The University of Montana
Department of Mathematical Sciences

Technical report #3/2012

The didactical nature of some lesser known historical examples in mathematics

Kajsa Bråting
Uppsala University, Sweden

Nicholas Kallem
The University of Montana

Bharath Sriraman
The University of Montana

Abstract

In the field of history of mathematics the work of famous mathematicians, such as Cauchy, Newton and Leibniz, have been carefully studied which certainly have provided valuable knowledge regarding the development of mathematics. The results are well documented in the literature. However, it may also be important to take into account the efforts of the less known (or sometimes unknown) mathematicians, contemporary to the famous mathematicians. For instance, by studying the work of the less known mathematicians we get more information of the struggle behind famous mathematical results, which often include valuable didactical knowledge. Moreover, the general view of certain mathematical concepts at particular time periods can be better understood on the basis of not only the work of the leading mathematicians, but also on the basis of contemporary mathematicians working in the shadow of the famous mathematicians. Furthermore, in the work of the less known mathematicians, one can sometimes find alternative solutions to a difficult mathematical problem, even before it was posed as a problem. However, these alternative solutions may not be as straightforward as the solutions documented in the modern textbooks. But they can provide valuable knowledge regarding mathematical thinking as well as the development in mathematics. In this paper we try to highlight the didactical nature of some historical mathematical examples. We use examples from some less-known mathematicians in order to show how didactics of mathematics is naturally interweaved in the methods devised in the history of mathematics to solve difficult problems.

Keywords: Didactics of mathematics; Björling; Hobbes and Wallis; History of Calculus; Basel problem; Indian mathematics; Islamic mathematics

AMS Subject Classification: 01, 97

Full Preprint unavailable due to publisher embargo. Excerpt from chapter to appear in: B. Sriraman (Ed). (2012) Crossroads in the History of Mathematics and Mathematics Education. Information Age Publishing, Charlotte, NC. Pdf (463 KB)