# Solving an Old Math Problem Nets Award, Trouble

The journal *Science's* "breakthrough of the year" for 2006 is the solution of a century-old math problem. The story behind the solution is quite a soap opera. It includes a Harvard math wizard, a reclusive Russian genius, a $1 million prize, an award-winning journalist and *The New Yorker* magazine.

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From NPR News, this is ALL THINGS CONSIDERED. I'm Robert Siegel.

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And I'm Melissa Block.

Every year the journal Science selects a breakthrough of the year. This time it's the solution of a century old math problem.

NPR's David Kestenbaum is digging into the story behind that solution and it is quite a soap opera. It involves a Harvard math wizard, a reclusive Russian genius, a million dollar prize, an award winning journalist, The New Yorker magazine and, of course, a lawyer.

DAVID KESTENBAUM: In August, The New Yorker magazine published a 14 page article called “Manifold Destiny: a Legendary Problem and the Battle Over Who Solved It.” The article is written by Sylvia Masser, whose book “A Beautiful Mind” inspired a blockbuster movie. She wrote the article with a science writer who had been a student of hers.

The legendary math problem is the Poincare Conjecture laid out by Henri Poincare back in 1904. Many tried to solve it and failed. Here's how Shing-Tung Yau describes it. He's the Harvard mathematician in this story.

Mr. SHING-UNG YAU (Harvard Mathematician): Poincare Conjecture is considered to be the Holy Grail of Geometry and Topology. For many topologists, they consider that to be their lifetime goal.

KESTENBAUM: Also it's worth a million dollars. A mathematics institute has an outstanding award for solving it. The Conjecture has to do with objects that could exist in four dimensional space. That's one more dimension than we have in real life so it is impossible to visualize this. But the challenge is to prove that every twisty-turny shape that doesn't have a hole in it can be reformed into a kind of sphere.

In 1982, a mathematician named Richard Hamilton proposed a new approach to solving it. It was revolutionary. He would use the sort of equations that governed heat flow in physics to smooth out the mathematical shapes. Hamilton has a reputation as a kind of surfer mathematician. Yau and Hamilton worked on the problem together, sometimes far from the chalkboard in Hawaii where Hamilton had a house.

Mr. YAU: And we worked together on a beach under coconut tree. It was nice setting, but it was hot. It was not what people think that we were just relaxed.

KESTENBAUM: Yau wrote a Chinese poem about this period. He describes Hamilton looking utterly exhausted. Quote, “The road was long and the sky far away.”

Hamilton made considerable progress over the decades but could not find his way past the remaining obstacles.

Then suddenly in 2002 came a mysterious mathematical paper published on the Internet. It was written by a Russian mathematician who had dropped out of sight named Grigori Perelman. Perelman published two more papers. The work appeared to break through the remaining barriers. Perelman made a trip to the United States. He had a beard and long fingernails. John Morgan met Perelman on that trip. Morgan is chair of the math department at Columbia University and talked to NPR this summer.

Mr. JOHN MORGAN (Columbia University): He worked for five or seven years, I'm not sure how long, incredibly intensively on this and he's incredibly brilliant and powerful, and he did something that I don't think anybody else could have done.

KESTENBAUM: Many people had doubts about Perelman's papers. They were spare and didn't spell things out. Yau couldn't tell if Perelman had in fact completed the proof of the Poincare Conjecture.

Mr. YAU: I could not know how to put the proof together presumably because I'm stupid. I'm not good enough to understand it. But most of the people of the best minds in the world had difficulty to put the proof together.

KESTENBAUM: There were only a handful of people in the world with the expertise to judge whether the Poincare Conjecture had been proven. Yau encouraged two of his protégées to flush out Perelman's arguments, Huai-Dong Cao and Zhu Xi-Ping. It took two years.

They've now published a 328-page paper titled in part “A Complete Proof of the Poincare”. Two other groups published similarly long explanations. Today mathematicians agree, Perelman's brief papers contained the final solution. But who should get the credit? Richard Hamilton, who came up with the approach and labored under the coconut tree? The Russian, Grigori Perelman, who carried it over the finish line? What about the Chinese mathematicians and the others who flushed everything out? What about Yau who helped lay the groundwork for the entire field?

