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Professor Deane Yang, Polytechnic University, Brooklyn, NY,
responds to the New Yorker article
September, 2006

Subject: Original version of letter I wrote to the New Yorker

As a mathematician with a longstanding interest in both the Ricci flow and Poincaré conjecture, I found Nasar and Gruber's article on the Poincaré conjecture entertaining and well written. The juxtaposition of Perelman's ascetism against Yau's ambitions makes for a dramatic story. I would, however, like to say a few words in defense of Yau.

When I was growing up, I used to hear a lot of gossip from my father (who was also a mathematician) and his friends. Based on this, I used to explain to my friends how Chern was the undisputed emperor of Chinese mathematics and how various people were fighting to be Chern's successor. However, when Yau came along, it quickly became clear, from both his prodigious talents and his personality, that he would be the one. Like anyone who becomes emperor (including Chern), Yau clearly had the outsized ego and ambition required. And like many with these qualities, Yau has done things that dismay his peers. Until Perelman scooped Hamilton and Yau by proving the Poincaré conjecture, all of this stayed within the mathematical community. But Nasar and Gruber have now exposed some of this to the public.

What I don't want to be forgotten are the enormous contributions Yau has made to the mathematical community. Beyond his groundbreaking research in differential geometry, algebraic geometry, differential topology, and mathematical physics, he is one of the greatest teachers, having trained — according to the Mathematical Genealogy Project — 34 students and 124 descendants in all, including many of the top geometers working today. And he has always been generous in his support of people who are stuck in less well known institutions but doing work that impresses him (my colleagues Erwin Lutwak and Gaoyong Zhang are two examples). Yau's impact on mathematics and the mathematical community is difficult to overstate, and it is virtually all positive.

Sincerely,
Deane Yang
Professor of Mathematics
Polytechnic University

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Professor Niky Kamran, McGill University, Montreal, Canada, responds to the New Yorker article
September, 2006

Dear Mr. Cooper,

I was very disturbed by the offensive and slanderous way in which Professor Shing-Tung Yau was treated in the article "Manifold Destiny" published in the New Yorker magazine.

I have had the privilege of collaborating in research with Professor Yau since 1998. During this time, I have had ample opportunity to witness how exceptionally generous and giving he is towards his students and colleagues, and how fair he is in not only giving due credit to the contributions of others, but also in promoting them. The level and impact of Professor Yau's contributions to mathematics continue to be tremendous, and the assertion made in the article to the effect that his research has been in decline is simply ridiculous. To cite but one example, I would like to mention the spectacular results I heard Yau present at Stanford in May on the construction of non-Kaehler complex manifolds solving the supersymmetric Strominger equations in string theory. The depth and significance of this work alone makes it absolutely manifest that the claim made in the article is completely unfounded. There are many more examples that I could add to the one that I just mentioned.

Sincerely,

Niky Kamran
Professor of Mathematics
McGill University
Montreal, Canada

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Professor Chang-Shou Lin, National Taiwan University, responds to the New Yorker article
October, 2006
Dear Mr. Cooper:

I am writing to you in regards to the article "Manifold Destiny" in the New Yorker. It really surprised me that such a prestigious magazine as the New Yorker whould publish this article. Obviously, every respect of professor Yau is so unfairly treated by the authors. The paragraphs about Yau are based on gossip and irrelevant stories. It is also clear to me that it distorts many interviewees' statements on purpose. I felt greatly horrified when I saw the cartoon which shows Yau gripping the Medal from Professor Perelman. It is so malevolent that I felt very upset for many days.

I have known professor Yau for more than twenty years. He is indeed a completely honest and honorable man, and, as remarked by my adviser Professor L. Nirenberg in his letter, Yau is a person with great passion for mathematics. It has almost become a legend that he organizes seminars three days a week for his students and colleagues. Thee seminars started from his Stanford years, and keep on going in the Institute of Advanced Study, San Diego, and Harvard. By saying "...Determined to retain controls over his field, Yau push his students to tack big problems. At Harvard, ...." (see the article), this is not only inaccurate, but also malicious with bad intention. Those statements completely pervert Yau's passion and devotion to mathematics, and derogate Yau's honor as well.

As the only person of Chinese descent who won the Fields Medal in the last 20+ years, Yau is naturally considered as the only heir of Professor S. S. Chern. This was never claimed by Yau himself. But I can confidently say all other Chinese mathematicians do think so. The reason why I want to point this out is to let you know how ridiculous this article is in this regard.

Yau has done a lot to promote the mathematics development in China, Hong-Kong and Taiwan. He visited Taiwan many times including one whole academic year, 1992–93. Thereupon, professor Yau conducted his legendary seminar each week in Tsing-Hwa University. In Taiwan, he kept on advising the Taiwan Government and University presidents to allocate more funds for mathematics research, and helped us to establish mathematics research centers, such as National Center for Theoretical Sciences (NCTS) and the Taida Institute of Mathematical Sciences (TIMS). Since I was the director of NCTS and am now the director of TIMS, I can ensure you that Professor Yau is always happy to help as an adviser to centers. But, he never interferes with any operation of both centers. Yau's generosity is the true image of him — definitely not the one malignantly portrayed inside the New Yorker article.

