Dr. Yau has demanded that The New Yorker and Nasar make a prominent correction of the errors in the article, and apologize for an insulting illustration that accompanied it.The old "you are not just attacking me, you are attacking all of mathematics" argument. Most of the mainstream media has not picked up this part of the story. The Boston Herald did and they also published the New Yorker's response."Beyond repairing the damage to my own reputation, we seek to minimize the damage done to the mathematics community itself, which is ludicrously portrayed as contentious rather than cooperative and more competitive than collegial," Dr. Yau said. "Mathematicians from the foremost institutions – from Beijing to Berkeley – have been appalled at the fictionalizing of our profession."

"Manifold Destiny," a 10,000-word article by Sylvia Nasar and David Gruber published in the August 28, 2006 issue of The New Yorker, is the product of more than four months of thorough, careful reporting and meticulous fact-checking. Ms. Nasar and Mr. Gruber spent over twenty hours interviewing Dr. Yau; they conducted approximately 100 other interviews with people in the field; corresponded by email with Dr. Yau and many others; and traveled to China where they conducted interviews and attended speeches and events discussed in the article. In addition, the magazine's fact-checkers spoke with Dr. Yau for approximately eight hours, they examined notes, tapes, and documents gathered by the authors, and the checkers conducted their own thorough research. Contrary to Dr. Yau's assertions, the article is nuanced and fair, and was prepared using ethical standards of journalism. Dr. Yau, his supporters and his point of view were given ample space in the article.Whatever the merits of Yau's claims (a reliable source tells me the article is mostly a reasonable and accurate reporting of events), Yau only hurts his reputation with this newest action. Yau should have written a short letter to the New Yorker editor with a pointer to a detailed discussion on his web site. Instead by having an argumentative letter written by a lawyer with the implicit threat of a lawsuit, Yau only encourages the very portrayal he tries so hard to fight against.

Can't we all just get along?

ReplyDeleteI disagree. I read the letter from Yau's Lawyer. The truth of what is in there is not really the point (though, it will be eventually). If Yau feels as this letter indicates, then his actions are very reasonable. I would probably do the same. Moreover, respect and reputation is clearly important to Yau and tends to be very important in the Chinese culture in general. So, Yau, more than I would, has a reason to be upset.

ReplyDeleteThat said, I don't know if Yau actually believes every accusation in the letter by his lawyer. Furthermore, Yau may have a distorted view of the events (due to his ego or some other reason).

The letter does make some pretty harsh accusations, and while reading it I was thinking: I am glad I didn't receive that email today! If even half of the accusations are true, those guys are in a world of hurt.

Finally, my judgment is marred by a general dislike of the media.

ReplyDeleteYau should have written a short letter to the New Yorker editor...A short letter would have accomplished nothing. If the accusations Yau makes against the New Yorker are true, then he has chosen the only prudent route toward recovering some of the damage done. Trust me, they have their own lawyers.

all this is just further proof that yau's a thug. visit the man's webpage to get an idea of what a bloated ego he has.

ReplyDeleteIs it not possible that Yau tried to communicate with the New Yorker, but they refused to publish his rebuttal or letter? It seems that he and others have sent them numerous e-mails which they have ignored. He may have been left with no choice here but to go the route he is on now.

ReplyDeleteI think that everyone is missing the point here: No publicity is bad publicity! A soap opera in the midst of mathematics, to bring our underappreciated field into the public spotlight? Brilliant!

ReplyDeleteI've seen all this crap discussed ad nauseum, and have as of yet to read a single account of what's going on who's claims I think I could remotely trust. Stupid messy politics and spin, I WANT TO KNOW WHAT ACTUALLY HAPPENED.

ReplyDelete

ReplyDeleteI WANT TO KNOW WHAT ACTUALLY HAPPENED.Unfortunately, we may never know the real story. But all indications (including that of Perelman declining the Fields) suggest that Yau has tried to seek credit for what wasn't really his work and has engaged in unethical behavior.

ReplyDeleteYau has tried to seek credit for what wasn't really his work and has engaged in unethical behavior.Furthermore, it seems that consensus is this isn't the first time Yau has tried to pull such a trick.

This is no way means he's not a top notch researcher. It's perfectly possible to be a very good mathematician and not a nice person.

