Here is a map of mathematics as it stands today, mathematics as it is practiced by mathematicians.

From simple starting points — Numbers, Shapes, Change — the map branches out into interwoven tendrils of thought. Follow it, and you’ll understand how prime numbers connect to geometry, how symmetries give a handle on questions of infinity.

And although the map is necessarily incomplete — mathematics is too grand to fit into any single map — we hope to give you a flavor for the major questions and controversies that animate the field, as well as the conceptual tools needed to dive in.

There’s no right or wrong way to explore. You can go in a straight line from topic to topic, or jump around, searching for something that catches your eye.

If mathematics is the poetry of logical ideas, as Albert Einstein once wrote, then through this we hope to provide an appreciation for all the beauty that it describes. Scroll down to begin.