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As we are having a little cake of our own today, we thought we'd look back on another great birthday celebration... Stephen Hawking's 70th birthday!

Hungry? Why not try one of Vi Hart's brilliant Tex Mex Hexaflexgons – maths has never tasted so good!

Are you reading this page because you decided to or because you were destined to from the start of time? Plus shares Mick's sentiment that we are free to do what we want, any old time. But what does physics and mathematics have to say about free will?

A team of physicists have curbed the hope that quantum physics might be squared with common sense. At least if we want to hang on to Einstein's highly respected theory of relativity. Their result concerns what Einstein called "spooky action at a distance" and it may soon be possible to test their prediction in the lab.

Make your childhood dreams come true and join the Paris Fire Brigade as part of the 2012-13 Mathematical Competitive Game.

Struggling to solve today's sudoku? Is your tried and tested method hitting a brick wall and you feel like you are going around in circles? New research might make you feel a bit better: you might not necessarily be stuck... perhaps you are just in a patch of transient chaos on your way to the solution.

The Travelling Salesman movie is coming to the UK! Get your tickets here and find out about the P vs NP problem.

Today is Ada Lovelace Day celebrating the work of women in mathematics, science, technology and engineering. To join in the celebrations we bring you a selection of our favourite female interviewees from the last 15 years.

How do you best allocate students to universities, doctors to hospitals, or kidneys to transplant patients? It's a tough problem that has earned this year's Memorial Prize in Economics.

The first ever National Biology Week is happening between October 13th and 19th 2012. It's organised by the Society of Biology and there'll be events around the country giving everyone the chance to learn about the second-most fascinating science (if you count maths as a science). But if you'd rather stay in and cuddle up with your laptop here are our favourite Plus articles on maths and biology.