I don't give a damn to Yau's letter because I don't have enough patience to read the 12 page letter but I do care about the NY article. That was an excellent article and they put a lot of effort (more than "Dr. Yau" and his committee (Asian Journal of Mathematics) did to review over 300 page paper of Dr. Yau's students).

ReplyDeleteSKU

Take a look at the slides of Yau's talk on the topic

ReplyDeleteStructure of Three-Manifolds

They are quite "interesting". For example, Yau cites himself as often as he cites Perelman.

As this story unfolds, it is becoming clear that Perelman is far more rational and less of a lunatic that it seemed, as big fame brings politics.

ReplyDeleteAs a side note, Yau has a relatively "famous" STOC paper, see

http://doi.acm.org/10.1145/258533.258675. While it's not related to the current events, he probably should not complain that other people do not provide all the details of a proof.

No one has pointed out Yau's contribution to our field: The paper with Fan Chung giving an O(1) approximation for the Sparsest Cut problem (recall that Arora, Rao, and Vazirani received the best paper award in 2004 for a measly sqrt{log n} approximation). The link is here.

ReplyDeleteThat was STOC 1994. Three years later in STOC 1997, the result was retracted.

I guess my point is: I would have liked to see Perelman solve Sparsest Cut before getting offered the Fields.

I am not a lawyer, but most of the "allegations" in the letter do not seem to be of much legal merit. What kind of legal letter has things like "she indicated she would put Hawkings' praise for me in the article and she didn't".

ReplyDeleteHe spends quite some effort trying to defend his position in the Givental story. But the references he comes up with are a pre-print and an article in Mathematical review. He then says other mathematicians have called the proof "obscure" and "misleading", neither of which actually contradicts the New Yorker article; both adjectives apply to the exposition, not the proof. He then claims that Givental's 3 page footnote "acknowledged the original work of Dr. Liu and his co-authors."

You can read the footnote on page 43 here. The footnote is an effort to explain how Liu et al.'s proof corresponds one-to-one to the original proof Givental gave. I did not find anything in the footnote that refers to Liu et al.'s original contribution; instead it concludes with:

The statement in theabstract that the paper [22] “is completing the program started by Candelas et al, Kontsevich,

Manin and Givental, [...] is also misleading: the paper is more likely to confirm that the program

has been complete for two years.

Finally, the allegation that he pushed through a journal article without review in 3 days, he does not even address!!

--kunal

"Yau should have written a short letter to the New Yorker editor with a pointer to a detailed discussion on his web site"

ReplyDeleteThis is as naive as one can get.

"a reliable source tells me the article is mostly a reasonable and accurate reporting of events"

ReplyDeleteConsidering the wide range of events depicted in the article, I would be shocked that such a source could exist and be trusted.

"The New Yorker, is the product of more than four months of thorough, careful reporting and meticulous fact-checking...."

ReplyDeleteThe New Yorker Magazine is obviously being craftily smart here. They purposely evaded all the points alleged by Yau's lawyer. Who cares how many hours were spent on this? They didn't dare to make a specific claim that the reported facts are all accurate, but rather use the abmiguous word "nuanced and fair". It is sad that the blogger didn't bring up any specific claim made by Yau but rather post this absurdly empty New Yorker response. I encourage the reader to take a look at Yau's letter. I am appauled at Nasar's ability to fincitonalize stories and now I have a serious doubt about the accuracy of "A Beautiful Mind".

ReplyDeleteThey purposely evaded all the points alleged by Yau's lawyer.Yau's points do not deserve a response: "I thought it was going to be a homage piece"... "I didn't get a chance to rewrite the article to my liking" what can you say to that?

Moreover most lawyers would recommend not making any specific statements outside of court about a trial in progress.

Considering the wide range of events depicted in the article, I would be shocked that such a source could exist and be trusted.I agree. Something as complicated as this is a he-said/she-said kind of thing where honest people can have conflicting opinions of what happened, and likely the truth is somewhere in the middle. However so long as the New Yorker has taped interviews stating their version of the story, they are legally covered.

Last but not least, is Yau prepared to have the court officially rule that the New Yorker is right on the facts? Now that would be *really* embarrasing. If Yau has any friends left, I hope they convince him that the way to fix this is through exemplary actions from him from now onwards (starting by an apology for rushing his protege's proof), not through a lawsuit.

