* Masha Gessen:A Genius and the Mathematical Breakthrough of the Century

Perfect Rigor:






In 2006, an eccentric Russian mathematician named Grigori Perelman
solved one of the world's greatest intellectual puzzles.


The Poincare conjecture is an extremely complex topological problem
that had eluded the best minds for over a century.


In 1998, the Clay Institute in Boston named it
one of seven great unsolved mathematical problems,
and promised a million dollars to anyone who could find a solution.


Perelman will likely be awarded the prize this fall, and he will
likely decline it.


Fascinated by his story, journalist Masha Gessen was determined to find out why.


Drawing on interviews with Perelman's teachers,
classmates, coaches, teammates, and colleagues in Russia and the US
--and informed by her own background as a math whiz raised in Russia--
she set out to uncover the nature of Perelman's genius.


What she found was a mind of unrivalled computational power,
one that enabled Perelman to pursue mathematical concepts
to their logical (sometimes distant) end.


But she also discovered that this very strength has turned out to be
his undoing:
such a mind is unable to cope with the messy reality of human affairs.


When the jealousies, rivalries, and passions of life intruded on his
Platonic ideal,
Perelman began to withdraw--first from the world of mathematics
and then, increasingly, from the world in general.


In telling his story, Masha Gessen has constructed
a gripping and tragic tale that sheds rare light on the unique burden of genius.




A Question & Answer with Masha Gessen, Author of Perfect Rigor:
A Genius and the Mathematical Breakthrough of the Century




Q: Grigory Perelman doesn't talk to journalists. How did you write this book?


A: Actually, at this point he really talks to no one.
When I first started researching the book,
he was still speaking to his lifelong math tutor,
his competition coach and, in many ways,
the architect of his life, Sergei Rukshin.


But sometime in the last couple of years,
Perelman stopped talking to him.


As far as I know, the only person
with whom he is in permanent contact is his mother,
with whom he shares an apartment on the outskirts of St. Petersburg.


Fortunately, while I had no access to Perelman,
I talked to virtually all the people who had been important in his life:
Rukshin, his classmates, his math-club mates, his high school math teacher,
his competition coaches and teammates, his university thesis adviser,
his graduate school adviser, his coauthors, and those who surrounded him
in his postdoc years in the United States.


In some ways, I think, these people were more motivated to speak with me
because Perelman himself wasn't doing it--and because they felt
his story had been misinterpreted in so many ways in the media.


Q: So not being able to talk to him was an advantage?


A: Funny as that sounds, in some ways, yes.
When you write a biography of a cooperating subject
--even if it is just a magazine story, never mind a book--
you are in constant negotiation with that person's view of himself.


And people tend to be terrible judges of themselves.


So you are always balancing your own perceptions
against the subject's aspirations,
and this can actually get painful for all involved.


All I had was research material and my own perceptions.


In this sense, this was more like writing a novel: I was constructing
this character.


Q: What made you think you could do this?


A: Actually, I made two erroneous assumptions.


I assumed that the journalists who initially wrote about Perelman,
around the time when he turned down the Fields Medal,
mathematics' highest honor, were wrong.


I assumed he was not as crazy, or as weird, as they made him sound.


I figured he was a familiar type of Russian scientist
--entirely devoted to his field, not at all attuned
to social niceties and bureaucratic customs,
and given to behaviors that can easily
be misinterpreted, especially by foreign journalists.


My second assumption, related to the first,
was that my background as a Russian math school kid
gave me the tools necessary to describe this type.


My background certainly helped--I am Perelman's age,
I come from the same kind of family, socially,
economically, and educationally, as he does
(Russian Jewish engineers with two children
living on the outskirts of Leningrad in his case
and Moscow in mine)--but it was barely a start.


Because Perelman turned out to be much stranger than I assumed.


Q: So he is as crazy as they say?


A: I think crazy generally means that a person
has an internally consistent view of the world
that is entirely different from the view most people consider normal.
I think this is true of Perelman. The interesting thing, of course,
was to figure out what this internally consistent view of the world was.


Q: And did you manage to figure it out?


A: I think so. I concluded that this view,
and the rigidity with which he holds to it,
is actually directly related
to the reason he was able to solve
the hardest mathematical problem ever solved.


He has a mind that is capable
of taking in more information,
and embracing more-complex systems,
than any mind that has come before.


His mind is like a universal math compactor.


He grasps hugely complex problems
and reduces them to their solvable essence.


The problem is, he expects the world of humans
to be similarly subject to reduction.


He expects the world to function
in accordance with a set of strictly laid out rules,
and he absolutely cannot take in anything
that does not conform to those rules.


The world of humans is unruly, though,
so Perelman has had to cut off successive chunks of it
until all that was left was the apartment he shares with his mother.


Q: Is that quality of his mind what the title of the book refers to?


A: Yes, it's that "perfect rigor".
But in fact that phrase comes from a quote by Henri Poincare,
he of the Poincare Conjecture fame--from his ruminations
on the nature of mathematical proof, which I quote in the middle of the book.


Q: So what is the Poincare Conjecture?


A: It is no more, actually. Now that Perelman has proved it, it is a theorem.


And it is a classic theorem of topology, one of the most wonderfully
weird mathematical disciplines.


Topology, to my mind, is something like the perfect mathematical discipline.


