Mindless searching
How stupid systems can use clever ways of finding things.

It all adds up
Present and future mathematicians celebrating women from across the mathematical sciences.

El Niño: What on Earth will happen next?
El Niño is a climate event without equal, causing droughts, floods, hurricanes and typhoons around the globe. How can we understand and predict it?

Finding your place in the world
What are those global coordinates used by GPS systems and human navigators around the globe?

Latitude by the stars
A little trigonometry shows why the North star helps to find out where you are.

The longitude problem
While it's easy to find out your latitude, longitude has presented one of the biggest scientific problems in history. Find out why.

Outer space: You guessed it
How to reduce the reward of guessing in multiple choice exams.

Eintein's general theory of relativity celebrates its centenary this year. To mark the occasion, here are some articles introducing you to the theory and looking at Einstein's struggle to formulate it. There will be more relevant articles later on in the year.

What is general relativity?
Physicist David Tong to explains the theory and the equation that expresses it. Watch the video or read the article!

Einstein and relativity: Part I
Read about the rocky road to one of Einstein's greatest achievements.

Einstein and relativity: Part II
General relativity, Einstein's rise to international stardom, and his legacy.

It's easy for us to picture a curve drawn on a piece of paper, or a two-dimensional surface, such as a sphere, sitting in three-dimensional space. But for most of us picturing anything in higher dimensions is impossible. Where our brains and imagination fail, we can use maths to paint the picture for us.

We need to generalise the idea of a surface or a line to higher dimensions. Most of the lines we come across, whether they are curved or straight, look like a straight line when viewed from up close (this is the basis for calculus). A surface, whether curved like a ball, rippling like a flag or flat as a table-top, viewed close up looks like a flat plane. Both lines and surfaces are examples of manifolds – mathematical objects that viewed up-close look like ordinary flat space, in which points are located using perpendicular coordinate axes and which is known as Euclidean space.

Manifolds exist not only in dimensions one (e.g. a curve) and two (e.g. a surface) but also in higher dimensions. The good thing about Euclidean space is that it's easy enough to deal with those higher dimensions: a point in n-dimensional space is given by a list of n coordinates. When you are dealing with a manifold, you can use this knowledge of Euclidean space when looking at it up close.

Formally, a manifold is a topological space in which each point x has a little neighbourhood that is homeomorphic to a piece of Euclidean space. Homeomorphic means that there is a bijective function from one to the other that is continuous in both directions.

The concept of a manifold is not as abstract as it may first appear. For example, CGI in movies uses the idea in order to approximate a complicated surface with lots of tiny flat pieces – this is how the killeroo in the image above was created. You can read more in It's all in the detail.

This website is a gallery whose exhibits are the crowning achievements of mathematics: its theorems. As of today there are a total of 237 theorems on the site, ranging from the famous Four Colour Theorem to the impressively titled Diaconis–Holmes–Montgomery Coin Tossing Theorem. No, we hadn't heard of that last one either, but luckily each theorem comes with an explanation and links to further information.

Happy theorem browsing!

Visit the theorem of the day website.