To the 2nd-to-the-last Anon:

ReplyDeleteBe careful, 'cause some guy will ask if you by any chance are Yau himself?

To the last Anon:

I am confused. As I am informed, cao-zhu had been invited to Harvard for one semester to explain their paper to the experts there. But your version of the story is that the paper was reviewed for only 3 days. That says enough about the media.

Also, I think the following link is worth reading, especially for those guys who claim Perelman's work is complete and correct, even though they don't understand it at all.

http://www.icm2006.org/press/bulletins/bulletin08#2

ReplyDeleteAlso, I think the following link is worth reading, especially for those guys who claim Perelman's work is complete and correct, even though they don't understand it at all.I doubt anyone claims Perelman work was complete. The question is how much credit is due for filling in the gap. The majority of the math community including two of the major players in filling the gap feel the credit is Perelman's. Yau thinks is his students'. You make your own conclusions.

Regarding the last comment to anon: we don't know if the New Yorker is right, the question is a hypotethical: is Yau prepared for the potential eventuality of the court ruling against him? Has he considered this possibility and its consequences?

ReplyDeleteYau thinks is his students'. You make your own conclusions.How come? Even the craziest man in the world would not think that is possible. Any pointers that make you believe that Yau wants to take the (major) credit?

Perhaps one factor you should consider is Chinese media is usually not very trustlful. See http://www.popyard.com/cgi-mod/npost.cgi?cate=3&page=1&num=107887&r=

I read the legal firm's letter and believe the arguments are weak. I doubt Yau will proceed much further. His lawyers are most likely telling him to back down.

ReplyDeleteThe American civil law system does not support Chinese cultural values and language, both which are more sensitive to one's public image and avoid the slightest intimation of wrongdoing or bad outcome. A drawn-out court case would end Yau's career as a mathematician and he would probably lose utterly. Why sow the seeds of your own destruction?

But if he does go to court and loses then he can always choose suicide, which in Chinese culture (and to some degree in the West) yields an effective "nolo contendere" judgement.

To the last Anon,

ReplyDeleteThis is quite racist. Yau is an American.

ReplyDeleteThis is quite racist. Yau is an American.Are you Shing-Tung Yau by any chance?

I am personally very impressed by Prof. Yau's mathematics, by his writing, by his teaching, and by what he is trying to achieve in China. Even speaking as an engineer, Yau's work has been both accessible and important to our QSE Group.

ReplyDeleteTherefore, it makes me sad to see Yau expend his talent and energy arguing with journalists, politicians, and lawyers. When my own wife served on the Seattle School Board, our whole family learned the hard way that such effort is mostly wasted.

If Yau refocussed his energy on mathematics and teaching, everyone would be further ahead.

ReplyDeleteThe American civil law system does not support Chinese cultural values and language, both which are more sensitive to one's public image and avoid the slightest intimation of wrongdoing or bad outcome.But it's okay to step on a face (Perelman's) when accumulating face.

Ms. Nasar Hunts Chinese Witches

ReplyDeleteChina N. Math

cnmath.blogspot.com

(1) In Ms. Nasar’s article with Mr. Gruber, she labeled both Professors Shing-Tung Yau and Shiing-Shen Chern as “the Chinese mathematician”. In fact, both are U.S. citizens born in China. It is important to note that only mathematicians of Chinese heritage were labeled this way in the article. This labeling is in contrary to the common practice of using the term “Chinese American mathematician” in the mainstream news media in both the U.S. and China. (In Chinese media, Yau and Chern are called “mei ji hua ren”-U.S. citizen of Chinese heritage.) Ms. Nasar went to length to describe the contributions of Yau and Chern to the scientific development in China but neglected to mention that both were awarded this nation’s highest scientific honor, the National Medal of Science. The subliminal message is that both Yau and Chern work only to advance the Chinese interest. Such bigotry is nothing new in this country: Jewish people have been subject to such stereotype for a long time.

(2) While there were extensive discussions on original ideas in mathematics in this 14-page long article, not a single sentence, as far as I know, associated mathematicians of Chinese heritage to originality. Even the originality of Yau’s Fields Medal work was downplayed. This article promotes the false and harmful stereotypes that mathematicians of Chinese heritage are “technical” but not “original”. (See an open letter to Ms. Nasar for more detail on this point.)