It leaves nothing to reality: though it deals with shape,
you never measure objects in topology--not with a ruler, anyway.


Rather, the concepts of topology are the products of their verbal definitions.


And much of topology is concerned with things
that are essentially the same as other things,
even if at particular moments in time they happen to look different.


For example, if you have a blob that can be reshaped into a sphere,
then the sphere and the blob are essentially similar,
or homeomorphic, as topologists say.


So Poincare asked, in essence,
whether all three-dimensional blobs
that were not twisted and had no holes in them
were homeomorphic to a three-dimensional sphere.


And it took more than a hundred years to prove that yes, they were.


Q: So? What's the use of something so abstract?


A: Mathematicians hate that question.


Mathematics is not here to be useful. It is beautiful, and that's enough.


But the fact is, such discoveries
generally have far-reaching--useful--consequences
that are rarely evident at the moment of the breakthrough.


The Poincare Theory will almost certainly
have profound consequences
for our understanding
of space--the universe that we inhabit.


Q: And Perelman will be awarded a million dollars for this proof?


A: Probably. And he will probably turn it down.


The commercialization of mathematics offends him.


He was deeply hurt by the many generous offers
he received from U.S. universities after he published his proof.


He apparently felt he had made a contribution
that was far greater than any amount of money
--and rather than express their appreciation
in appropriately mathematical ways,
by studying his proof and working to understand it
(he estimated correctly that it would take specialists
about a year and a half to understand the proof),
they were trying to take a shortcut and basically pay him off.


By the same token, the million dollars will probably offend him.


At the same time, if he chose to accept the money,
he would find a way to make that consistent
with his system of rules and values.


But I really don't think this is likely.


----


Review
Gessen, Masha


PERFECT RIGOR: A Genius and the Mathematical Breakthrough of the Century


The story of Russian mathematical prodigy Grigory Perelman,
who solved a problem that had stumped everyone for a century
—then walked away from his chosen field.


Gessen (Blood Matters: From Inherited Illness to Designer Babies,
How the World and I Found Ourselves in the Future of the Gene, 2008, etc.)
tells Perelman’s story from the viewpoint of a former student
in the educational system of which he was a product.


Soviet mathematicians worked in isolation
from their Western counterparts during the Stalinist era,
but were encouraged because of their value to the state.


Perelman, an unusually gifted student,
was identified early and his talent nurtured,
even though, as a Jew, he faced
crippling handicaps under the Soviets.


He won the attention of an innovative math coach, Sergei Rukshin.


The coach and student bonded early,
and Perelman was accepted at a prestigious university
and then at a top graduate school.


As a star, he was allowed an unusual degree of eccentricity,
which in his case included an almost total disregard of other people.


Numerous contemporaries attest to his fanatical adherence
to a set of ideals that essentially ignored the realities of the Soviet state.


Politics, prejudice,
making friends and getting ahead in the world
—these meant nothing to Perelman.


During postdoctoral work in the United States,
he refused to cut his hair and nails
and turned down job offers
because he felt it
beneath his dignity to apply for them.


Meanwhile, he was homing in
on a solution to the Poincaré Conjecture,
a topological riddle so puzzling
that the Clay Institute in Boston
offered a $1 million prize to anyone
who could solve it.


When, in 2002,
Perelman posted a solution on the Internet,
he seemed to expect instant recognition.


Instead, the world’s mathematicians meticulously checked his proof,
which Perelman took it as an insult and turned down
a Fields medal, the math equivalent of a Nobel.


To this day, there is significant doubt
about whether he will accept the Clay prize.


Though Gessen was unable to interview her subject,
she paints a fascinating picture of the Soviet math establishment
and of the mind of one of its most singular products.


An engrossing examination of an enigmatic genius.


(Agent: Elyse Cheney/Elyse Cheney Literary Associates)


(Kirkus Reviews 20091101)


Gessen, Masha. Perfect Rigor: [A Genius] + [The Mathematical
Breakthrough of the Century].
Houghton Harcourt. Nov. 2009. c.256p. index. ISBN 978-0-15-101406-4. $26. MATH






The "genius" here is Russian mathematician Grigory Perelman,
who announced in 2002 a proof of the Poincaré Conjecture,
a complex problem that had resisted the best efforts
of the world''s mathematicians for almost a full century.


Strangely, since that moment of apparent triumph,
Perelman has progressively withdrawn
from contact with the mathematics community
and with most other humans as well.


Russian American journalist and author Gessen
(Slate, New Republic; Blood Matters)
now tells of Perelman''s very unconventional life and career.


Denied access to Perelman himself,
she interviewed many people
who knew him as a student
and (later) as a researcher.


Gessen details the special Russian schools
for young mathematical prospects
that Perelman attended and describes
apparently incorrigible Russian anti-Semitism.


Most important, the gist of her excellent discussion
of the Poincaré Conjecture and its proof should be intelligible
even to readers lacking a background in higher mathematics.


VERDICT General science buffs curious
about how researchers go about creating new mathematics
or about the eccentric personalities in this field will be fascinated
by Gessen''s book.


More advanced readers can also turn to Donal O'Shea's `
The Poincaré Conjecture: In Search of the Shape of the Universe?
Jack W. Weigel, Ann Arbor, MI