implications of Deleuze's philosophical reception and appropriation of Riemann's thought remain unexplored. In the first part of the paper I will begin by reconsidering the first explicit mention of Riemann in Deleuze's work, namely, in the second chapter of Bergsonism (1966). In this context, as I intend to show first, Deleuze's synthesis of some key features of the Riemannian theory of multiplicities (manifolds) is entirely dependent, both textually and conceptually, on his reading of another prominent figure in the history of mathematics: Hermann Weyl (1885–1955). This aspect has been largely underestimated, if not entirely neglected. However, as I attempt to bring out in the second part of the paper, reframing the understanding of Deleuze's philosophical engagement with Riemann's mathematics through the Riemann–Weyl conjunction can allow us to disclose some unexplored aspects of Deleuze's further elaboration of his theory of multiplicities (rhizomatic multiplicities, smooth spaces) and profound confrontation with contemporary science (fibre bundle topology and gauge field theory). This finally permits delineation of a correlation between Deleuze's plane of immanence and the contemporary physico-mathematical space of fundamental interactions.


2020 ◽  
Vol 50 (1-2) ◽  
pp. 58-66
Author(s):  
Giuliano Pancaldi

Here I survey a sample of the essays and reviews on the sciences of the long eighteenth century published in this journal since it was founded in 1969. The connecting thread is some historiographic reflections on the role that disciplines—in both the sciences we study and the fields we practice—have played in the development of the history of science over the past half century. I argue that, as far as disciplines are concerned, we now find ourselves a bit closer to a situation described in our studies of the long eighteenth century than we were fifty years ago. This should both favor our understanding of that period and, hopefully, make the historical studies that explore it more relevant to present-day developments and science policy. This essay is part of a special issue entitled “Looking Backward, Looking Forward: HSNS at 50,” edited by Erika Lorraine Milam.


Author(s):  
Jed Z. Buchwald ◽  
Mordechai Feingold

Isaac Newton’s Chronology of Ancient Kingdoms Amended, published in 1728, one year after the great man’s death, unleashed a storm of controversy. And for good reason. The book presents a drastically revised timeline for ancient civilizations, contracting Greek history by five hundred years and Egypt’s by a millennium. This book tells the story of how one of the most celebrated figures in the history of mathematics, optics, and mechanics came to apply his unique ways of thinking to problems of history, theology, and mythology, and of how his radical ideas produced an uproar that reverberated in Europe’s learned circles throughout the eighteenth century and beyond. The book reveals the manner in which Newton strove for nearly half a century to rectify universal history by reading ancient texts through the lens of astronomy, and to create a tight theoretical system for interpreting the evolution of civilization on the basis of population dynamics. It was during Newton’s earliest years at Cambridge that he developed the core of his singular method for generating and working with trustworthy knowledge, which he applied to his study of the past with the same rigor he brought to his work in physics and mathematics. Drawing extensively on Newton’s unpublished papers and a host of other primary sources, the book reconciles Isaac Newton the rational scientist with Newton the natural philosopher, alchemist, theologian, and chronologist of ancient history.


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