Richard E Borcherds

This is the channel of Richard Borcherds, a British mathematician and Professor of Mathematics at the University of California, Berkeley. He was awarded the Fields Medal in 1998, one of the highest honours in mathematics.

Most videos are recordings of his graduate lecture courses on subjects such as algebraic geometry, number theory and group theory. He writes by hand under a document camera and talks through each idea. There are also a few shorter talks pitched at undergraduate or school level. Much of the material is very advanced, so this channel suits students who already love maths and want to see where it leads.

Some highlights include:

This first lecture in an introduction to number theory is one of the most accessible starting points on the channel.

This short talk shows how to construct the Leech lattice, a remarkable pattern of points in 24 dimensions.

This lecture introduces category theory, a way of linking different areas of mathematics together.

The channel has over 83,000 subscribers.

Engineering does not need maths at this level, but students thinking about maths, physics or theoretical computer science may enjoy seeing how a leading mathematician thinks. Number theory also underpins modern cryptography, which keeps online banking and messaging secure. Treat this as stretch material rather than revision. The number theory course is the gentlest place to begin.