EMPG Blog

Our very own Sir Michael Atiyah was in Spain recently for the 100th anniversary of the Real Sociedad Española de Matemáticas, the Spanish mathematical society, and was interviewed by Lluís Amiguet, a journalist from the Barcelona newspaper La Vanguardia.

The interview is available in both Spanish (online) and Catalan (as a photo, courtesy of Sebastiá Xambó via Sir Michael).

Enjoy!

Update: A second interview has appeared, this time by Bernarno Martín from the Madrid newspaper El País. This time it’s only available in Spanish.

Update: As requested, I’m including my attempt at translation into English. Here’s a rough and ready translation of the interview from La Vanguardia:

“The shortest path towards creation is a long detour.”

“I’m 82 years old: I do not concentrate as well as when I was young, but I am better at synthesis. I was born in London. My wife and three children studied Mathematics. God is the rationality of the universe. I support Labour because it is most rational to help the weak. I collaborate with the Real Sociedad Matemática Española.”

He flows. If they ask him to have an answer tomorrow, he will not have it, but if they give him a month, it is very possible that he will have it tomorrow. Sir Michael Atiyah is one of the fathers of contemporary Mathematics, and therefore is full of advice about how to be creative: “Work very hard at first and enjoy yourself later. Great ideas come when you are relaxed. But neither before nor after should you force yourself to obtain anything by force: do everything out of desire and the most difficult problems will turn into enjoyable games. Make an effort, but do not force yourself, do not get stressed and don’t let yourself be pressured: creativity always comes hand in hand with freedom. Creativity is not so much focussing as keeping an open mind.”

“The great mystery is why we are able to understand the world. Why can the universe be explained rationally?”

Do you believe that the world is rational?
What surprises me every day is that we can reason and fathom its laws.

And what if we don’t understand it?
When our reason fails to explain the world, our lives become a sequence of senseless images and experiences. But do not think of mathematics like the refuge of four geniuses. In essence, mathematics is simple: the truth is always elegant and understandable.

How do you know?
If you have two solutions for a problem, choose the simplest one. We mathematicians cannot compare our results with experiment, thus beauty, conciseness and elegance become the measures of their reliability. If a solution is beautiful, it is very possible that it is also true.

Mathematics per se aren’t exact?
If you were to put all mathematical formulae in a computer, you could not get anything. Mathemacians are not calculators. On the contrary, our work is closer to that of a poet or any artist.

I suffered much studying them.
Because instead of playing with them, you wanted to cram them. The best hint that you are on the right path in Mathematics is that you enjoy them. The best formulae are short in form, but long in meaning.

Like a good verse.
“To be or not to be” is a great formula.

But the world seems more complex.
Complexity emerges when you apply simple ideas to concrete realities. But in their formulation, the law of gravitation or that of electromanetic fields, even fractals have a simple elegance.

Is there room for God in this simplicity?
I only speak of God when I explain Einstein, because he did mention him profusely. But it is not so much a question of whether Einstein believes in God, but that he creates a god. Because Einstein creates a god to suit himself, whom he questions continuously.

What is Einstein talking about when he mentions God?
Of this intelligibility of the world that I mentioned. For Einstein, God is the rationality of the Universe.

Do you believe in men that create gods?
Those men create gods in their image. And those personal gods do not interest me. I do not look for a god to solve my equations.

How do you solve your problems?
We mathematicians create rather than solve. When I’m stuck, I avoid the obstacle. I flow. I leave the office and go for a walk and, often, on the way back home I see the solution.

Does it always appear while moving?
To have a great idea while walking you must have worked very hard before, of course. But it is also true that you will not have the idea if you concentrate on having it.

Why?
Creativity is not about concentration, but on the contrary: it is about keeping an open mind. When you create, the shortest path between where you are and where you want to go is a detour.

How?
You have to relax after having worked very hard to find something. For me it’s good to move: ideas emerge in the bus. It’s like trying to remember the title of a book or a film you have forgotten… You concentrate a lot and you can’t. So relax, do something else and after a while you’ll remember!

Is it better not to pressure oneself?
Our minds do not work under pressure, but in freedom: making an effort while playing.

