The dome of St Paul's, rising elegantly above London since the cathedral was rebuilt late in the seventeenth century, hides an intriguing early example of the interplay between maths and architecture.
Sometimes people are nasty when it would have been better to be nice.
Topology considers two objects to be the same as long as you can morph one into the other without breaking it. But how do you work with such a slippery concept? One useful tool is what's called the fundamental group of a shape.
The dramatic curved surfaces of some of the iconic buildings created in the last decade, such as 30 St Mary's Axe (AKA the Gherkin) in London, are only logistically and economically possible thanks to mathematics. Curved panels of glass or other material are expensive to manufacture and to fit. Surprisingly, the curved surface of the Gherkin has been created almost entirely out of flat panels of glass — the only curved piece is the cap on the very top of the building. And simple geometry is all that is required to understand how.
Suppose you're trying to decide which university to go to. You find out that last year the university you're interested in admitted 30% of male applicants but only 21.3% of female applicants. Looks like a clear case of gender bias, so you're tempted to go somewhere else. But then you look at the figures again, this time broken up by department, you see a bias in favour of women. What's going on?