history of mathematics
How to derive the famous quadratic formula from pictures, just like the Babylonians did. 
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. 
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? 
Georgian school maths: bushels of corn, kilderkins of beer and feeding soldiers. All without algebra! 
The Fibonacci sequence – 0, 1, 1, 2, 3, 5, 8, 13, ... – is one of the most famous pieces of mathematics. We see how these numbers appear in multiplying rabbits and bees, in the turns of sea shells and sunflower seeds, and how it all stemmed from a simple example in one of the most important books in Western mathematics.

A commonly held belief about medieval Europe is that academic pursuits had fallen into a dark age. The majority of scholars were churchmen, and their enquiry often related to some principle of church practice. But is there a value to respecting the tenacity of historic mathematicians? 
Compass & Rule: Architecture as Mathematical Practice in England, 15001750, is a lovely online version of the physical exhibition help at the Museum of the History of Science, Oxford, in 2009. Compass and Rule focuses on design and drawing, exploring the role of geometry in the dramatic transformation of English architecture between the 16th and 18th centuries. 
When it comes to describing natural phenomena, mathematics is amazingly — even unreasonably — effective. In this article Mario Livio looks at an example of strings and knots, taking us from the mysteries of physical matter to the most esoteric outpost of pure mathematics, and back again.

According to one mathematician, god created the whole numbers, with everything else being the work of humanity. Why, then did god not equip us with a good way of writing them down? Chris Hollings reveals that our number system, much used but rarely praised, is in fact a work of genius and took millennia to evolve.