(3) Seven mathematicians of Chinese heritage were named in the article: Yau, Chern, Gang Tian, Huai-Dong Cao, Xi-Ping Zhu, Kefeng Liu, Bong H. Lian (implicitly, as the coauthor of Liu and Yau). While there was only minimal coverage on Chern, all six others were alleged, one way or another, to involve in plagiary and/or claiming undeserved credits. More importantly, in the article, no other mathematicians but only those of Chinese heritage were alleged to involve of such unethical practices. This is biased, prejudiced, and, in fact, racist. To illustrate this point, substitute all Chinese names by Jewish names, China by Israel, and Chinese by Jewish. This article would then have been easily recognized as anti-Semitic.

(4) This is not the first time Ms. Nasar spews anti-Chinese venom. In her article Best Business Book 2003: Globalization, she promoted the book World on Fire by Amy Chua. Here is what Ms. Nasar wrote:

"Chua compares the wealthy Chinese, like her aunt, who dominate the markets of many Asian countries to the successful Jews of Europe in the 1920s. “In the Philippines, millions of Filipinos work for Chinese; almost no

Chinese work for Filipinos. The Chinese dominate industry and society at every level…. When foreign investors do business in the Philippines they deal almost exclusively with Chinese.” When she was 8 years old, she recalls,

she stumbled into the servant quarters in her aunt’s villa: “My family’s houseboys, gardeners, and chauffeurs … were sleeping on mats on a dirt floor. The place smelled of sweat and urine. I was horrified.” "

This is bigotry, pure and simple. It is now well established that Ms. Nasar distorted other people’s statements to fit her own agenda. (“As it appears in her article, she has purposefully distorted my statement and made it unforgivably misleading.” ---Dan Stroock of MIT.) There were also controversies regarding Ms. Nasar’s A Beautiful Mind about the anti-Semitic statements that she attributed to Mr. John Nash. (See, for example, An Anti-Semitic Mind? by Tom Tugent at The Jewish Journal.)

The following is translated from the Chinese news paper QIANJIANG EVENING NEWS, dated August 24, 2006. Here is the link to the Chinese original:

ReplyDeletehttp://qjwb.zjol.com.cn/html/2006-08/24/content_1163764.htm

Four fields medals awarded -- Why the Chinese who verified the Poincare Conjecture

didn’t get a medal ? Professor Kefeng Liu (of UCLA) explains.

The Chinese “Kicked” Perelman onto the Podium

By Yu Xu Na of this paper.

At the 2006 ICM held at Madrid, world famous mathematician, US National Academy of Science member Hamilton said: “Yau and I developed a program ---using Ricci flow to solve this problem (the Poincare conjecture). ” “Based on several manus posted on the internet, Russian mathematician Perelman claimed that he has completed this program. A complete exposition was recently given by Cao and Zhu.”

As the “commander in chief” in the proof of Poincare, Hamilton’s lecture, together with the Fields Medal awarded to Perelman, is viewed as confirmation that the century old puzzle is finally solved. And what Hamilton said in his lecture is undoubtedly a confirmation of the great role played by the Chinese mathematicians.

“It can be said that it was the Chinese mathematicians who ‘kicked’ Perelman onto the podium to receive the highest honor in mathematics.” Professor Kefeng Liu of UCLA and director of the Mathematical Sciences Center at Zhejiang University, who has been watching the ICM closely, told us in our interview with him yesterday.

Chinese mathematicians kicked the ball into the goal

Numerous mathematicians have tried to attack the century old conjecture. But this June, Fields medalist and Harvard professor Shin-Tung Yau, through the press, announced to the world: the century old Poincare conjecture has finally been proved by the Chinese mathematician Zhu Xiping who is a professor at Zhong Shan University, and another Chinese mathematician Cao Huai-Dong. Mr. Yau opined that in the process of the whole proof, they (Cao and Zhu) solved the final problem, sealing the rooftop.

But at the ICM this year, it was Russian mathematician Perelman who got the medal for the conjecture.

“This is not surprising, because Perelman was the original one”, Kefeng Liu commented. “Perelman’s work opened the gate to a gold mine. But his papers contained gaps, it was still one step away from the final proof. It was the Chinese mathematicians who sealed the proof.”

“Of course, another reason Zhu and Cao didn’t get the medal was that they were beyond 40, because the Fields Medal is only awarded to mathematicians aged 40 or younger”, professor Liu added.