Here's where The New Yorker magazine comes in. It tackled the question in its August issue. The story suggested that Yau was trying to steal the spotlight. A full-page cartoon in the article captures the tone. It shows the Russian mathematician Grigori Perelman with a medal around his neck and Shing-Tung Yau of Harvard grabbing the medal. Yau remembers getting a copy of the magazine from the newsstand and feeling shocked.

Mr. YAU: I was totally amazed because I forced to to write only about the Poincare Conjecture.

KESTENBAUM: Did you feel the article was inaccurate?

Mr. YAU: Yes.

KESTENBAUM: The article caused a big fuss. Mathematicians felt it made them look bad and petty at a time when they should be celebrating a major achievement. Some saw the article as a hatchet job. One called it hideously unfair.

But Yau is a controversial figure in the math world. He's gotten into some academic scrapes in China, and some colleagues feel there have been times when he could have been more generous about acknowledging the work of others.

One key moment in the New Yorker story takes place at a press conference in China. It touches on the question of who deserves credit for solving the Poincare Conjecture. The New Yorker quotes a Chinese mathematician as saying that Yau and his protégées deserve 30% of the credit for solving the Poincare Conjecture. And it quotes Yau himself, apparently affirming this, saying, quote, “that Chinese mathematicians played a 30% role is by no means easy.”

Yau says Sylvia Masser, the New Yorker writer, was not at the conference, was not even in China, as far as he knows. And he says those quotes are flat wrong.

Did you say that?

Mr. YAU: No.

KESTENBAUM: Did you say anything like that?

Mr. YAU: No, not at the press conference.

KESTENBAUM: Did you say it at any time?

Mr. YAU: There could be a misunderstanding of what things were said.

KESTENBAUM: Yau says he may have later said something about Chinese mathematicians playing a big role in the field of Geometry.

Mr. YAU: I was trying to encourage the Chinese youngsters. China is a huge country with many, many young mathematicians. They are beaten and they need to be helped.

KESTENBAUM: Yau says he did not mean to downplay Perelman's contribution.

Mr. YAU: Perelman's idea is truly original and genius, so we are happy with that.

KESTENBAUM: And this is where a lawyer gets involved with a hundred year old math problem. Shing-Tung Yau hired an attorney who is now trying to get an apology from the New Yorker and correction of what he says are errors. Fifteen mathematicians have written letters defending Yau.

Mr. DAN STRUCK (MIT): Yau is a very robust mathematician.

KESTENBAUM: Dan Struck is a mathematician at MIT.

Mr. STRUCK: He has a muscular approach to problems and I have often felt that he solves problems by scaring them to death.

KESTENBAUM: Struk wrote, “like the rest of us, Yau has his fauls. But unlike most of us, his virtues out weigh his faults.”

The New Yorker article covers a lot of ground and Yau has a long list of complaints. We looked in at that quote at the press conference. NPR translated an audiotape of the press conference provided by Yau. It does not include any references to percentage credit. We interviewed the other mathematician who is quoted at the press conference, who denies anything about percentage credit.

Sylvia Masser declined repeated requests for interviews for this story. The New Yorker issued a statement saying it stands by the story. The magazine said it was the result of approximately 100 interviews. Some mathematicians we spoke to chalk the dispute up to differences in style, mathematical style. Here's Dan Struck from MIT.

Mr. STRUCK: Yau comes from a tradition in which you build empires. That's part of being a great mind, and this is really counter to the post 1960s culture of mathematics where you're supposed to be just one of the fellows and nice guy and everybody does beautiful work. Yau doesn't take that point of view. He thinks highly of some people and he thinks poorly of others and he does not make much effort to hide his opinion of either.

KESTENBAUM: Mathematicians often talk about that transcended nature of mathematical truth. But the daily labor is done by humans with all of the attendant complications. Henri Poincare wrote thought is only a flash in the midst of a long night, but this flash is everything.

David Kestenbaum, NPR News.

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