Sincerely,

Chang-Shou Lin
Professor of Mathematics
National Taiwan University

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Professor Feng Luo, Rutgers University, New Brunswick, NJ, responds to the New Yorker article
October, 2006
Dear Mr. Cooper:

I am writing you regard the New Yorker article of August 28 by S. Nasar and D. Gruber. I found the article's treatment of Prof. Yau's contributions to developing mathematics in China out of fact and unacceptable. It is well-known to all of us that Yau has worked tirelessly for so many years to help rebuild mathematics in China. As a mathematician he is very creative and productive. He has helped to train generations of mathematicians in China. He has now collaborations with a number of young scholars in China. He also tries to create opportunities for much more people in China to work in a better environment. I believe that he has conducted himself with great honor and integrity throughout his efforts to the development of mathematics in China.

Prof. Yau has spent tremendous amount of time to reenergize mathematics in centers such as Beijing, Hangzhou, Taiwan and Hong Kong where he helped to created several mathematical institutes. He has provided his genuine help for the institutes through advising scientific programs, fund raising, building library and recruiting talented students. He has brought prominent scientists around the world to China to help promote and energize mathematical activities at those institutes, and he has reached out to generations of young mathematicians throughout China and encouraged them to pursue their passions. His working style is down to the earth. For example he has helped to set up two scholarships in Zhejiang University and the University of Science and Technology of China. Many of those students benefited from Prof. Yau's program are now studying mathematics in China and in US.

Prof. Yau has spent much time in raising fund for mathematics in China and he himself has donated several millions of RMB to mathematical institutions in China. However he himself has not accepted any allowances. He flies to China several times every year and he paid tickets all by himself. He offers his help without any personal financial gain.

As recognition Prof. Yau was awarded the international cooperation prize in China in 2004 which is the highest honor for contributions to developing sciences in China for international scientists. It is hard to overestimate Prof. Yau's contribution in helping developing mathematics in the largest developing country. I all appreciate it very much, I believe most mathematicians in China agree as well, of Prof. Yau's fruitful and productive efforts to the development of mathematics in China.

You may use this letter in the court in supporting Professor Yau's case.

Sincerely yours,

Feng Luo
Professor of Mathematics
Rutgers University
New Brunswick, NJ 08854
USA

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Professor Chin-Lung Wang, National Central University, Taiwan, responds to the New Yorker article
November 3, 2006

Dear Mr. Cooper,

The New Yorker article "Manifold Destiny" by Nasar and Gruber on August 28th is an imbalance report with the obvious intention to slander Professor Shing-Tung Yau. I would like to point out some issues raised there with which I'm familiar and where I think the report is completely misleading. This letter grows out as an expanded version (namely with more mathematical details) of the one I sent to Nasar on August 23rd after I saw the preliminary version of their article. Clearly my letter had no influence on their final report. I am among one of the many people who wrote to them before August 28th. When there were still chances for Nasar to listen to different voices she still chose to listen to one side of words. This had disappointed all of us and made us suspect the real purpose of that report. Please freely use this letter in situations where it may be of help.

1. On page 52, "At Harvard, he ran a notoriously tough seminar... Each student was assigned a recently published proof and asked to reconstruct it, fixing any errors and filling in gaps. Yau believed that a mathematician has an obligation to be explicit, and impressed on his students the importance of step-by-step rigor".

As a former student of Yau at Harvard (1993 – 1998), I benefited a lot from these intense seminars. A significant part of the seminars is to go through some established important theories which were unavailable in courses during that time. Most of us learned from others through it. In fact, we are grateful to Yau for spending so much time with us and sharing with us his insight generously. While some people may consider our seminar tough, many more people in the mathematical community have a great regard for it. Another significant portion of our seminars is to study recent major progresses in Mathematics. This is no doubt the best way to do research. And only in best schools can such activities be run successfully.

By the way, step-by-step rigor is always the necessary ingredient for a mathematical theory to be finally accepted. You may base your research only on results that can be reconstructed. In natural sciences, experimental results can be accepted only if they can be repeated. In Mathematics, a theorem can be accepted only if the proof can be reconstructed without gaps. This is a common sense since the ancient days of Euclid. The above quotation was written purposely to give readers the wrong impression that Yau did not encourage his students to create their own ideas.

2. On p.52 to 53 about the mirror conjecture: "On at least one occasion, Yau and his students have seemed to confuse the two, making claims of originality that other mathematicians believe are unwarranted".

