A young man of striking looks, his long brown hair framing his face, his suit offset by an oversized wine-red cravat and a trademark spider brooch the size of a palm, is being followed around a vast hall by a film crew. He is one of the four men about to be honoured by an award that is among the rarest accomplishments in any field of intellectual endeavour—the Fields Medal.
The award’s monetary prize is insignificant—about $15,000—but the prestige it offers is incalculable. The actual medal, made of 14 carat gold, is 9 cm in diameter and bears the head of Archimedes in profile with an inscription in Latin from a passage by Manilius, a first-century Roman poet: Transire suum pectus mundoque potiri (‘To pass beyond your understanding and make yourself master of the universe’). The inscription on the obverse side translates to: ‘The mathematicians assembled here from all over the world pay tribute to outstanding work.’
Given once every four years for outstanding mathematical work completed before the age of 40, in the 70 or so years since the Fields Medal has been instituted, just 52 have been awarded—four of them this year at the International Congress of Mathematicians (ICM) underway in Hyderabad, the first time in over a century of its existence that the conference is being held in India.
Three thousand assembled mathematicians rise in tribute as President Pratibha Patil awards the medal to the chosen four: Elon Lindenstrauss from Israel, Stanislav Smirnov from Russia, Ngo Bao Chau from Vietnam (originally, though now a naturalised citizen of France), and Cedric Villani from France (the man in the cravat).
Their work is varied, but in each case it is marked by deep and surprising connections between different areas of mathematics. “That’s what mathematicians love, making links between invisible things,” Villani explains, quoting Henri Poincare, one of the greatest mathematicians of all times, to elaborate his point—“Doing mathematics is giving the same name to two different objects.”
The medal was the idea of Canadian mathematician John Charles Fields, who was hoping to reconcile the mathematical world in the aftermath of the First World War, when losing powers such as Germany were kept out of the ICM in 1920 and 1924. The medal was first awarded in 1936. It is unclear when the age limit was set, but today the criterion is clear: a recipient’s 40th birthday must not occur before 1 January of the year in which the Fields Medal is awarded.
According to Timothy Gowers, an English mathematician who won the medal as a 35-year-old in 1998, “There may not be a precise answer. It was certainly not in the rules and may possibly have been implicit that the prize was not just for achievement but also for promise. Gradually, it has settled into a rigid rule with a precise cut-off date. It is unlikely to ever be relaxed, given that Andrew Wiles did not get the medal even after his proof of Fermat’s last theorem.” Wiles had first presented his proof in 1993, but the gaps were only plugged by 1994, by when he was 41.
Whatever the genesis of the age limit, it has lent a mystique to the award in the popular imagination, a kind that even the Nobel does not possess. The 1997 movie Goodwill Hunting tells the story of a child prodigy with a troubled past. Working as a janitor at MIT, he comes in contact with a Fields medalist after solving a difficult problem left behind on the blackboard. Interestingly, the MIT mathematician Daniel J Keitman, who was consulted on the screenplay, has related that “they told me the movie was about a young man they had originally envisioned as being a genius in physics, but after talking to Sheldon Glashow (Nobel Prize winner in Physics) of Harvard, they decided his being a mathematician was more plausible.”
This identification of mathematics with prodigies and troubled minds is reinforced by the few books and movies that have struck a chord with people at large. Hollywood has taken the story of John Nash, wonderfully told by Sylvia Nasar in A Beautiful Mind, and exaggerated precisely these elements. In Proof, Anthony Hopkins—whose thespian image fits the stereotype perfectly—plays a maths professor who goes crazy, leaving behind a notebook with what could be a solution to a famous problem. Finally, of course, there is the story of Ramanujan which requires no exaggeration in conforming with the image of the mathematical genius who dies young.
This image is the legacy of 19th century high romanticism, argues Amir Alexander, a historian of science. ‘Portraits of the tragic mathematical heroes of the early nineteenth century show an unmistakable affinity to those of the poets and artists of the age. These romantic images depict young men with blazing eyes, focused not on us but on greater truth beyond the horizon. The portraits of these mathematicians are very different, however, from the portraits of the great geometers of the Enlightenment, as well as those of nineteenth-century scientists. These depict active and engaged men in the prime of life, directly addressing and engaging the viewer,’ he notes in a recent book, Duel at Dawn: Heroes, Martyrs, and the Rise of Modern Mathematics, the title of which is drawn from the life of Evariste Galois, a French mathematician who at least in popular legend invented an entire field of mathematics, unsurprisingly named Galois Theory, the night before a duel that led to his death at the age of 20.
