Click here for a pdf file Jeremy Morgan emailed me yesterday. Its quite clear that on reading it that not only did they copy the same argument/idea from Kleiner/Lott paper, but even the sentence construction is same at many places. In the pdf file, the left column is the stuff from Kleiner/Lott paper posted at www.arxiv.org and the right column is the stuff from Cao/Zhu paper posted at Asian Journal of Mathematics. Read it and form your own opinion.

Remember how the media was going boo-boo over Kavya Vishwanathan ? I don't know if there will be the same reaction this time. Kavya was a teenager, could be easily intimidated and hence a soft target for the media. Kavya claimed that the similaritites were "completely unintentional" and that she "internalized" the details. Cao/Zhu in their erratum claims that they had "forgotten" that they had studied and "incorporated" Kleiner/Lott work in their notes!

Personallly, I don't see ANY difference between Kavya and Cao/Zhu. If the former was bashed for plagiarism, so should the latter. Atleast the latter could have displayed some maturity gained out of age. I wonder what Yau's role is in all this. He definitely seems to be knowing Kleiner/Lott work and even comments on their work in his 24 page review article “Structure of Three-Manifolds — PoincarĂ© and geometrization conjectures”. In the article, he mentions

In the last three years, many mathematicians have attempted to see whether the ideas of Hamilton and Perelman can hold together. Kleiner and Lott (in 2004) posted on their web page some notes on several parts of Perelman’s work. However, these notes were far from complete. After the work of Cao-Zhu was accepted and announced by the journal in April, 2006 (it was distributed on June 1, 2006). On May 24, 2006, Kleiner and Lott put up another, more complete, version of their notes. Their approach is different from Cao-Zhu’s. It will take some time to understand their notes which seem to be sketchy at several important points.Yeah right, their approach is different from Cao-Zhu modulo a couple of arguments and sentences used to fill in Perelman's approach.

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Cao-Zhu's paper also copied many old results of R.Hamilton. The beginning few hundred pages of their papers are just direct copies of results of Hamilton, Perelman, and others working on Ricci flow.

On the other hand there are also many big mistakes in the Tian-Morgan's 473 pages paper on Ricci flow. Their paper cheats in many important steps and said, by standard method this is true boo-boo-boo... Both the Tian-Morgan and Cao-Zhu and Perelman cheats in the proof of Poincare conjecture.

All are cheating in this problem.

Unbelievable! I guess this is what happens when you have a 3-day review (that excludes the editorial board) and you spend more effort hiring PR Firms and giving press conferences than checking the proof!

I'm a mathematician and the postings here are nonsense. Cao-Zhu know Hamilton very well and they give him credit for everything they write. As for the pdf file, you are confusing standard mathematical phrasing with plagerism. In fact, on page 4 of the pdf file, they are not even using the same arguement. Kleiner-Lott are describing Gromov-Hausdorff convergence and obtaining a C 1 limit while Cao-Zhu quote a theorem of Hamilton to get C infinity convergence. These are very different things to a mathematician.

The three day review is also nonsense. They presented their work over 6 months at Harvard university to a panel of experts and then submitted it to Asian Journal where the editor in chief was one of those experts. It should have undergone further review, but it wasn't just a 3 day review.

There are no full professor at Harvard working on Ricci flow and no full professor there published any papers on Ricci flow. One can check this at AMS Math Science net. So who are the panels of experts on Ricci flow at Harvard?

Ricci flow involves so many evolution equations. I wonder who are the 5 experts on evolution equations at Harvard University

that have the ability to checck Cao-Zhu's work. Cao-Zhu should tell us this list of experts.

Other than Hamilton, there are no other mathematicians working on Ricci flow (who have published papers on Ricci flow) said that Cao-Zhu have great contribution to Ricci flow and completes Perelman's work. So if Cao-Zhu has so much contribution, how come no one else in the field of Ricci flow said so.

It is strange that Peter Li, Ben Chow and other real experts on Ricci flow didn't say anything about the correctness of the Cao-Zhu paper.

Thanks for the posting. S-T Yau certainly owes the entire mathematics community one BIG apology! I see that the dramatic "complete proof" paper has now been retracted and renamed "Hamilton-Perelman's Proof of the PoincarĂ© Conjecture and the Geometrization Conjecture."

Most people working in geometry

knows that S.T. Yau has switched

to working on Superstring theory

for at least ten years and has no published any paper on Ricci flow for the last ten years. So how can he has the ability to review and judge that the Cao-Zhu paper completes the Poincare conjecture.

