If I ruled the world: Marcus du Sautoy

If I ruled the world, the first thing I would do is to make sure that everyone understood Euclid’s proof that there is an infinity of prime numbers. To some people that might seem like a strange suggestion, so let me explain. In itself, Euclid’s proof is not particularly useful for anything. But what it shows is the power of analytical thinking and the magic of mathematics. Studying Euclid would plant a seed in people’s minds that would grow into an appreciation of how this extraordinary tool can help us to navigate the world. Mathematics helps us predict the future. We know about climate change, for example, because of mathematical equations.

Mathematics is not only about utility—it’s also about wonder and beauty. This goes to the heart of the problems with mathematical education in the UK. Governments want to teach mathematical skills that will be useful to the person on the street. But most of the stuff pupils learn at school—quadratic equations, trigonometry—they are never going to use. What they are being taught is the power to string together a logical argument, to see patterns in behaviour. With Euclid’s proof, you see how a finite series of logical arguments can get you to an extraordinary revelation: that you can conceive of the infinite. That, for me, is an amazing breakthrough in human thought.

The way we teach mathematics now, it is as though a pupil learning to play a musical instrument were allowed to do scales and arpeggios but never listen to any real music. You need to have both strands. One is the technical side—the arithmetic—the other is the creative. It’s like the way English language and English literature complement each other. My kids are learning Shakespeare, studying romantic poetry, great novels—all tough but exciting. The system is failing by not teaching the Shakespeares and the Keateses of the mathematical world.

Another of my missions would be to break down barriers between school subjects. We have this terrible silo mentality, compartmentalising the timetable into a mathematics class, a history class, a music class. I would love to reach a moment where, for example, you could move fluidly between mathematics and music. History, as well, is a very important part of the mathematics story. How does Euclid’s proof fit into the context of Greek thought? Why did it emerge at the time it did? I see, though, that Finland may have beaten me to this revolution. They want to introduce a more horizontal learning process.

It horrifies me when people declare as a badge of honour that they are “terrible at maths.” I think it’s a British thing—you wouldn’t have anyone in India or the far east admitting to this. People in those countries, adults and children, realise that being mathematically literate gives you incredible power. It would be part of my mission, as a world-ruler, to stop it being OK to say you’re bad at maths. There’s a lot of evidence that a mathematically literate society leads to a successful one. Changing society’s attitude towards maths could lead to economic prosperity. Mathematics can also help us solve the mysteries of life—like whether or not the universe is infinite. While writing my new book What We Cannot Know, I had a revelation. Euclid’s proof of prime numbers shows that something can, in fact, go on forever, even though we might not ever be able to observe it doing so. The power of the human mind might be able to show that, for example, a finite universe contradicts the laws of physics and that it must be infinite—even though, just as with Euclid’s proof, we’ll never be able to explore right the way to the end. The thought that you might be able to prove that the universe goes on forever, that’s mind-blowing.

There’s a big philosophical debate involved here. Some people believe that mathematics is a construct of the human mind and our way of articulating what we see around us, others that it is embodied in the physical world itself. My belief is that prime numbers would be there even if we weren’t. That’s why often when science fiction writers have an alien visiting Earth they show them communicating using mathematics. In Carl Sagan’s novel Contact, and its wonderful 1997 adaptation starring Jodie Foster, the aliens communicate through numbers. The quarks and electrons that make up everything around us are bits of embodied mathematics. Equations exist outside time. It’s like the equation 0=1-1. You can have nothing and suddenly change it into one positive thing and one negative thing. Mathematics is not just a tool to navigate our universe, but at the heart of why we have this universe—how we get something out of nothing.