According to Liu, in 1982 Hamilton created a new kind of equation--- the Ricci flow, which later became an effective tool to tackle the conjecture. Hamilton and Yau divided the difficulties in the proof into three kinds, and what Perelman solved was exactly the most difficulty kind.

But 4 years ago, Perelman didn’t openly publish his proof. Instead he posted three articles on the internet, and disappeared soon after. “His papers caused a sensation in the math community, many mathematicians saw these articles, but they were impossible to understand at many places, nobody dared to assert that his proof was correct.”

And that’s where Zhu and Cao made their biggest contribution. Kefeng Liu said their paper filled the gaps in Perelman’s work, giving a complete explanation. “As a matter of fact, before the medals were awarded at the ICM, committee members have been hesitating whether to award Perelman the Fields medal, because his work is not openly published, and contained gaps. But the work of Zhu and Cao convinced committee members that Perelman was correct.”

Hamilton also emphasized that Cao and Zhu, based on work of Perelman and others, have given a complete and detailed deion of the proof of the Poincare conjecture. He said: “I am very happy that these two outstanding scholars (have written) this paper. They introduced their own new ideas, making the proof easier to understand.”

……..

(In the rest of the report Liu basically went on to brag about his acquaintance with his UCLA colleague Terrence Tao….. )

Hamilton speaks up.

ReplyDelete"Far

from stealing credit for Perelman's accomplishment,he has praised Perelman's

work and joined me in supporting him for the Fields Medal.And indeed no

one is more responsible than Yau for creating the program on Ricci Flow

which Perelman used to win this prize.

"

Howard M Cooper

Todd & Weld LLP

28 State Street

Boston,MA 02109

Direct Dial (617) 624-4713

Fax (617) 227-5777

hcooper@toddweld.com

Dear Mr. Cooper

I am very disturbed by the unfair manner in which Yau Shing-Tung has

been portrayed in the New Yorker article. I am providing my thoughts below

to set the record straight. I authorize you to share this letter with the New

Yorker and the public if that will be helpful to Yau.

As soon as my first paper on the Ricci Flow on three dimensional manifolds

with positive Ricci curvature was complete in the early '80's,Yau immediately

recognized it's importance;and although I had proved a result on which

he had been working with minimal surfaces,rather than exhibit any jealosy he

became my strongest supporter.He pointed out to me way back then that the

Ricci Flow would form the neck pinch singularities,undoing the connected

sum decomposition,and that this could lead to a proof of the Poincare conjecture.

In 1985 he brought me to UC San Diego together with Rick Schoen and

Gerhard Huisken,and we had a very exciting and productive group in Geometric

Analysis.Huisken was working on the Mean Curvature Flow for

hypersurfaces,which closely parallels the Ricci Flow,being the most natural

flows for intrinsic and extrinsic curvature respectively.Yau repeatedly urged

us to study the blow-up of singularities in these parabolic equations using

techniques parallel to those developed for elliptic equations like the minimal

surface equation,on which Yau and Rick are experts.Without Yau's guidance

and support at this early stage,there would have been no Ricci Flow program

for Perelman to finish.

Yau also had some outstanding students at San Diego who had come with

him from Princeton, in particular Cao Huai-Dong,Ben Chow and Shi Wan-

Xiong. Yau encouraged them to work on the Ricci Flow,and all made very

important contributions to the field.Cao proved existence for all time for the

normalized Ricci Flow in the canonical Kaehler case ,and convergence for

zero or negative Chern class.Cao's results form the basis for Perelman's exciting

work on the Kaehler Ricci Flow,where he shows for positive Chern class

that the diameter and scalar curvature are bounded. Ben Chow,in addition to

excellent work on other flows,extended my work on the Ricci Flow on the

two dimensional sphere to the case of curvature of varying sign.Shi Wan-

Xiong pioneered the study of the Ricci Flow on complete noncompact

manifolds,and in addition to many beautiful arguments he proved the local

derivative estimates for the Ricci Flow.The blow-up of singularities usually

produces noncompact solutions,and the proof of convergence to the blow-up

limit always depends on Shi's derivative estimates; so Shi's work is central to

all the limit arguments Perelman and I use.

