PRIZE WITHOUT WINNER

Science helps us make sense of the world around us and make it better. However, it is becoming increasingly difficult to impress us with the wonders of technology. Primeval natural phenomena, like lightning, are a different matter. They flash and inevitably light you and your place in the world. ‘Lightnings’ like these might be the most precious science of today.

Event

The world is getting weary of news. “Why bang on the door like this?” A thousand years ago a message barged in on you with the thud of a horse’s hoofs and a shuddering breath of a dead tired messenger; half a century ago a teletypewriter was rattling away to get your message delivered. Today all of this has been reduced to a quiet ‘blip’ of an incoming email. On 12 November 2002 about ten people heard this blip. They read an email saying, among other things, that ‘... we are also checking several statements of the programme for proving Thurston's geometrization conjecture for a closed 3-manifold...’

It is unlikely that anyone in the world except for those ten people could fully grasp the importance of this message, but it goes without saying that all of them were utterly amazed. The sender was informing them, in a rather cold manner, that he had proven the Poincaré conjecture.

Problem

A physicist or a chemist can, with some effort, explain what their work is all about to a milkmaid or even an art historian. Modern mathematicians, however, do not have this privilege to be understood. Maths that we use in everyday life was essentially developed by ancient Greeks and Frenchmen of the D’Artagnan era. Even the most advanced engineering professions use maths of the 19^th century and partly of the 20^th century. Modern mathematics, however, is definitely ahead of its time. Mathematical abstractions have reached the level where any layperson trying to comprehend them would almost certainly result in a headache.

The conjecture suggested in 1904 by a French mathematician Henri Poincaré states that every simply connected, closed 3-manifold is homeomorphic to the 3-sphere, without breaking a range of rules. A sphere is the surface of a unit ball: circumference is a one-dimensional sphere, leather or plastic the unit ball is made of are examples of two-dimensional spheres. A three-dimensional sphere is a surface of a four-dimensional ball, while a manifold is a surface of any object. If the manifold is three-dimensional, then the object will be four-dimensional.

Ideally we also need to understand what ‘simply-connected’ and ‘closed’ mean, as well as the what rules of transformation are. Unfortunately, this wouldn’t leave us enough space for the airport news or an article on spine treatment in this issue. Besides, you might get carried away and forget all about where you are going and who you are.

The problem with proving the Poincaré conjecture was not only the fact that is about some strange four-dimensional things. Six years later it was proved for spaces with six or more dimensions. In 1982 mathematician Michael Freedman, 31, proved it in dimension four. However, Poincare was talking about dimension 3, and this seemed to be the dead end.

Tens and hundreds of mathematicians dreamt about solving this problem, to them everything else paled into insignificance. Such was their ambition and excitement that they simply couldn’t let it go.

It was an unconquerable mountain, its slopes being covered with dead climbers. Obviously, nobody died for real, but the conjecture has devastated many people’s careers. Mathematicians obsessed with this problem spent their whole lives in fruitless attempts and as a result were left with nothing.

Almost a century after it was first proposed, in 2000, the Poincaré conjecture was included into the seven Millennium Prize Problems, for which the Clay Mathematics Institute (a private, non-profit foundation funded by a Boston businessman Landon Clay, which is dedicated to increasing and disseminating mathematical knowledge) a offered a $1,000,000 prize for the first correct solution. The mathematical community was on the verge of concluding that the conjecture was insoluble or that it would be another 100 years until it could be proven, which was the case with the famous Fermat theorem.

The emails confirming that the Poincaré conjecture had been proven were sent two years after that, and the sender was a Russian mathematician Grigory Perelman, from St. Petersburg.

Ivory towers

Genius is thought to be a volatile mixture of nature and nurture. As far as the ‘nature’ is concerned, it is possible that Grigory inherited his mathematical gift from his mother, who was a promising mathematician.

However, she sacrificed her academic career for the sake of her son and went to teach at a vocational college. Quite naturally, when Grigory’s mathematical talent became apparent, she wanted to believe that he would achieve what she could not. She inspired her son and protected him from the everyday and the trivial. Most importantly, when Grigory was 10, she enrolled him in the afterschool maths classes in Leningrad Palace of Pioneers.

The USSR could boast several unique types of educational know-how: specialised physics and maths schools, scientific afterschool classes and a system of ‘Olympiads’ that aimed to identify the brightest children. However, all these methods were an exception rather than the rule: the Soviet schools in general adopted the one-size-fits-all approach and were quite good at strangling any talents. The lessons were designed to cater for the lowest common denominator, and the most intelligent children quickly got bored. Besides, the Soviet school system was there to instill collective spirit and absolute obedience, which is why any inkling of individuality, inquisitive mind or reluctant socialising were punished.

