What We Do

We teach maths, philosophy and related subjects in various contexts.

We believe anyone can benefit from an encounter with maths however traumatic their experience with it may have been in the past. We like to connect purely mathematical topics with historical, cultural and philosophical subjects that cast interesting light on them, and we believe mathematicians can learn as much from the arts and humanities as vice versa.

This summer we're offering an intensive, week-long geometry course to the general public through ArtsCom. The course has been developed in partnership with the BA Fine Art programme at Central Saint Martins and is aimed at introducing artists and other practitioners to Euclidean and non-Euclidean ideas through practical drawing and constructions. No previous experience or mathematical ability is required.

We've also developed two courses with City Lit as part of its summer programme: a day-long session on the maths of puzzles and games and an introduction to ideas in modern maths (offered in two formats).

Once a month we meet at the Costa Coffee on the corner of Ramillies Street and Great Marlborough Street for an evening of practical geometry. All are welcome.

Here are some examples (mostly made by other people) of the kind of material we cover in our courses. See the links above for course outlines.

Ruler-and-Compass Constructions

This is an ancient mixture of drawing, design and mathematical deduction; intellectually satisfying, mathematically deep and a practical skill as well. Even constructing objects as simple as regular polygons can get surprisingly complicated, as the video below shows. How many can you do yourself, and can you prove they really are regular, not just approximations? Some of these have surprising connections with other areas of maths; perhaps the most famous is the intimate link between the pentagon and the Golden Ratio.

Tiling Patterns, Arches and Other Elements of Design

Ruler-and-compass constructions have been used for centuries to produce some of the most recognisable elements of design from Gothic arches to Islamic tiling patterns. These offer applications of our skills but also objects for further investigation. Recent discoveries suggest they can be even more complex than had previously been imagined!

Perspective, Maps and Non-Euclidean Models

There are close connections between the geometry of perspective drawing, cartographic projections of maps and "models" of exotic non-Euclidean geometries.

Symmetry

We learned about "symmetry" as small children, but it's an idea that can be generalised by abstract objects called "groups". The theory of groups is deep and rich, and symmetries -- some more geometrical than others -- now play a central role in most fields of maths and many applied areas as well. Although usually only taught at undergraduate level and above, group theory requires no essential prior knowledge and can be learned by anyone.

Topology

Topology studies the qualitative properties of a shape or space without worrying about lengths, angles, areas, volumes or similar things. It leads very naturally to the study of exotic kinds of space and provides interesting and useful ways to represent and analyse more familiar ones.

Numbers and Counting

Like symmetry, these are things we learn at an early age are more interesting than most people think. There are exotic number systems -- some, like the "complex numbers" better-behaved than the ones we use most of the time; others much more strange and awkward. There are systems in which the numbers can be interpreted as rotations in space, or as numerical functions; others in which there is no "1", or no "0". And counting things is, it seems, often very hard indeed.