THE CORE QUESTION COMES TO WHAT HAVE THEY EACH DISCOVERED OR DEVELOPED OR INVENTED? IF ALL THE FRAME WORK FOR THE PROOF OF POINCARE CONJECTURE IS LAID OUT AND THE TOOLS ARE HANDILY AVAILABLE, THEN PROVING THE POINCARE CONJECTURE IS JUST LIKE WORKING ON AN EXTREMELY LENGTHY OLYMPIAD MATH PROBLEM, WHICH REQUIRES ONLY TIME AND EFFORT BUT LESS INGENUITY.
HAMILTON--HE IS THE FOUNDER OF RICCI FLOW; PERELMAN--REVOLUTIONARY WORK ON Thurston's geometrization conjecture, a result that includes the Poincaré conjecture as a particular case. THESE ARE ALL THAT YOU NEED TO PROVE THE POINCARE CONJECTURE.
We must admit that Cao and Zhu, Morgan and Tian, and Kleiner and Lott have done extremely important work on the Poincare Conjecture. However, they do not yet invent anything or develop any revolutionary ideas in the course. What distinguishes a genius from a good mathematician is his or her ability to invent and develop new ideas. Take a look at what we call the science giants in history: Newton, Leibniz, Einstein, Bohr, Copernicus etc. they have all have revolutionary inventions and discoveries in science. INVENTION OR DISCOVERY OR REVOLUTIONARY IDEAS, whatever you want to call it, is the single most important thing in science and math! In my regard, SS Chern is still the greatest Chinese mathematician that we have: Super Talented, Humble, Dedicated, and of good influence. I highly respect him. I wish we have more mathematicians as great as Dr. Chern. 杨振宁先生 once wrote a poem praising him as one of the GREATEST GEOMETERS in HISTORY! Dr. Chern well deserves that praise!
Isn't it pretty obvious that Hamilton's and Perelman's work (as well as Thurston's and the other who had made significant contribution to Poincare before) are more important than just completing the proof. The completion of the proof of Poincare Conjecture is valuable piece of work, but it is like an expository type of thing. Nevertheless, Each of those who have done this amazing work if proven correct(ie. Zhu and Cao, Morgan and Tian, Kleiner and Lott), they certainly deserve the Veblen and Steel Prizes and honors at this level. For Fields medal? Hmm... not sure. For the millenium prize? Any Chance? I don't think so.
--------------------------------------------------------
I really don't like that Yay misled the Chinese people and tried to gather fame for himself and his supporters. In the Chinese Weekned Newspaper, called "Qiao Bao" July 9th 2006 issue, Yau in his interview claimed that the Chinese, namely, Chinese' contribution is no less than 30% of the entire work. His using of the word "Chinese" is somewhat wickedly tricky--seems to be an attempt to draw our Chinese people to his side. He claimed that there is the 50% credit for Hamilton. Dr. Hamilton would certainly be happy to hear that--this is Yau's similar trick to draw Hamilton to his side. Since Perelman has no interest in prize and fame, he perhaps would not care what Yau says. And Yau doesnt have much connection with him either so he would not be shy to low-grade Perelman's work and upgrade his supporter's importance in the Poincare Conjecture, which eventually brings a fame to himself--Zhu is his friend and Cao his loyal student, both of them as well as Hamilton undertook Poincare with his guidance, suggestion, and encouragement. I do not know if Yau can do anything else as significant as this Poincare problem. Some people said it might be his last chance to draw public attention by emphasizing the work of Zhu and Cao and by the way to show the Chinese people that he is the most famous Chinese in mathematics--which I think is not inaccurate. He is already the most influential and famous Chinese mathematician.
I personally admired Yau a lot while I was in HK, respect him almost like my hero. However, after reading so much about him and what he says here, I became quite annoyed by his abusing his power as a leading mathematician. What annoys me most is that he once claimed that one of his student, who won the Veblen, namely, Tian Gang, is not a successful mathematician. He said Tian's work is not first rated by any means but because of his influence Tian got the Veblen. You can find this article or interview article easily online. The AMS Veblen committee should be responsible for this IF WHAT HE SAYS WERE TRUE. This is simply unfair! But I personally think Tian deserved the Veblen, even without Yau's influence, he would get it sooner or later. Now I respect Perelman so much more. He is the one who has done a truly revolutionary work in the area but claimed no credit for it; he does math for just a pure joy in discovery. But let me make myself clear here, I have no intention to attack Yau or anyone. Dr. Yau is certainly a great mathematician as well as a great mentor. He is one of the best mathematicians nowaday. Maybe I shouldn't be influenced too much by what other people said about him, but I also think that I am not someone who just listen and not think and analize.
Congratulations to all of you who have contributed to the Poincare Conjecture! As far as i remember, I think the following people are some of the main contributors: Smale? Freedman, Thurston, Milnor, Hamilton, Perelman, Cao, Zhu, Morgan, Tian, Kleiner, Lott, Yau... feel free to list the heroes in Poincare Conjecture!!!
Remember, it is important to maintain a healthy and fair academic environment. THANK YOU!
