## Poincaré, Perelman, Hamilton, Yau: Knowledge Collision in the Fields of Mathematics

### December 30, 2006

“It’s just the way it is,” isn’t anymore. As I read the Nasar and Grubermanifold *New Yorker* article (2006) I was deeply moved by the life story of Gregory Perelman who can live on a $100 a month and who managed to wipe out an entire branch of pure mathematics in a few years by working alone, even isolated in the slow world. He is described as an idealist, an ascetic, a Russian Jew who lives with his mother in a gray neighbourhood of gray apartment buildings. But in this article he shines brilliantly. He may be part of the answer to my own puzzle, the ethical dilemma of being an academic in the 21st century.

Henri Poincaré created a True Knowledge Gap in mathematics, giving rise to an entire branch in his discipline when he slipped in an offhand question that became the legendary problem of the 20th century (Nasar and Grubermanifold 2006).

By the nineteen-sixties, topology had become one of the most productive areas of mathematics, and young topologists were launching regular attacks on the Poincaré. To the astonishment of most mathematicians, it turned out that manifolds of the fourth, fifth, and higher dimensions were more tractable than those of the third dimension. By 1982, Poincaré’s conjecture had been proved in all dimensions except the third. In 2000, the Clay Mathematics Institute, a private foundation that promotes mathematical research, named the Poincaré one of the seven most important outstanding problems in mathematics and offered a million dollars to anyone who could prove it.

In 1992 when Gregory Perelman (b. 1968) posted his solution to the problem on the Internet on a site used by mathematicians working with advanced concepts, he supplied enough information for the handful of minds capable of understanding to know that he had cracked it.

It took me a few days to feel I had understood enough of their article to appreciate it. I used my new Firefox add-on Gnosis.[1]

Why then did this story continue to unfold on some very messy battle Fields? Politics, power and control. To understand more fully, I worked out some of the ideas at Tim’s and in an easy chair playing with pictures. I also had to map out a brief timeline and the biographies of the main characters: Perelman, Hamilton, Yau, Tian, Zhu, Cao, Ball and Thurston. I played with the concepts of Knowledge Collisions in the Battle Fields of Mathematics but this was not about knowledge collisions on a level playing field.

Poincaré’s bagel, coffee mug handle, soccer ball and noose knot were great for starters. The table itself was easily transformed into a topology of Battle Fields. Cigars and necks protruded on the topological landscape like stalagmites. I laid a silk cloth over it all so it could drape over the edge of the table. I left a space on the table edge for a dented fender. The True Gap gaped like a crevice in an otherwise relatively level playing field. The coffee mug with its insignia of Stephen Hawkings casts a long shadow and the handle represented the branch of mathematics called topology. Since we are looking at a cross section of topological field the branch that has disappeared over the edge represents a small sorrow [2]

I didn’t know where to put Gregory Perelman my new hero, so I put a spoon in the coffee mug which he of course had stirred up. Then I balanced a swing at the top of it giving him a higher vantage point from which he can quietly survey the field. He swings slowly back and forth without those below noticing. All they can see is the spoon and the bottom of his swing. I turned him into a pearl and remembered a quote, “Not every sea has pearls . . .”

My early experiences in academia were entirely positive. It was only when I was in my fifth year of graduate studies, my second in my PhD that I began to realize the hidden power and politics behind the scenes in the ivory towers as one professor after another sought to gain control over academic and/or grant capital at any cost. I caught myself transforming campus towers into Freudian phallic symbols as I watched with dismay my PhD slipping away from me. I was disgusted mainly with my own naïvity, my lack of campus street-smarts but by then it was too late. It seems my university students in their twenties had figured it out long before I did. No wonder we all make fun of Ph.D.s!

So here I am typing away in my living room office with my old PC perched on this great glass-topped Business Depot computer desk, reflecting Mount Tzuhalem with the fire crackling off to my left and our family sound asleep. I’m emptying my PC into a dozen or more free Web 2.0 sites.

I’m not a Perelman but he is my hero. If you can only learn to live on $100 a month, keep access to the Internet, connect one’s PC’s memory to the free Web 2.0 you can sit back in the slow world and quietly watch a lifetime of experience upload to this strange virtual space we call the Internet.

Perelman’s copyright took the risk of losing his intellectual capital. For some Yau and his students really did deserve the Fields Award he received from Ball.

But for me I would rather face the perils of a Perelman Risk, tie my intellectual capital to my Creative Commons stake and at least let people share some of the amazing experiences I was privileged to have before the Fawlty Towers crumbled around me.

**Footnotes**

[1] See the article on ClearForest. I had to select a chunk of the article at a time for Gnosis to do its magic but undeniable it makes digesting lengthy, complex articles less cumbersome. At the most elemental level it is similar to the Google generated highlighted key words in .pdf files found in response to a user’s Google search inquiry. Gnosis uses a number of colour codes to highlight a number of themes which I am just trying to work out now.

[2] Its a bit like the death of a meteorite in a fiery explosion would be to the person who had named and followed the passage of the meteorite for decades.

[I have even heard on academic hearsay which is as reliable as Frank I suppose, so I should not repeat this but . . . this is not a journal it is a blog . . . an archaeologist explained to his First Nations guide (who later whispered this to me) that he would not reveal their findings in the field since it would be so hotly contested by his colleagues in his branch it would consume his entire career to defend it. Academic hearsay. Fireworks, not a meteor. Take away 5 credibility, legitimacy points from this author immediately!]

For more reading on science on Web 2.0 see yanfeng.org

**Selected webliography**

Swaminathan, Nikhil. 2006. peer_review_is_sooooo_old_school

Scientific American Blog. December 22, 2006.

Nasar, Sylvia , Grubermanifold, David. 2006.”Manifest Destiny.” *The New Yorker*: Fact. Annals of Mathematics. *A legendary problem and the battle over who solved it. *Issue of 2006-08-28; Posted 2006-08-21; accessed December 22, 2006.

July 2, 2010 at 9:45 am

In the popular versions of Perelman’s work (NYT, WaPo, USA Today…), there is not even a mention of the controversy sorrounding the proof of the Poincare conjecture or how a competing research group tried to pass Perelman’s proof as their own.

How Clever.

Why did Perelman reject the award? Oh, he is just a recluse.

How convenient.

Grigory is not just stopping with his contribution to mathematics. By rejecting this “award,” he is making a tremendous contribution to ethics in mathematics, science and other

research oriented disciplines. He *is* doing something about it by bringing the cheating, stealing and plagiarism of other people’s original ideas into the glare of public light. The

best way for progress is by shaming the research community. The fruits of this shame will be worth more than a million dollars and it will be a benchmark and a warning for

generations to come.

Bravo Grigory!

July 2, 2010 at 6:09 pm

“In 1992 when Gregory Perelman (b. 1968) posted his solution to the problem on the Internet”

2002, not 1992.