Mathematics, Beauty and Art
Paul Ernest, Education, Exeter University, UK
What is beauty in mathematics? What dimensions of mathematical beauty can be distinguished? Provisional answers to these questions are given, and mathematical beauty is illustrated by means of an example from visual art. Since beauty is shared by both mathematics and art, what parallels, including similarities and differences, can be drawn between mathematics and art?
Mathematical Modelling – Hiding or Guiding?
Jens Højgaard Jensen, IMFUFA, Department of Sciences, Roskilde University
The increasing scientific management of technology and society, supported by increasingly powerful information technologies (ICT), has lead, and leads to increasingly widespread use of mathematical models. This development gives rise to a democratic problem: How can ordinary people judge the conclusions delivered by mathematical models? Are the conclusions to be believed, since “mathematics does not lie”? Or is it better to go with: “There are lies, damned lies, and statistics”? In the talk I will illustrate a crude distinction between mathematical models derived from theories, and ad-hoc mathematical models without references to more global theories. The distinction cannot be used to evaluate whether specific models are “hiding” or “guiding”: theory-derived models may be too idealized to be trusted; and ad-hoc models may be trustworthy due to their richness of input data. The value of the distinction, however, is that it makes clear that some mathematical models, the theory-derived models, besides the possibility of evaluating them by comparing with empirical data, may also be evaluated by theoretical considerations. Evaluating ad-models are, in contrast, restricted to being done by empirical control only. Thus, the distinction between theory-derived models and ad-hoc models may help ordinary people, not to distinguish between trustworthy and non- trustworthy models, but to distinguish between the different qualities of the evaluation processes behind different sorts of models.
Making Decisions in a Complex World: Teaching How to Navigate Using Mathematics
Annie Savard, Faculty of Education at McGill University, Canada
We are living in a very complex world and the complexity is increasing by the knowledge needed to make relevant decisions for ourselves, and similarly for our communities. Community, crisis, economy, identity, health, sustainability and technology are some of the prominent facets of this complexity that make the world we used to know a different place to be in today. The world is changing so fast, without strong knowledge and skills, it is hard to navigate it. How can we support our students to make relevant decisions for themselves and their communities? How can we teach them knowledge and skills when the jobs they will have don’t exist yet? This plenary session will present how critical thinking using mathematics might support the decision making process from an ethnomathematical perspective.