Computers represent information using bits — that's 0s and 1s. It turns out that Claude Shannon's entropy, a measure of information invented long before computers became mainstream, measures the minimal number of bits you need to encode a piece of information.

An idea called Occam's razor states that the simplest answer is always the best. But is this really true? Computer scientist Noson Yanofsky is trying to find out, applying Kolmogorov complexity to a branch of mathematics known as category theory.

Not just the ingredients for a fairy tale...

In the TV game show Two Tribes teams can have unequal sizes. Is that fair?

Folding a piece of paper in half might be easy, but what about into thirds, fifths, or thirteenths? Here is a simple and exact way for fold any fraction, all thanks to the maths of triangles.

Why the humble average can be grossly misleading.

How to approximate the English language using maths.

Take a trip into the never-ending.

The telescope discovers the oldest solar system to date.

Two mathematicians' visit to the desert sheds new light on avalanches.

Observers are, of course, vital in physics: we test our theories by comparing them to our observations. But in cosmology, as Jim Hartle explains, we could be one of many possible observers in the Universe and knowing which one we are is vital in testing our theories.