Things to Make and Do in the Fourth Dimension

by Matt Parker

This is exactly the sort of maths I wish more people knew about: the surprising, the unexpected and, most importantly, the type that wins you free drinks.

Sadly, very little school maths focuses on how to win free drinks in a pub.

Part of the strength of mathematics is that it expresses universal truths but is able to express them in different ways.

I can’t resist retelling the already too-oft-told maths ‘joke’ based on just such a misunderstanding, normally seen in the form of a hilarious T-shirt with this written on it: ‘There are 10 types of people in the world, those who understand binary and those who don’t.’ To explain the hilarity: ‘10’ means 2 in a binary number system, so only those who understand binary would know it means 2 and not 10. I’ll give you a second to finish laughing and compose yourself. I am slightly scathing of this joke solely because, being a mathematician who also works as a stand-up comedian, I am told it all the time. Normally, people start with, ‘OK, have you heard this joke? Well, it kinda doesn’t work when you say it, but …’ and then proceed to try to tell a joke which only works when it’s written down. That’s the problem with binary jokes: they either work, or they don’t.

That may be my favourite definition of maths: a game where you choose the starting rules – the things you assume to be true or which are allowed – and then try to prove as many new facts as possible from there.

Since the dawn of time, 90,525,801,730 has existed as a number and been a 31,265-agon number as well as a 31,265-agon-pyramid number, but I was the first human to spot that.

The MathWorld entry currently ends with the quiet plea: ‘A modern survey would be welcome.’

As far as newspaper headlines go, ‘PRIME NUMBER DISCOVERED BY GIMPS’ is up there with the best of them.

The square of every prime number is one more than a multiple of 24.

physicists now had a growing table of the prime knots needed to build the other possible knots. Frustratingly, having done all this work on categorization and tabulation, it turned out that the universe was not made of knots.

This is how they correctly predicted that Spain would beat the Netherlands in the final. That the mathematician Javier López Peña at QMUL who started all this is Spanish of course had no impact on his conclusion.

there’s something delightfully human about programming and algorithms in general. Writing good computer code requires a person who is creative as well as mathematical. Writing efficient algorithms is very much an art, and a highly sought-after one at that.

Should you try to solve the online 5D Rubik’s Cube, your screen is showing you the 2D projection of the 3D projection of the 4D projection of the 5D cube. Confused? Good.

So, the next time you’re on a ship that is not crashing into another ship, you can be grateful that people like Colin can feel their way around spiky balls.

More numbers contain the complete works of William Shakespeare than don’t.

there is no obvious reason why mathematics, as a subject born out of pure human thought, should be so useful in the real world. The phrase ‘unreasonable effectiveness’ has since come to represent this enigma.