This is how an alternative educational system with its ‘genius incubators’ came about. The Olympiads developed not just an enthusiastic but obsessive attitude to mathematics. The element of competition was a great driver for children, as well as their parents and mentors. The legendary Leningrad maths club did not tolerate other interests in children: if, apart from the maths club, you also went to the chess club, you had to choose. Teenage members were punished for any attempts to get in contact with the opposite sex. The idea behind these measures was that in the modern world you had to concentrate to become a truly great professional and win.

At the end of the day, these children were taught to be themselves. After the release of Rain Man the world found out what psychiatrist had known for a long time already – that autistic people often had exceptional mathematical talents. However, the converse is also true: great mathematical skills are not possible without a certain degree of autism. The brain cannot sit on two stools: either it works on a mathematical problems or it is busy communicating with others. Besides, the world of the people is illogical and far from concrete. When we are trying to understand others, we destroy the gift for maths and logic.

In 7 years Grigory Perelman grew to be the USSR Maths Olympiad and the International Maths Olympiad winner, while his failures were exceptionally rare. In the light of these facts his outlook and his attitude towards himself were understandable. He got used to the idea that the knowledge and talent get a quick, fair and unquestionable appreciation, like it was at the maths Olympiads. He then realised that he could be a judge for himself – if he made a mistake, he worked hard to find it.

After school and university Perelman got a job at a research institute, and in the 90s he moved to the US. He became a part of the world’s academic elite, but there were two unpleasant surprises in store. He counted on a permanent tenure in an American university, but the very same people who spoke so highly of his achievements asked him to send his CV. He just couldn’t understand what good the CV could do if he was known all over the world. In addition to that, he did not succeed in the path that he had chosen.

He returned to Russia and virtually stayed out of touch with his colleagues. Until that very letter.

This is not an award

It took his colleagues almost a year and a half to get their heads around the proof that he had published – Perelman had even predicted how long it would take them.

There was one thing, however, that he couldn’t possibly fathom. Perelman’s predecessors that besieged the Poincaré conjecture refused to accept his success. We are only human, so it is understandable: they spent dozens of years working on the problem, while Perelman only spent several years. However, Grigory did not think of them as humans: to him they were mathematicians.

It was getting more and more interesting: a group of Chinese mathematicians announced that it was not Perelman who had proven the conjecture, but their group. As an evidence, they provided the works written on the basis of Perelman’s publications. They claimed that he had not taken the final step, which they had to take. The gurus of mathematics only vaguely commented the situation, not wanting to disagree with the influential ‘Chinese mathematical mafia’. Finally, somebody published an Internet article with a detailed analysis of the Chinese publication. It became apparent that, besides having failed to prove anything, they actually ‘borrowed’ quite a lot from the first comments on Perelman’s work.

After that, Perelman was inundated with offers from foreign universities, and even more people just wanted to give him money. He refused. He didn’t want to become somebody’s trophy or a part of somebody’s PR campaign.

Meanwhile, the Clay Mathematics Institute announced the beginning of a two-year period that had to pass after the solution to one of the Millennium Prize Problems was found and before the prize was awarded, so that there was time to find possible mistakes. Two years have passed, and no mistakes have been found. The Institute announced that it was going to award the one million dollar prize to Grigory Perelman.

However, Perelman refused to accept the prize or inform the Institute on what to do with the money. Neither did he accept any other award. Moreover, he gradually stopped talking to anyone who was trying to convince him to accept the prizes. Now he doesn’t see anyone except his family.

Based on the bits and pieces of information circulating around, one could make an assumption as to why he did not accept the money. Having published the proof, he claimed that the proof was correct. But instead of accepting this, his colleagues started checking his calculations to decide whether he, Perelman, deserved the prize. To make matters worse, this was mostly done by the people who weren’t even close to solving the Poincaré conjecture. From Perelman’s point of view there is only one person who can assess his work and award him a prize, and he had done that before all the fuss began. This person is Perelman himself.

You could ask a different question – what is a million dollars? Jennifer Lopez earns 20 million for showing off her butt in a new film. It follows that Perelman’s colleagues were trying to tell him that his genius was worth about a twentieth part of Lopez’s rear. This is truly a great lesson in life. Dear reader, when next time your boss gives you a bonus, get your calculator out and see what part of Jennifer Lopez’s butt you are worth, and think of what had the people who made this decision had achieved in their field of work.

“…Oppression be revenge for his departure”

Amidst the media hysteria around the prize Perelman left the Institute where he was on payroll. He announced that he was not going to do mathematics anymore.

Nobody knows what he is up to these days, except for his family. Rumour has it that after the media has lost interest in him, he started to venture outside and he can be seen walking along the banks of Neva on the outskirts of St. Petersburg.

Many people would shrug their shoulders and say that the rules are in place for everyone, genius included. But the real question is whether the humanity needs the genius or the genius needs the humanity. The ever triumphant all-out ‘levelling’ averts geniuses and talented people. After all, it is not even the money they are after – they are happy being recognized for something they do better than others. Unfortunately, ‘others’ would never admit this.

It looks like Perelman is doing just fine without the humanity. In a hundred years or so we’ll find out whether the humanity can do without geniuses.