A Mathematical Genius, Good mathematicians! The difference.
THE CORE QUESTION COMES TO WHAT HAVE THEY EACH DISCOVERED OR DEVELOPED OR INVENTED? IF ALL THE FRAME WORK FOR THE PROOF OF POINCARE CONJECTURE IS LAID OUT AND THE TOOLS ARE HANDILY AVAILABLE, THEN PROVING THE POINCARE CONJECTURE IS JUST LIKE WORKING ON AN EXTREMELY LENGTHY OLYMPIAD MATH PROBLEM, WHICH REQUIRES ONLY TIME AND EFFORT BUT LESS INGENUITY.
HAMILTON--HE IS THE FOUNDER OF RICCI FLOW; PERELMAN--REVOLUTIONARY WORK ON Thurston's geometrization conjecture, a result that includes the Poincaré conjecture as a particular case. THESE ARE ALL THAT YOU NEED TO PROVE THE POINCARE CONJECTURE.
We must admit that Cao and Zhu, Morgan and Tian, and Kleiner and Lott have done extremely important work on the Poincare Conjecture. However, they do not yet invent anything or develop any revolutionary ideas in the course. What distinguishes a genius from a good mathematician is his or her ability to invent and develop new ideas. Take a look at what we call the science giants in history: Newton, Leibniz, Einstein, Bohr, Copernicus etc. they have all have revolutionary inventions and discoveries in science. INVENTION OR DISCOVERY OR REVOLUTIONARY IDEAS, whatever you want to call it, is the single most important thing in science and math! In my regard, SS Chern is still the greatest Chinese mathematician that we have: Super Talented, Humble, Dedicated, and of good influence. I highly respect him. I wish we have more mathematicians as great as Dr. Chern. 杨振宁先生 once wrote a poem praising him as one of the GREATEST GEOMETERS in HISTORY! Dr. Chern well deserves that praise!
Isn't it pretty obvious that Hamilton's and Perelman's work (as well as Thurston's and the other who had made significant contribution to Poincare before) are more important than just completing the proof. The completion of the proof of Poincare Conjecture is valuable piece of work, but it is like an expository type of thing. Nevertheless, Each of those who have done this amazing work if proven correct(ie. Zhu and Cao, Morgan and Tian, Kleiner and Lott), they certainly deserve the Veblen and Steel Prizes and honors at this level. For Fields medal? Hmm... not sure. For the millenium prize? Any Chance? I don't think so.
--------------------------------------------------------
I really don't like that Yay misled the Chinese people and tried to gather fame for himself and his supporters. In the Chinese Weekned Newspaper, called "Qiao Bao" July 9th 2006 issue, Yau in his interview claimed that the Chinese, namely, Chinese' contribution is no less than 30% of the entire work. His using of the word "Chinese" is somewhat wickedly tricky--seems to be an attempt to draw our Chinese people to his side. He claimed that there is the 50% credit for Hamilton. Dr. Hamilton would certainly be happy to hear that--this is Yau's similar trick to draw Hamilton to his side. Since Perelman has no interest in prize and fame, he perhaps would not care what Yau says. And Yau doesnt have much connection with him either so he would not be shy to low-grade Perelman's work and upgrade his supporter's importance in the Poincare Conjecture, which eventually brings a fame to himself--Zhu is his friend and Cao his loyal student, both of them as well as Hamilton undertook Poincare with his guidance, suggestion, and encouragement. I do not know if Yau can do anything else as significant as this Poincare problem. Some people said it might be his last chance to draw public attention by emphasizing the work of Zhu and Cao and by the way to show the Chinese people that he is the most famous Chinese in mathematics--which I think is not inaccurate. He is already the most influential and famous Chinese mathematician.
I personally admired Yau a lot while I was in HK, respect him almost like my hero. However, after reading so much about him and what he says here, I became quite annoyed by his abusing his power as a leading mathematician. What annoys me most is that he once claimed that one of his student, who won the Veblen, namely, Tian Gang, is not a successful mathematician. He said Tian's work is not first rated by any means but because of his influence Tian got the Veblen. You can find this article or interview article easily online. The AMS Veblen committee should be responsible for this IF WHAT HE SAYS WERE TRUE. This is simply unfair! But I personally think Tian deserved the Veblen, even without Yau's influence, he would get it sooner or later. Now I respect Perelman so much more. He is the one who has done a truly revolutionary work in the area but claimed no credit for it; he does math for just a pure joy in discovery. But let me make myself clear here, I have no intention to attack Yau or anyone. Dr. Yau is certainly a great mathematician as well as a great mentor. He is one of the best mathematicians nowaday. Maybe I shouldn't be influenced too much by what other people said about him, but I also think that I am not someone who just listen and not think and analize.
Congratulations to all of you who have contributed to the Poincare Conjecture! As far as i remember, I think the following people are some of the main contributors: Smale? Freedman, Thurston, Milnor, Hamilton, Perelman, Cao, Zhu, Morgan, Tian, Kleiner, Lott, Yau... feel free to list the heroes in Poincare Conjecture!!!
Remember, it is important to maintain a healthy and fair academic environment. THANK YOU!