# What happens when a raindrop hits a puddle?

Have you ever taken a walk through the rain on a warm spring day and seen that perfect puddle? You know, the one where the raindrops seem to touch down at just the right pace, causing a dance of vanishing circles?

# We’ve found a quicker way to multiply really big numbers

What is the best way to multiply two big numbers together?

# How the zebrafish got its stripes

Stripes are common in our lives. It’s a pretty basic pattern, and easy to take for granted. As an applied mathematician who studies how patterns form in nature, though, I am wowed by the striped patterns the zebrafish wears across its body and fins.

# When did humans first learn to count?

The history of math is murky, predating any written records. When did humans first grasp the basic concept of a number? What about size and magnitude, or form and shape?

# The great mystery of mathematics is its lack of mystery

In one sense, there’s less mystery in mathematics than there is in any other human endeavour. In math, we can really understand things, in a deeper way than we ever understand anything else. (When I was younger, I used to reassure myself during suspense movies by silently reciting the proof of some theorem: here, at least, was a certainty that the movie couldn’t touch.) So how is it that many people, notably including mathematicians, feel that there’s something ‘mysterious’ about this least mysterious of subjects? What do they mean?

# Nothing matters: how the invention of zero helped create modern mathematics

A small dot on an old piece of birch bark marks one of the biggest events in the history of mathematics. The bark is actually part of an ancient Indian mathematical document known as the Bakhshali manuscript.

# Maths: why many great discoveries would be impossible without it

Despite the fact that mathematics is often described as the underpinning science, it is often not given enough credit when scientific discoveries are presented. But the contribution of mathematics and statistics is essential and has transformed entire areas of research – many discoveries would not have been possible without it. In fact, as a mathematician, I have contributed to scientific discoveries and provided solutions to problems that biology was yet to solve.

# Mathematics is beautiful (no, really)

For many people, memories of maths lessons at school are anything but pretty. Yet “beautiful” is a word that I and other mathematicians often use to describe our subject. How on earth can maths be beautiful – and does it matter?

# The maths behind ‘impossible’ never-repeating patterns

Remember the graph paper you used at school, the kind that’s covered with tiny squares? It’s the perfect illustration of what mathematicians call a “periodic tiling of space”, with shapes covering an entire area with no overlap or gap. If we moved the whole pattern by the length of a tile (translated it) or rotated it by 90 degrees, we will get the same pattern. That’s because in this case, the whole tiling has the same symmetry as a single tile. But imagine tiling a bathroom with pentagons instead of squares – it’s impossible, because the pentagons won’t fit together without leaving gaps or overlapping one another.