How a question about rainbows led to an entire field of mathematics.
Maria Bruna has won a Whitehead Prize for finding a systematic way of simplifying complex systems.
The number pi can be expressed beautifully in terms of infinite sums. For practical purposes though, these sums are rather disappointing: they converge slowly, so you need to sum a large number of terms to get accurate estimates of pi. Here's a clever way to make them converge faster.