The Rubik's Cube, that tantalising 3-D puzzle invented by the Hungarian Ernõ Rubik in 1974, is having an amazing revival: it is the prized possession of the eponymous hero of Pixar's recent film WALL-E - a rubbish-collecting robot who is amazed when his clever robot girlfriend EVE solves it in seconds.

Anyone who visited Liverpool's Biennial last year may have spotted a very puzzled-looking George W. Bush sitting in the café at the Tate gallery there, battling with the cube - in fact he was a satirical wax model made by Alison Jackson for her series of images exploring the slippage between fantasy and reality. Perhaps Bush would have coped better with the cube on the cover of Elbow's album Seldom Seen Kid: all the squares are white.

Last week, Graham Parker, a Hampshire builder, was in the news for solving the cube in record time. What usually makes headlines is a feat such as that of Erik Akkersdijk, who managed to complete the cube last year in 7.08 seconds. Parker's achievement, though, was based on endurance, not speed - he had been trying to solve his cube for 26 years and spent almost 27,400 hours twisting and turning it before he finally managed to rotate the last piece into place.

Many solutions and algorithms created by mathematicians are available on the internet - YouTube can speed you towards a solution - but Parker was determined to crack the cube himself.

I understand such desire. He was after the same the buzz that I get when I solve a mathematical problem. The reason why I will dedicate a decade to trying to prove a conjecture is the rush of adrenaline when everything finally clicks into place - and

I can't bear the thought that someone might get there before me and tell me how to do it.

The “aha” moment is the drug of doing mathematics - and the harder the problem, the more satisfying it is to solve it. That is why Matt Damon decides not to become a mathematician at the end of Good Will Hunting and runs away with the girl instead. Maths was too easy for him; she represented a bigger challenge than solving mathematical conundrums.

One thing that makes the Rubik's Cube so challenging is that, despite there being only 26 cubes to move around, there are about 43 quintillion arrangements of the colours. That's a number with 20 digits. Even the credit crunch hasn't got us into this realm of numbers. The Ideal Toy company, which marketed the cube, boasted that it had more than “three billion possible states” - revealing how bad we are at understanding large numbers. That would be like McDonald's announcing proudly that it had sold more than 100 burgers.

To get a sense of how big 43 quintillion is, if you lined up that number of cubes in a row, they would stretch more than halfway to the nearest star outside our solar system. Yet despite there being so many possible combinations, the mathematician Tomas Rokicki proved last year that it takes a maximum of only 22 moves to solve the cube from any of these positions.

This sort of analysis is very important in navigating networks such as the internet, the national grid or even neural networks. You can think of the 43 quintillion different Rubik's Cube arrangements as internet sites and a move from one to another as a link between sites. To know how many clicks it takes to get from one internet site to any other is an important piece of information about how connected the web is.

Ten years ago, analysts concluded that, on average, you needed only 19 steps to get between two randomly chosen websites. They predicted that this figure would rise to 21 as the internet exploded by 1,000 per cent over the next few years.

Although the cube can be cracked in seconds, this simple toy still poses analytical problems for mathematicians, who are currently trying to prove that any cube can be solved in 20 moves. Graham Parker may have displayed unlimited resolve, but my advice would be to seek advice from Erik Akkersdijk instead.

Marcus du Sautoy will be speaking at Tate Modern on Saturday in an event to celebrate the 50th anniversary of C.P. Snow's influential 1959 lecture The Two Cultures

Conundrum

What's the smallest number of cuts you need to cut a large cube into 27 smaller cubes?

Answer: Six. You can't do it in fewer than six cuts. Think of the 27 small cubes arranged in a 3x3x3 configuration like the Rubik's Cube. There is no way of creating the cube in the centre without making six separate cuts. You need one cut for each face.

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