11:36 PM | Author: Siva
It is this problem "Poincare's Conjecture" that started it all. The problem is in the area of topology. I am not going to pretend to understand this area. The problem has been in the list of millenium problems of Clay Mathematical Institute and it was open for nearly 100 years vouches for the difficulty of proving it. Then Grigori Perelman, a Russin mathematician, claimed he had a proof for the conjecture and started posting them in arXiv. It is not the usual way. Especially when you have proof for one of the toughest problems around you don't just post it. You will normally publish it in a peer reviewed journal. But he chose not to do that. He just posted the proofs and then gave a series of lectures in US about it. That is all he did. He never attempted to publish it. All this happened way back in 2002.

It took 3-4 years for some great people to verify it and convince themselves that the proof is correct. But these 3-4 years didn't go without controversies. Grigory Perelman had used Richard Hamilton's earlier works in the field as a basis to prove the conjecture. There were other proofs. Recently when Perelman was awarded the Fields medal there was an article in New Yorker by Sylvia Nasar (It is a long one, but will give you some background) . This had some serious allegations against Harvard Mathematician Dr.Yau. Dr.Yau was one of the collobarator and friend of Hamilton. Two of his other students worked on the proof too and recently published the proof in a journal where Dr.Yau is the chief editor. Some people find the proof similar to Perelman's proof. Dr.Yau is a Fields medalist himself. That is the highest honor in math. What is his motivation for wanting more ? I don't see any. The article says

“It’s all about their primacy in China and their leadership among the expatriate Chinese,”

Now that is some serious allegations against an eminent mathematician. Another quote says

“Yau’s not jealous of Tian’s mathematics, but he’s jealous of his power back in China.”

Dr.Tian is Dr.Yau's student. Every teacher will be proud his student's achievements. I doubt they will be jealous. Dr.Yau supporters' letters are in his web page. But so far there is no letter from the student objecting the Newyorker article which is suspicious. Meanwhile, Perelman didn't accept the Fields medal.

Meanwhile The New York Times has another article with the title Emperor of Math.(Again a long one, this supports Dr.Yau) The subsection on Poincare's Conjecture is with a title "Messy Proof". It is unfortunate for such a problem's proof to be in this controversy.

When I started my higher studies, academics appeared to be a field where there is no groupism, politics, greed. Especially mathematics departments where materialistic things like a Benz is often frowned upon and bicycle is the preferred mode underlined those beliefs. Sadly, all of those problems exist. It is not to a level they affect the work done in these departments. But they do exist. It is rarely for money. But sometimes for power, fame and legacy. Hope they remain too small to affect the work done in these departments.
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2 comments:

On 5:14 PM , senthil said...

I'm really interested in what you wrote here. Any man worth his salt is always trying to prove his intellectual, material and if feasible, physical superiority over his fellow human beings. I believe this as the basic tenet of living. When you are in the field of scientific research, this is natural. But judgement of a scientific researcher about the motives of doing some research is not something which seems to be the right thing to do. Critics are a group who are actually doing this job. But I believe they often forget what they are supposed to be judging. Dr.Yau might have thought that his proof might be better. Who knows! If this world only had researchers, there would not have been any kind of politics or greed or any other thing of that kind. But in this world, the scientific field consists of the researcher, the donor for the research, the critic and the enduser (anything ranging from a big company which can use the research to another mathematician). Now, when the researcher is being constantly judged by his last work, he would naturally like to appease his customers (donor, critic and end user). And hence we have a lot of non-sense.

 
On 11:36 AM , Siva said...

Senthil
One small correction to what you said. It is not Dr.Yau who has the new proof. But it is students. But you guessed corect. He mentions their proof is better and complete.

As far as the basic tenet of living you mentioned it is true for most of the times. But sometimes when you are attacking problems of this stature it is like you vs the problem. A lot of people believe that just solving it is the best motivation.

But it appears, as it involves humans, that motivation is not sufficient and once the problem is solved your basic tenet will take over.

Another thing I wanted to clarify - funding and acknowledgement from end users are factors for budding researchers. All those involved in this controversy are highly accomplished. Funding organizations like NSF will be more than willing to fund them anytime. They will always be remembered for their other contributions by fellow mathematicians. Leave critics for now.

Still they follow that basic tenet. Why ? I think it is because of the fame associated with solving such problem. You will always be remembered as the guy who solved Poincare. It is sad. But, yes, it is the need of intellectual superiority that is driving this whole thing.