Seminar

The process of illustrating mathematics is in some ways the reverse of mathematical modelling. Instead of trying to make systems in mathematics that reflect the physical world, it tries to create images and objects in the world and that reflect mathematical structure. What does it mean to tie models as closely as possible to abstract ideas, and how can this help both study mathematical ideas and also find new applications for mathematics, especially in manufacturing?

The LEGO system offers possibilities far beyond its core identity as a children’s toy.  In particular it allows for near-instantaneous experimentation with mechanisms, while at the same time allowing for sophisticated and beautiful constructions that demonstrate physical and mathematical principles.  I will demonstrate this by presenting some old and new inventions and discoveries (as well as a few mysteries) involving linkages, unusual gearing, mechanical computation, recursion and more.  I will also discuss practicalities of getting started with the medium as well as some of its limitations.

LEGO® is a trademark of the LEGO Group of companies, which does not sponsor, authorize or endorse this content.

According to Poincaré, "geometry is the art of reasoning well from badly drawn figures" [1895].  In this talk I will give an informal discussion of some famous attempts to draw mathematical figures: some more, and some less, badly drawn.  I will finish by discussing some of my own work (with Henry Segerman) in this direction, attempting to use computer graphics, interactive web apps, and 3D printing to illustrate mathematics.

A recording of the talk is available here: https://www.youtube.com/watch?v=iaI6lsqL-_0.