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There is more to order than just numbers

Try to imagine having to find the largest set of numbers that cannot be broken down into  any other set of numbers, technically speaking the largest simple group: a group of finite order, a number. It is such a difficult undertaking that in mathematics it has been defined “the Monster group M”. Two mathematicians managed to unearth the Monster. Simon P: Norton is one of them. 

A child prodigy, he was already reciting the 91 times table at the age of five. “I had a special feeling for numbers,” he politely explains over the telephone, “a connection.” Norton is the subject of the biography The Genius In My Basement, written by his Cambridge tenant, Alexander Masters. The numerous snap-shots reproduced in the book show a hirsute man with Einstein-style hair. He is clearly a compulsive reader, the kind who can commit bus timetables to memory. As a child he identified with the number “5” and renamed his beautiful,  beloved mother “45”.

He was a researcher at Cambridge, he tracked down the Monster and, moreover, discovered its relationship with elliptic functions, he  invented games of logic, mathematics and linguistics. At the age of 33, however, he suffered a breakdown because he got a calculation wrong. It had never happened to him before.

Today, the 62-year-old Norton lives in a basement which shows no sign of order, in a chaos of notes, books and cans of food. Well-mannered and from a good English family, but unkempt and completely indifferent to fashion and elegance, this mathematical genius finds beauty in the enigmas of numbers. And in his free time he roams the city by bus, conserving the route maps. Talking with him induces a continuous state of faint astonishment. It is hard to believe that such a complex mind is capable of seeing the chaos of the world and humanity in such simple terms.

They say you are a genius. How would you define yourself?
I am just a competent mathematician. Do you know why they call me a genius?

Because I was precocious.

At 5 years old, you knew the 91 times table: you were a prodigy.
I had a special feeling for numbers. Then I discovered that many other mathematicians also had this as children. I remember I liked the number seven because my family had Italian domestic staff and they taught me to play scopa.

Then what happened?
By the time I was 20, other mathematicians had reached my level.

It was you, however, who constructed a mathematical group called the Monster. Do mathematical laws emerge from human intelligence or are they discovered?
Numbers are real things. They are reality.

So you agree with Galileo: the book of nature is written in the language of math?
Yes, the mathematician is a scientist. Just as the scientist investigates the laws of nature, the mathematician investigates the relationships between numbers.

So when you look at the world, do you see a clear order?
In terms of physical laws, of course. But if the question is: how was the universe designed, well, that’s more difficult. In human affairs there’s not much that’s designed. There’s no order.

Are our lives plotted by coincidence or by destiny?
By coincidence, I think, by the intersection of events.

Does science have an influence?
I think science can bring benefits to humanity. But only if it’s applied correctly. Otherwise it can be used to accelerate destruction, of the environment for example.

Is that how it is now?
Now it’s not clear. There’s a challenge, a contest in progress.

Between good and evil?
Between good and bad application of science. And I don’t know which direction we’re going in.

Perhaps in a more chaotic direction?
The weather is certainly becoming more chaotic.

Are you referring to climate change?
Of course. We have had a lot of typhoons and damage caused by bad weather: it’s an arrow launched by nature.

A message?
For 20 years we’ve been reacting the wrong way.

In what sense?
We’ve been thinking about climate change, about global warming, as a given, as something inevitable: it will happen. But actually we could have done something.

When people see these upheavals, they should start treating the Earth and the environment around them better: they should react together, as a community.

In your biography you said: to anyone who is lonely I recommend politics and public transport. Why?
Public transport takes you to interesting places. And at the same time it helps limit environmental problems, which are the most serious risk humanity is facing.

And politics? These days not many people believe in it.
And I think they’re wrong, we’re all wrong. Those who are elected are among the few people involved in change. If you don’t know who they are and what they’re doing, you will never be able to change things. And you’ll never see anything you really want being accomplished.

Do you think social order corresponds more or less to the idea of the common good?
Yes, that’s why it worries me to see people who don’t recognise the importance of public assets and services in their own lives.

For example?
For example, when I hear people say that the economy would fare better if we had fewer public services, I simply can’t understand it.

What are the most beautiful things in your own life?
Mathematics and logic. And travelling, visiting interesting places. Apart from that, my main activity is reading.

What can’t you stand?
I can’t stand seeing some people’s satisfaction when faced with a system that doesn’t work.

And if you could make a wish for the world and for yourself?
My greatest wish is to see the world working for everyone in society. As for myself, I’d be happy to be a member of that intelligent society.

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