In '82 Yau and Peter Li wrote an exceedingly important paper giving a

pointwise differential inequality for linear heat equations which can be integrated

along curves to give classic Harnack inequalities. Yau repeatedly urged

me to study this paper,and based on their approach I was able to prove Harnack

inequalities for the Ricci Flow and for the Mean Curvature Flow. This

Harnack inequality,generalized from Li-Yau,forms the basis for the analysis

of ancient solutions which I started, and which Perelman completed and uses

as the basic tool in his canonical neighborhood theorem. Cao Huai-Dong

proved the Harnack estimate for the Ricci Flow in the Kahler case,and Ben

Chow did the same for the Yamabe Flow and the Gauss Curvature Flow.

But there is more to this story. Perelman's most important is his noncollapsing

result for Ricci Flow,valid in all dimensions,not just three,and thus

one whose importance for the future extends well beyond the Poincare

conjecture,where it is the tool for ruling out cigars,the one part of the singularity

classification I could not do. This result has two proofs,one using an

entropy for a backward scalar heat equation,and one using a path integral.The

entropy estimate comes from integrating a Li-Yau type differential Harnack

inequality for the adjoint heat equation,and the other is the optimal Li-Yau

path integral for the same Harnack inequality; as Perelman acknowledges in

7.4 of his first paper,where he writes "an even closer reference is [L-Y],where

they use "length" associated to a linear parabolic equation,which is pretty

much the same as in our case".

Over the years Yau has consistently supported the Ricci Flow and the

whole field of Geometric Flows,which has other important successes as

well,such as the recent proof of the Penrose Conjecture by Huisken and

Ilmanen,a very important result in General Relativity. I cannot think of any

other prominent leader who gave nearly support to our field as Yau has.

Yau has built is an assembly of talent,not an empire of power,people

attracted by his energy,his brilliant ideas,and his unflagging support for first

rate mathematics, people whom Yau has brought together to work on the hardest

problems.Yau and I have spent innumerable hours over many years working

together on the Ricci Flow and other problems,often even late at night. He

has always generously shared his suggestions with me,starting with the observation

of neck pinches,never asking for credit. In fact just last winter when I

finally managed to prove a local version of the Harnack inequality for the

Ricci Flow,a problem we had worked on together for many years,and I said I

ought to add his name to the paper,he modestly declined.It is unfortunate that

his character has been so badly misrepresented.He has never to my knowledge

proposed any percentages of credit,nor that Perelman should share credit for

the Poincare conjecture with anyone but me; which is reasonable,as indeed no

one has been more generous in crediting my work than Perelman himself.Far

from stealing credit for Perelman's accomplishment,he has praised Perelman's

work and joined me in supporting him for the Fields Medal.And indeed no

one is more responsible than Yau for creating the program on Ricci Flow

which Perelman used to win this prize.

Sincerely yours,

Richard S Hamilton

Professor of Mathematics,

Columbia University

To Anon 28,

ReplyDeleteI wouldn't trust anything published by the Chinese media, as I wouldn't trust anything distorted by the American media, e.g., the New Yorker. Both are basically profit driven commercial forces and do not hesistate to do things to sentatilize stories to gain readers. The Chinese media more blatant, the American media more subtle. But no fundamental difference.

Yau obviously behaved very inappropriately to push his students paper to be published without proper review process, and there is no denial that Yau has an overblown ego and is a highly polotical figure. But to go so far as to devise a story of Yau grabbing medal from Perelman as Nasar did is really a distrust of the rigorourness of the whole field of mathematics. The contribution is clearly cut and Yau, as a first rate mathematician, would be exceedingly stupid to deny it. The field we are talking about is the clear and rigorous field of mathematics, not philosophy or psychology.

Read the Hamilton letter, and read Cao-Zhu's paper. Perelman is appropriately credited.

The one who steals credit from Perelman is the media itsefl rather than Yau. The Chinese media created a story, and the American media further distorted and benefited from that story. Both gain at the expense of the distorted reputation of the mathematics field.

Media is not solution to the problem; media is the problem.

ReplyDeleteYau obviously behaved very inappropriately to push his students paper to be published without proper review process, and there is no denial that Yau has an overblown ego and is a highly political figure. But to go so far as to devise a story of Yau grabbing medal from Perelman as Nasar did is really a distrust of the rigorourness of the whole field of mathematics.From the outside, this sounds like a good summary of the events to me.

dsfsdfa

ReplyDelete