MATHS, 1 caucher birkar, 41, at VERSION cambridge university, photographed by Jude edginton REPR O OP heard the one about the asylum seeker

SUBS who wandered into a british university... A RT and came out a maths superstar? PR ODUCTION CLIENT

Caucher Birkar grew up in a Kurdish peasant family in a war zone and arrived in Nottingham as a refugee – now he has received the mathematics equivalent of the Nobel prize. By Tom Whipple

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ineteen years ago, the mathematics Caucher Birkar in Isfahan, Receiving the Fields Medal If that makes sense, congratulations: you department at the University of Iran, in 1999 in Rio de Janeiro, 2018 now have a very hazy understanding of Nottingham received an email algebraic geometry. This is the field that from an asylum seeker who Birkar works in. wanted to talk to someone about The problem with explaining maths is

REPR algebraic geometry. not, or at least not always, the stupidity of his They replied and invited him in. listeners. It is more fundamental than that: O OP N So it was that, shortly afterwards, it is language. Mathematics is not designed Caucher Birkar, the 21-year-old to be described in words. It is designed to be son of a Kurdish peasant family, described in mathematics. This is the great stood in front of Ivan Fesenko, a professor at triumph of the subject. It was why a Kurdish Nottingham, and began speaking in broken asylum seeker with bad English could convince

SUBS English. That was when his life changed. a tenured professor he was a serious intellect. It is also, though, its tragedy. “If I am a painter, The young Caucher Birkar did not usually I can show you a painting,” says Birkar. “For a roam the campus of Nottingham University. mathematician, what can you do?” Sometimes, when he wasn’t meeting maths Across the table from us is Ivan Fesenko, professors, he would present his government- the professor Birkar first approached in issued food vouchers at the local supermarket Nottingham. Conscious that we have stopped

A and the cashiers wouldn’t know what they midway through the technical explanation, RT were. They would hold them up to the light, he gamely chips in. “Parameterisation is a or call a manager for assistance. substitute of counting,” he says. “You want This was one of the humiliating parts some accountancy to keep track of all the of being an asylum seeker. structures in a compact way.” Most of the time, though, his life at that Birkar, revived, heads back into the fray. time was just boring. For a year, Birkar, until “There are infinitely many of them, yes, but his eventual acceptance into the country, had what I showed is that it is not as wild as you PR

