This hairy hermit could save maths
By Simon Singh
Guardian 17/08/2006
The Russian Grigory Perelman is being called the cleverest and craziest
person on the planet. He has come up with the greatest mathematical
proof of the 21st century, while sporting the sort of facial hair that
makes him look like Rasputin's twin. He has been offered the most prestigious
prize in mathematics, but it is unlikely that he will bother to claim
it.
The reclusive Perelman is reinforcing the stereotype that mathematical
geniuses are strange eccentrics, and he seems to be exactly the sort
of person who puts people off maths. At a time when Europe is trying
to encourage young people to study maths, why can't our topnotch mathematicians
be beautiful, witty extroverts? Why can't they drive around in fast
cars and fill the tabloids with gossip about their Hollywoodstyle orgies?
Realistically, mathematicians are never going to be very glamorous,
and moreover it could be that Perelman is exactly what mathematics needs
in order to promote itself. Perversely, however, I believe that this
hairy Russian hermit could be the poster boy who helps create a new
generation of mathematical geniuses. First, it is clear that Perelman
is a genius. It is widely accepted among scholars that he has solved
the notorious Poincaré conjecture, which had mathematicians baffled
for more than a century.
The conjecture is about spheres that live in a higher dimension. Although
mathematicians knew how to define a normal threedimensional sphere,
it had been hard to pin down the properties of the fiendishly abstract
fourdimensional sphere, until Perelman came along. His proof of the
Poincaré conjecture runs to several hundred pages of dense mathematics
and is considered a mathematical masterpiece.
In 2000, to add some glitz to numbercrunching, the Clay Mathematics
Institute in America offered seven Millennium Prizes of $1 million each
for the solutions to seven major problems in mathematics, including
the Poincaré conjecture. None of the other problems are close
to being solved, so Perelman would be the first to claim $1 million,
but he has shown no interest in becoming a millionaire and spurned any
approaches by the prize organisers.
The majority of the population will find this type of behaviour bizarre,
and it will serve only to reinforce their antipathy towards mathematics,
mathematicians, all numbers bigger than a million and any polygon with
more than four sides. Unfortunately, mathematicians are never going
to be fun, cuddly folk who appeal to the masses, because what they do
is inherently extremely esoteric.
More importantly, however, Perelman might appeal to a small, but critical,
audience  namely the tiny fraction of the teenage population who have
a talent and enthusiasm for abstract mathematics. They are currently
awaiting their exam results and wondering what to do next. Those around
them might be saying that studying mathematics could lead to a career
as an accountant (which is an important profession) or perhaps to becoming
a teacher (an even more important job), but these opportunities are
not necessarily going to inspire every mathematically inclined teenager.
In contrast, Perelman shows that studying mathematics can also offer
another path. It can lead to a romantic, obsessive lifestyle that is
on a par with being a poet or a musician. Perelman spurns money, medals
and honours, because the highest reward for him is simply the opportunity
to create wonderful mathematics.
Perelman is not unique  the history of maths is full of heroes who
exhibit a purity of spirit and utter determination that make mathematics
the sexiest discipline on the planet. For example, Sophie Germain had
to disguise herself as a man in order to overcome the prejudices of
early19thcentury Paris and make discoveries that eluded earlier generations.
At roughly the same time, the 20yearold Evariste Galois knew that
he was going to die in a duel and spent his final night writing down
all his mathematical ideas. If he was going to die, then he did not
want his maths to die with him, and, sure enough, his radical ideas
continue to influence modern research.
More recently, Paul Erdõs, the most prolific mathematician of
the 20th century, shared many of Perelman's traits. He worked for 19
hours a day, fuelled by coffee and amphetamines. Erdõs would
often say: "A mathematician is a machine for turning coffee into
theorems." His entire belongings fitted easily into two battered
suitcases, and instead of buying a house, he lodged with fellow mathematicians.
His motto was: "Another roof, another proof."
Erdõs was not interested in wealth and gave away his money by
offering rewards for the solution to various problems. Once, when the
outstanding rewards totalled $15,000, a colleague pointed out that Erdõs
would be bankrupted if all his problems were solved, to which he replied:
"But what would happen to the strongest bank if all the creditors
asked for their money back? The bank would surely go broke. And a run
on the bank is much more likely than solutions to all my problems."
The last time that mathematics had a hero figure was when Andrew Wiles
proved Fermat's last theorem, which required seven years of secret devotion
and a similarly formidable proof. Although Wiles has accepted his prizes,
totalling several hundred thousand dollars, his real motivation was
mere curiosity and the desire to explore the uncharted regions of the
mathematical universe. Wiles, Erdõs, Germain, Galois and Perelman
all share a desire for knowledge and wonder, as opposed to money and
fame.
Next week Perelman will get another chance to show his disdain for baubles
and fancy prizes, because it is likely that he will be offered the Fields
Medal  the mathematical version of the Nobel Prize. Perelman has already
refused to give a lecture at the International Congress of Mathematicians
in Madrid, where the medal is to be awarded, which means that he will
probably refuse to accept the medal. It will be the ultimate act of
defiance, as the Fields Medal can only be awarded to mathematicians
aged 40 or less, and Perelman's 40th birthday was earlier this summer.