The portrait Alexander describes has its charm, especially for fictional portrayals. But as the ICM reality reveals, this portrait is misleading. At the very ceremony where the Fields Medals have been awarded, the first ever Chern Medal (named after the Chinese mathematician SS Chern) for lifelong achievement in mathematics has been awarded to 85-year-old Louis Nirenberg. Unlike the Fields, it comes with the very substantial sum of $500,000.
Nirenberg sits down to speak to me after attending an ICM seminar where another mathematician has proved a question posed several years earlier by him. He is still an active mathematician, publishing regularly at the highest level, and in each of the last ten years, the 15 most cited papers in mathematics include at least two by Nirenberg. “There is never an end to mathematics,” he says, “It is very hard for me at my age even to keep up with developments in my own field.”
He is at the ICM because of the Chern award, but he offers another reason why mathematicians are seen at conferences so often: “I have always found it hard to learn mathematics by reading mathematics. I have always learnt by talking to other mathematicians about their work.” Most of his papers have been written in collaboration, as is true of much of the work of the four latest Fields medalists. The myth of the mathematician also hides the reality of how mathematics is actually a social and collaborative effort. But that does not mean the myth is entirely without basis. Among Villani’s mathematical heroes listed on his webpage are Ludwig Boltzmann, who developed the concept of Entropy, Alan Turing, who more or less laid the theoretic framework for modern computer science, and John Nash, who is now well known to the world’s film-goers thanks to A Beautiful Mind.
Boltzmann and Turing both committed suicide. Nash has consistently fought against his mental demons. The passage from Manilius inscribed on the Fields Medal actually goes on to conclude that ‘the toil involved rarely matches the rewards to be won, nor are such high attainments secured without a price’, but Villani is quick to counter any dark suppositions about mathematical genius. “It’s not related to mathematicians,” he says, “Maybe it’s related to people who are creators, to people who live very intensely. If you accept life that is there and just live your own quiet life, then of course you don’t have a problem. If you fight against the world, against the unknown, if you are an explorer, then it’s much more complicated.”
For Villani, the image of the mathematician as a romantic hero also serves a purpose: “The existence of romantic figures in mathematics is an important thing… so that people can get identified with them at least in their dreams, and can, yes, can dream while they are reading about the life of mathematicians… for instance, this book Men of Mathematics by Bell. Okay, the stories, the lives of mathematicians are a bit arranged, like a bit of a novel, but this has made generations of kids dream about these lives.”
On recent evidence, India could do with a few kids dreaming about these lives. It may not be apparent in a culture which continually seeks intellectual self-affirmation through its hoary discovery of the zero, but the field of mathematics is not flourishing in India. “Mathematics in India is in crisis,” says Rajat Tandon, secretary of the ICM’s organising committee and head of the maths department at University of Hyderabad, “There are not enough mathematicians to go around. Good people cannot be found to fill existing positions at the senior level.”
It is an attitude reflected at the ICM, which has succeeded as an event in spite of the Indian Government. Eight years ago, when it was held in China, it was an event of national importance. Here, it has passed virtually unnoticed. The budget for the entire exercise, hosting 3,000 of the world’s best mathematicians over nine days, is a meagre Rs 6 crore. Home Minister P Chidambaram’s stringent guidelines on entry visas to India in the wake of the David Headley case have not managed to keep left wing or Islamist terror at bay, but have managed to make life difficult for prominent mathematicians trying to attend the conference. This government apathy has also ensured that the ceremony to award an honorary degree at the ICM to world chess champion Viswanathan Anand had to be postponed because some hidebound bureaucrat had doubts about his nationality.
For Tandon, the change in our attitude towards mathematics lies in our recent past, with Indians having begun to see mathematics as a tool to a very different end. “It has to do with liberalisation,” he observes, “You look around and you see money is the most important thing for most Indians. This was not true 35 years ago… we could dream. Now there is this horde for MBA degrees at the Indian Institutes of Management. I find the current set of values nauseating.”
Unsurprisingly, in a city where some of our better minds are working away on deadening backend jobs for companies such as Microsoft, the conference arouses very little interest. None of them is around to listen to Daniel Spielman, winner of the Nevanlinna Prize (the equivalent of the Fields Medal in theoretical computer science): “The rules that govern computers are the physical implementation of a certain kind of mathematics. But given the connections that emerge from other areas of mathematics, I can only say nature is miraculous.”
After the ceremony, Fields medalist Stanislav Smirnov refers to a well known piece by Eugene Wigner, The Unreasonable Effectiveness of Mathematics in the Natural Sciences: “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.” He then turns to the media and says, “The fact that the universe is understandable is a mystery we don’t understand, but in the meantime we can certainly profit from it.” What he means by ‘profit’ is certainly not what new India makes of it.