Introduction For this session, I have been thinking of which discipline I should focus my speech. Is it Algebra? Calculus? Or Geometry? Eventually, I decided to talk about the status of geometry today. Specifically, and for many reasons, geometry is alive, well and sound, it has not died. For, it is essential to many other huma n activities and is so deeply embodied in how people think. I am
... [Show full abstract] inspired by my colleague, Walter Whiteley of York University, Toronto, Canada, who gave an independent, but related, description of the decline and rise of geometry through the 20th century [1]. The availability of computers with dynamic graphic capacities and the realization of a variety of ways of learning, our current state of affairs in the field of geometry offers an unprecedented opportunity for geometers and others whose interest is visualization and informal reasoning. I. The Fall of Geometry: Why and How As the mathematics community knows that a field of mathematics 'dies' when it is no longer considered as an 'important' area of mathematical research. Geometry 'died'' in this sense by the mid 20th century in North America and the rest of the world. Over the last few decades, the path of this fall proceeded from the graduate schools to the elementary classrooms passing through the high and middle schools [1 p. 7]. In sum, the decline proceeded from left to right passing through the center! Knowing this path may help us plan strategies for speeding up and accelerating the rise of geometry. "We do not have a half-century to spare for a comparable, gradual 'rise' of geometry". In a mini history over the 19th and 20th centuries, Philip Davis gave an account on the fall and rise of geometry focusing on a specific field of discrete geometry known as 'triangle geometry' [2]. In this regard, Eric T. Bell states that "The geometers of the 20th century have long since piously removed all these treasures to museum of geometry where the dust of history quickly dimmed their luster" [3, p. 323]. Walter Whiteley states that: "Discrete geometry virtually died as an 'important' field of mathematical research through the twenties and the thirties and the forties, at least in North America and parts of Europe. It survived in pockets (Hungary, Germany, Switzerland, Austria, Russia ...) and through a few key people in other places (H.S.M. Coxester, D. Pedoe, B. Grunbaum). In the Canadian context, this death was confirmed as Professor Coxeter retired at the University of Toronto several decades ago. The department followed a policy of not hiring in discrete geometry and shifted to the 'hotter' areas such as algebraic geometry" [1, p. 8]. This state of affairs in discrete geometry shows how the situation has been deteriorated. It marked the turning point toward a chain of events that explains how the decline was transmitted down from 'research activities' to the rest aspects of mathematics education. It reminisces the 'domino effect' sequence of events. In particular, as research in geometry declined, the importance of teaching geometry in graduate programs declined, and so the number of faculty proposing courses in geometry declined. As a result, teaching geometry in pre-service teacher education programs declined. After a few decades, there were new graduates moving out to teach undergraduate mathematics who possessed no experience in discrete geometry as an important and vital field of mathematics and who may not studied any geoemetry course. Over a span of a few more decades, the decline of teaching geometry at undergraduate level resulted in having a generation of school teachers who hardly have any geometry within their undergraduate program. Thus, we have teachers in the classrooms who, more likely, will implement their curriculum leaving geometry to the end of the year, a situation often ended into no time left for geometry. Such understanding that geometry is something extra or optional continues to spread wider and wider among curriculum designers, writers, teachers, and the parents.