## history of mathematics

How to derive the famous quadratic formula from pictures, just like the Babylonians did.

Euclid's fourth axiom says that all right angles are equal. But isn't that obvious?

Does light have weight? Newton thought so. His laws predicted that gravity would bend light, two centuries before Einstein's revolution.

The Mayan civilisation brought forth many great things — including this clever way of making a right angle.

Something called *quantum field theory* has been hugely successful in describing the fundamental forces and particles. But what exactly is it? This series of accessible articles traces the history of quantum field theory, from its inception at the beginning of the twentieth century to the tantalising questions that are still open today. It's a story of pain and triumph, hardship and success.

There's no doubt that information is power, but could it be converted into physical energy you could heat a room with or run a machine on? In the 19th century James Clerk Maxwell invented a hypothetical being — a "demon" — that seemed to be able to do just that. The problem was that the little devil blatantly contravened the laws of physics. What is Maxwell's demon and how was it resolved?

How a cute 18th century puzzle laid the foundations for one of the most modern areas of maths: network theory.

The natural logarithm is intimately related to the number e and that's how we learn about it at school. When it was first invented, though, people hadn't even heard of the number e and they weren't thinking about exponentiation either. How is that possible?