What do you mean?
The mind selects ideas in the same way that nature selects genes: following the evolutionary paradigm. We retain whose ideas that best fit our necessities and we discard the rest; just like nature preserves the fittest.

Can we help that selection?
To accelerate that process one must play with the mental magma: let the more evolved ideas float in your mind and allow the others to be forgotten.

Why are the best mathematician very young?
To begin with, because when you are young you are not yet part of the system and thus you can defy and question it with your ideas. Besides, you still don’t know too much…

…?
And it is easier to learn than to unlearn. Excess accumulated knowledge is heavy. All that you believe you know weighs you down and it is harder to believe yourself capable of creating something new.

They used to say that knowledge takes no space.
The belief of knowing dissuades innovation. Finally, it is purely physiological that young people are able to concentrate better. Having said that, I will add that only in maturity can you synthetise accurately and with originality. You have perspective.

Why are maths so difficult to learn?
Because there are very few good teachers. The reason is that good mathematicians are everywhere in demand: finance, engineering, informatics, statistics. And very few content themselves with a teacher’s salary.

But you did.
I enjoy research. What I advise is not to focus on the technology, but to learn basic science and mathematics, because techonologies evolve and disappear, but basic science remains.

and here’s one from that of El País:

“Mathematics is like a gothic cathedral”

He is 82 years old, but he starts to talk and he rejuvenates until he becomes the boy who found his calling in numbers. Michael Atiyah (London, 1929), one of the wise men of our era, has visited Madrid because of the centenary of his colleagues at the Real Sociedad Matemática Española (RSME). He speaks enthusiastically about science, but he seems interested in everything and returns the questions to the journalist: “Has there been an eruption in the Canary Islands? Is it dangerous?” If, in the words of Azorín, one grows old when one stops being curious, he has only just reached adolescence.

Atiyah, Fields Medal in 1966 and Abel Prize in 2004 (both equivalent to the Nobel prize), son of Lebanese father and Scottish mother, who spent his first years in the Sudan and Egypt, has a frugal breakfast — cereals, lettuce, tomato and a few small slices of salami — and looks jovial. “My father used to say that the first indication of my good disposition for numbers was that I understood and took advantage of the exchange rate.” That would be the genesis of an enourmos body of mathematical work, collected in six volumes adding up to more than 4,000 pages.

Are we dealing with a scholar trapped in his thoughts? Apparently not at all. “There are introverted mathematicians, but in general we all have a sense of humour. It is our way to balance the study of such a serious matter”, he says. And his smile, which doesn’t leave him during the entire breakfast, is the proof.

He dispatches the chocolate cereals while he explains the speech he prepared for the proceedings of the RSME. A promenade through the history of Mathematics starting with Pythagoras, conceived as a choral work. “It is a construction of great ideas, each one adding something to the one before. Like a gothic cathedral”, he says. “That’s why it is similar to architecture, but we are constantly reviewing the foundations, and that’s not good for a house…”, he jokes. He likes the analogy and it amuses him: “But the mathematicians construct not a building but a city. An empire! But a good, democratic empire.” And he vindicates the scientists: “Plato believed in the wise leading the people. We should be the leaders of our civilisation.”

And is it possible for that gigantic endeavour to end? That one day nothing will remain to be discovered? “I see no limit”, he says. “From one theory springs another and we cover more ground.” Thus there is no danger of an end to this flow of happiness that this wise man finds in his work. A flow of happiness and also of beauty, another word which he mentions repeatedly. He likes beauty because it is undisputed, because “you see it at once”. And also because it can be “a torch which guides you to the truth, because in Mathematics both concepts often go hand in hand.”

The breakfast ends and one feels guilty for having stolen a few minutes from a mind that ought to be occupied in loftier tasks. But Atiyah sets us at ease. “Because Mathematics requires an intense concentration, it is good to talk with other people, to combine the solitary thought with a good conversation. And, if possible, with a good glass of wine!” At 8am it is too early for a drink, but we take him at his word for another day.

Hotel Atlántico, Madrid.

Buffet breakfast for 2: fruit juice, café au lait, fruit, salad, sausages, chocolate cereals.

Total: 18 euros.

Correction: Atiyah categorically denies eating chocolate for breakfast!