ODUCTION no control over his life. He could not work; imagine. There is a structure to it. It’s in some he could not choose where to live. But there sense finite. It’s not really finite, but finite in was one thing he could do, one thing that the sense …” Then, again, he tails off. is untroubled by borders, legality or even Birkar will not talk about how he initiated language: he could do mathematics. his asylum claim. Nor will he say how he got When he arrived in Britain, somewhere “Often we would be in the classroom and powers of two at the age of four; nor did his to Britain. What we do know is that in the in Whitehall a computer – or perhaps a suddenly hear the sound of an aeroplane. We mother discover him arranging Lego bricks third year of his degree in Tehran he made CLIENT ‘we’d be in the classroom and hear the bombs. human – had made a wholly arbitrary and would run out for our lives,” he says. “Many into prime groups. Instead he says he just had the journey from Iran, presented himself to utterly fateful decision: it settled Birkar in times I would see the planes drop the bombs. “a feeling … nothing serious”, that he was we’d run for our lives. lots of people got killed’ the authorities and began the process of Nottingham. And, although this was probably We were right on the border. The aerial threat drawn to mathematics. settling in the UK. not a top consideration of the Home Office, was always there; a lot of people got killed.” A feeling should have been how it stayed. For someone who wanted to become the University of Nottingham happens to These days, recounting his youth while He had no internet, he was in a war zone, he to understand mathematics in a deeper sense,” marks the point at which they have been a professional mathematician, it must have have a strong mathematics department. sitting in an upmarket Nottingham restaurant, was a member of a persecuted minority and he says. “I picked a problem or invented called upon to explain their subject to been terrifying. The career of a mathematician So Birkar, finding himself stuck in his is the dispassionate air of someone his family were peasants. What he did have, something.” Later, when he finished secondary a layperson. is a little like that of a ballet dancer or bureaucratic purgatory and with nothing better describing events that happened to a different though, was a brother six years older who school and was accepted into Tehran “So Fano varieties,” Birkar begins briskly, footballer. At the highest level of intellectual to do, went to the campus to see if he could person. “It wasn’t,” he adds, “the best decided to push him. “Even though we grew University, he would discover that this work he “they are spaces in algebraic geometry that achievement minds deteriorate as surely as find someone to listen to his ideas about maths. environment for education.” up during the war and people were just trying embarked upon – original proofs and problems have a positive curvature. Everyone has a bodies, and there is a short window in which Nineteen years later, nineteen years after According to geography, Birkar’s national to survive, he was always thinking about other – had not been new after all. Others had got feel of curvature. For instance, a sphere is just you can do your best work. The Fields Medal that day when he tentatively made contact, allegiance in that brutal conflict was to Iran. things, trying to create,” says Birkar. there first; he just did not know it. But that, he a ball. It has positive curvature, it is round goes only to mathematicians under 40 he is back, for a ceremony organised by His house was in Marivan, which sits where “When I was around ten, he started to says, was not important. “These things I did everywhere …” He looks at me across the – a stipulation that rarely excludes research Fesenko to honour one of the most illustrious Iran bulges into Iraq. But he was also Kurdish, teach me a bit of mathematics beyond my were not significant, but that’s not the point. lunch table, entreating me to understand. So of importance. mathematicians ever to come out of the which meant that his real nation – a nation textbooks. He didn’t teach me these things In mathematics, you try to do something new.” far, I do. “If you fix the dimension of the Fano Birkar, then in his early twenties, was university. The ceremony celebrates an that still waits to be born – straddled the to get good grades. He just tried to convey Every day, walking the corridors of the variety, to prove you can parameterise this spending that precious window of time living academic who is now at Cambridge and border with Iraq. It also meant that both an idea that I should learn these things Tehran mathematics department, he had a space with finitely many parameters …” Birkar in a house with three other asylum seekers, who has just received the Fields Medal, the sides hated him: this war was not his war. because they are beautiful.” reminder of what it meant to do something has supervised students at Cambridge, so is unable to work, paying for food with vouchers mathematical equivalent of the Nobel prize. He had cause to hate them, too. Once, To Birkar, they were, and so he decided, new. There, on the walls, were pictures of trained in spotting the blank signs of silent and in a limbo of indeterminate length. That academic is Birkar, and his story long before he was born in 1978, his family there on the mountainous border of Iran and the stars of his chosen profession, of the men incomprehension. He tails off. “It was extremely tough,” he says. “At that – the story of a dirt-poor Kurdish boy who were wealthy landowners, but they had their Iraq, between shellings and bombings, that he (they were, at the time, all men) who had seen Perhaps it is better to begin at the beginning, point, ideally I wanted to be in a top school of won the most prestigious mathematics prize fields taken from them. “We became simple was going to be a professional mathematician. further than any before: the Fields medallists. with algebraic geometry. In mathematics, mathematics.” But he could neither study nor in the world – is one of the most unlikely peasants,” he says. “We had a piece of land The problem was, he had no idea what that “I looked at them and wondered if I would equations are sometimes also shapes. So work. If he could, he barely had English and in mathematics. and did traditional agriculture. Wheat, barley, meant. “I was completely isolated. There was ever meet them,” he says. x+y=2 is a straight line, while x2+y2=1 is a circle. had no hope of meeting his family, still in vegetables, fruit.” His father had some no one to talk to. The teachers wouldn’t go Algebraic geometry is about studying all the Kurdistan, for years. Still today, his mother The Iran-Iraq war raged throughout Birkar’s education, his mother had none – neither beyond the textbooks.” There is a particular expression – resignation, shapes that can also be described by equations. has visited only once; the visa process – even primary-school years. He remembers how he needed much for their farming work. Without a clear path to take, throughout followed by a weary once-more-unto-the- These include three-dimensional shapes such for people visiting Cambridge professors – is ges would watch as the jets flew over his village, Even leaving aside the subsistence lifestyle, his secondary-school years he set off into breach rallying, followed by resignation again as spheres, multidimensional shapes that too traumatic.

y ima just across the border from Iraq, their engines his is not the stereotypical childhood of a mathematical terra incognita – trying to – that you come to recognise when you cannot be visualised at all, and less regular “Psychologically it was very difficult. For

gett shattering the peace of the mountain valleys. maths prodigy. He didn’t start reciting the create his own new mathematics. “I wanted interview mathematicians. This expression shapes that might, say, have holes or handles. some people the asylum application takes

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ten years, and in the end you are kicked out. computer science jokes and – all too often One room, another room. I sit on the sofa I know a lot of people whose youth was wasted.” – the facial hair of an adolescent off to join sometimes for an hour. Or a chair. Anywhere In his meeting with Professor Fesenko, Isis, are the undergraduates. I feel comfortable. You really focus; you forget though, he gained hope that it would not For them at least, there is an honour that about everything else.” all be in vain. “We have a belief that the commands all the awed respect of the Nobel, He worries that his chosen profession, a

REPR deepest things in mathematics are determined a prize which, even here, marks out a top tier profession where sitting staring on a sofa then by other forces that are above us,” says of mathematicians: the Fields Medal. Once walking to the kitchen counts as work, is so O OP Fesenko. Many mathematicians think their every four years up to four mathematicians removed from the lives of the people who pay discipline is not created but discovered receive this, the highest award in the subject. for it that one day they will just stop. It is hard – that the purity of the prime numbers and Last year Birkar, nominated by Fesenko for his to justify mathematics. His research has no the equations they find are signs of a deeper work on classifying equations, was one of clear purpose now, although if you apply order. “I’m sure it was not pure coincidence those four. probability theory – a discipline considered

