Learning mathematics by travelling through it

Most mathematics is met as a sequence: one topic, then the next, in an order someone else chose. Mathematical Worlds starts from a different picture. Each field of mathematics is a universe of its own, and you learn by visiting it, looking around and following whatever catches your eye.

The same universe should look different depending on who arrives. A five-year-old in the world of geometry might find shapes that can be stretched, folded and counted. A school student might meet the same shapes with angles and areas attached. A university student might find the symmetry groups acting on them.

The goal is simple: make exploring mathematics fun at every level, so that learning happens along the way.