Euclidean geometry
The impossible becomes possible when you move into the third dimension. 
Did you learn at school that the angles in a triangle always add up to 180 degrees? If yes then your teacher was wrong. Find out why here. 
The only good thing about a washout summer is that you get to see lots of rainbows. Keats complained that a mathematical explanation of these marvels of nature robs them of their magic, conquering "all mysteries by rule and line". But rainbow geometry is just as elegant as the rainbows themselves. 
Squares do it, triangles do it, even hexagons do it — but pentagons don't. They just won't fit together to tile a flat surface. So are there any tilings based on fiveness? Craig Kaplan takes us through the fivefold tiling problem and uncovers some interesting designs in the process.

Runner up in the general public category. Great minds spark controversy. This is something you'd expect to hear about a great philosopher or artist, but not about a mathematician. Get ready to bin your stereotypes as Rebecca Morris describes some controversial ideas of the great mathematician David Hilbert.


The famous mathematician Euclid is credited with being the first person to axiomatise the geometry of the world we live in  that is, to describe the geometric rules which govern it. Based on these axioms, he proved theorems  some of the earliest uses of proof in the history of mathematics. 