SUBS that sent Caucher here.” Much of Birkar’s career since Nottingham irredeemably grubby and practical to Fesenko began his career in St Petersburg has been about creating order and structures pure mathematicians – you would say University. There, he says, “I dealt with amid the endless infinities of algebraic the chances are that one day it will. The many people like him, from many different geometry. The task of mathematicians pointless mathematics of 100 years ago is the backgrounds, who were extremely bright. For like him is to be a zoologist of shapes and mathematics that today powers the internet. me, it was not at all a surprise to receive a equations, spotting how to classify them. Pure mathematics funding priorities do message from a refugee.” There was another When people look at animals and first try seem, though, for a boy who once watched

A way in which the orderly gods of mathematics to classify them, they might group together Iraqi MiGs on bombing runs over his home, RT were smiling on Birkar that day. In Russia, all the furry creatures, or all the ones that very much a first-world problem. Birkar has a mathematics exams are oral rather than swim, or perhaps lump them together by way of making his journey to this point – from written. “Because I had a vast experience colour. Then as they gain sophistication, they Iran to Britain, from peasant to mathematics of arranging such exams, I just needed five minutes talking with him to see he is very, very strong,” says Fesenko. he lived with three asylum seekers, unable In particular, when Birkar mentioned PR ODUCTION the work of Igor Shafarevich, a Russian to work and paying for food with vouchers number theorist and algebraic geometer who was so talented he once met Stalin, it was “like a password” that let Fesenko know he might amend the categories – mammal, superstar – seem almost mundane. Indeed, was serious. reptile, amphibian. The same is true for he tries to convince me it should even “If Caucher had gone to another place mathematics. So rather than saying all round be expected. and started to talk to some other UK shapes are the same type, or all pointy ones, “Because of the politics relating to refugees CLIENT mathematician, it’s not clear what would people look for deeper congruences – the you mostly see negative aspects in the news,” have happened.” mathematical equivalent of mammals, reptiles he says. “Go beyond the negative, and being As soon as the asylum application went and amphibians. a refugee and a scientist is not a strange thing. through, Birkar’s PhD place was assured. This means that when faced with an I’m not even the first refugee Fields medallist And as soon as it was clear just how good apparently weird shape, mathematics’ version for the UK.” He is right – that honour goes he was, so too was his subsequent position of a duck-billed platypus, they can spot an to Klaus Roth, whose Jewish family fled the at Cambridge. analogy to a simpler, more easily understood Nazis in the Thirties. And yet, his is still an one. And this is what Birkar did. He made astonishing life. At around the same time as Birkar fled important advances towards what is known Einstein, the most famous refugee scientist Iran, Cambridge had begun building a new as the minimal model program, which aims of all, once remarked, “If relativity is proved mathematics faculty. It was designed to reflect to classify algebraic geometric objects in a right the Germans will call me a German, the beauty of the equations within, so its smarter way. His work has also fundamentally the Swiss will call me a Swiss citizen, and the central building was a large elegant curve. improved our understanding of one of the key French will call me a great scientist.” The It was intended to blend into the background, objects in the field, known as Fano varieties. same, Birkar has found, is the case for him. so its roof was covered in turf. With an award like the Fields Medal, which In Kurdistan, after the news of the award, The result is elegant but, with its grass resulted from that research, comes freedom. a mural was painted to mark his success. dome, is also – it’s difficult to avoid the Sometimes Birkar works at the faculty, a big In Britain, Cambridge issued a triumphant comparison – a little like a Tellytubby land beast sweeping through the cafeteria at whom press release, while Nottingham, where it for mathematicians. Except, that is, that the others glance, as they once did Hawking, in all began, organised the ceremony he has Tellytubbies were often easier to understand. admiration. But he prefers these days to spend returned to attend. Here, scuttling among the equation-laden the day at home, with his family. In his last And Iran? He doesn’t know for sure blackboards and student-laden lecture rooms, year of his PhD he met an economics student – he can’t return – but he says he has heard you find the mathematician in its natural from Thailand. They have a five-year-old son, they too have celebrated his achievement. habitat. This is a place where, until 2017, you fluent in Kurdish, Thai and English, whom she Perhaps even now on the wall of the Tehran could catch Stephen Hawking wheeling looks after while he works. Not that it would mathematics department there is a portrait through the cafeteria. In the same cafeteria, necessarily look like “work” if you saw him. being prepared of the world’s newest Fields too, are the lesser but more populous “If you come to my house you don’t see medallist – a man who once looked up at the creatures of the mathematical tundra. This any signs of intellectual activity. I don’t have same row of foreign mathematicians and distinctive breed, marked by practical hiking a desk,” he says. “Changing places is quite wondered if he would ever be privileged shoes, T-shirts emblazoned with convoluted important. I will walk for one hour nonstop. enough to meet them. n

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