S.T. Yau supports them for the sole reason they are his friend and beloved former Ph.D. student.

I wonder whether S.T.Yau understands Perelman's paper at all. None of the Ph.D. styudents

he trained in the past ten years

works on the Ricci flow.

On the other hand many recent Ph.D. students trained by Gang Tian

works on Ricci flow. So Gang Tian knows more and have more research ability in Ricci flow than S.T.Yau is transparent. S.T.Yau have done a great hurt to the mathemtics community in supporting his friends' faked results.

S.T. Yau support Cao-Zhu because of

the following reason:

1. After Gang Tian did not received the Fields Medal, many Chinese mathematicians blame S.T.Yau for not supporting a chinese mathematician to get a fields medal. So in order to block other's blame on Yau, Yau promoted Cao-Zhu (since both are over 40 years old and cannot get the Fields medal) so that the Chinese

Mathematician will shut up on blaming Yau. Yau do not care about research at all. All he cares is to promote someone to fight Gang Tian in China and these guys must and cannot be a threat to Yau. Cao and Zhu just happen to satisfy this carteria. It is well known that Yau give many prizes to his friends. For example in the International congress of chinese mathematicians, S.T. Yau gave most prizes to his friends, post-doc and students-- e.g. Jun Li, C.L. Wang, C.S.Lin, S.S.Lin, etc.

2. His good friend Hamilton is already old and want a share of the glory of the Poincare conjecture. So despite that fact that there are so many gaps in Perelman's papers and Cao-Zhu's paper are copies of other's results

R.Hamilton join S.T.Yau in this biggest lie and cheating to the mathematics society. They owe the mathematics community a big apology.

Gang Tian and J. Morgan support Perelman and said that Perelman have proved the Poincare conjecture

despite there are so many mistakes in Perelman's paper because they both want a share of the glory of Poincare conjecture and this will hit S.T. Yau in research. They wrote a very long paper claiming the credit of explaining Perelman's

work to others. However they notes have many big mistakes. Gang Tian and J. Morgan like Yau also owe the mathematic community a big apology.

Cao-Zhu, S.T. Yau, Perelman, Gang Tian and J. Morgan all cheats the mathematics society in particular the geometry research field. They claimed that they have proved everything (faked) so that no others (except their friends) can work in this field again. All cheats in this big problem in particular they are well-known geometer. What a shame to the mathematics community.

May be the American mathematics society or ICM should have a conference asking Cao-Zhu, Perelman, Gang Tian and J. Morgan and Kleiner and J. Lott opoen a forum to let others ask questions on the Poincare conjecture.

Cao-Zhu, J. Morgan-Gang Tian, Hamilton, S.T. Yau are like people hiding in the dark in their declaration of the proof of Poincare conjecture. Why don't AMS or ICM organize a open Poincare conjecture inviting experts and researchers working on Poincare conjecture to challenge Cao-Zhu, S.T.Yau, Hamilton, Morgan-Gang Tian

etc. publicly on their claimed complete proof or complete exposition of Perelman's proof of Poincare conjecture. Then one will find that they all lied in this conjecture.

Sujit Nair says:

"Personallly, I don't see ANY difference between Kavya and Cao/Zhu. If the former was bashed for plagiarism, so should the latter."

If you're going to go there, then you must condemn *all* forms and ranges of plagiarism, from the worst kind (habitual and large portions) to the mildest kind (one-time lesser offense, maybe copying just one sentence that contains little original thought). I wonder how many writers are left standing.

I would think that plagiarism in mathematics is very hard to get away with, since peer review is so rigorous and results are clearly documented in the form of a proof. This is certainly the case for such an extremely high-profile problem. One can be sure that the Clay Mathematics Institute (and others) will go through all relevant published documents line by line. As an outsider not involved in geometry at all (and certainly am neutral about the various parties involved), I am inclined to believe that it was most likely an oversight on Zhu's part, like he said. Perhaps Lott might recall whether he had presented his arugments in a seminar where Cao or Zhu could have attended and taken notes (including copying from the slides?). One of them could have gotten those notes mixed up with, I'm sure, piles of other notes and such. There's got to be a lot to cover in their 400+ pages of paper. So unless a mathematician has a history of plagiarism, maybe he should be given the benefit of the doubt. And I don't remember reading anything about either of them being accused of plagiarism before this, and they've been mathematicians for a long time.

BTW, I posted the above comment just to provide another point of view. It seems like everyone here is jumping on the accusation bandwagon.

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