In the 1980's, the urge to understand the structure of Calabi-Yau manifolds came from two completely different aspects, one in the classification theory in algebraic geometry, another one in string theory. Since then Yau's school at Harvard including his collaborators, post-doctors and students had started an extensive study on this subject. String theory predicts the existence of mirror family of Calabi-Yau manifolds which should give rise to the same quantum field theory as the original Calabi-Yau. In 1991, Candelas et al had made the prediction precise in the case of quintic three-folds which states that the pre-potential of instanton invariants should agree with the pre-potential of special geometry on the complex structure moduli space of the mirror quintics.

The progress in proving the mirror prediction and in particular the formula of Candelas et al is best explained by the existing literatures following the time order, and from which one finds promptly that the above quotation is baseless:

Givental's article in 1996 was the first claiming to prove the mirror prediction. Givental's argument involves Floer homology and the theory of equivariant quantum cohomology, experts did find difficulties in following his argument. Manin in his 1996 Max Plank preprint said that "some work remains to be done in order to complete his arguments".

In 1997, Lian, Liu and Yau published their proof of the mirror prediction and introduced a number of new ideas. The first one is the concept of Euler data which enabled them to give a direct argument and made their results applicable to many important situations beyond the formula of Candelas et al. Another crucial new idea in LLY is the special geometry relation between the one-point invariants and the instanton pre-potential. The Mathematical Review MR1621573 (99e:14062) of LLY by Gathmann said that "however, his (Givental's) proof was hard to understand and at some points incomplete. The current paper of Lian, Liu, and Yau now gives the first complete rigorous proof of the physicists' formula".

[to be continued]

...

After the appearance of LLY, Pandharipande's 1998 report in Seminar Bourbaki (math.AG/9806133) explains some of Givental's argument. It says that "A complete proof of the Mirror prediction for quintics by Lian, Liu, and Yau using localization formulas has appeared recently in [LLY]. The argument announced by Givental in [G1] yields a complete proof of (i)-(iii)". The AMS book by Cox and Katz in 1999 explains some details of both proofs. This book follows LLY's proof closely, but in discussing Givental's proof details are often sketchy or referred to Pandharipande's report instead.

The work of LLY is of course not totally independent of earlier works. It was written explicitly in their introduction that their Mirror Principle is a combination of ideas initiated and developed by many people including Kontsevich, Givental, Witten and Candelas et al. Indeed Givental's work was also inspired by Kontsevich and others. No one works totally independently and we all rely on one another. Most mathematicians give credit to both papers since their viewpoints are all very helpful to later developments in this field.

I would like to highlight some importance feature of Euler data through one example. Already in the LLY paper Euler data was applied to concave bundles and to the study of local mirror symmetry. The concave bundle case was also handled by Givental in his subsequent papers dated after LLY. In my earlier investigation on the invariance of small quantum ring under simple flops in 2004, Euler data for three-point functions for concave bundles plays a decisive role in forming the philosophical basis that such an invariance statement is possible. The final proof (math.AG/0608370, joint with Lee and Lin) turns out can be carried out inductively. The starting point then can be based on either LLY's result on one-point invariants or Givental's. Yet without the earlier inspiration of Euler data, my research on this problem will probably have not started.

3. On p.52, "More than a decade had passed since Yau had proved his last major result".

I am not sure how such a ridiculous statement is drawn (by a reporter?!). It is already funny to identify "his last major result". Maybe they meant the existence of complete Kahler-Einstein metrics in late 1980's, or maybe they meant the Donaldson-Uhlenbeck-Yau theorem on the existence of Hermitian-Yang-Mills connections on stable bundles. This later result, proved by Donaldson in 1985 for the two dimensional case and Uhlenbeck-Yau in 1986 for general dimensions is indeed of fundamental importance in algebraic geometry as well as in physics. The theorem became much more prominent in the 1990's. In physics literatures, they call it DUY theorem. Recently in 2004 Li and Yau solved an important system of equations of Strominger based on the HYM-DUY connections.

On the other hand, it is well-known that in 1996 Strominger, Yau and Zaslow initiated the so-called SYZ program which provides a ground-breaking insight into the structure of Calabi-Yau manifolds. Together with Hamilton's Ricci flow, which Yau has played a significant role in its development without asking for a formal credit (see Hamilton's letter for Yau's insight on Ricci flow), they form the most important two subjects in differential geometry in the past ten years. While Yau does prove many major results (including the mirror prediction) in recent years, as a world leading figure in geometry he also directed and promoted frontier researches more than anyone else in this field.

Before SYZ, researches on general Calabi-Yau manifolds are limited to algebro-geometric methods and there was indeed no satisfactory mathematical explanation of the full mirror symmetry phenomenon. It was also unsatisfactory that mathematicians play only the role to verify (though highly non-trivially) the physics predictions or even just to make their predictions mathematically meaningful. Geometers seemed to lack of some fundamental thinking in attacking these problems. It was the SYZ program which took the major task to reveal the underlying structure of Calabi-Yau manifolds and brought together other fields in mathematics including differential geometry and non-linear analysis into the study. This approach opens new research directions in geometry and has since then been very fruitful.

Calabi-Yau manifolds serve as the underlying spaces of string theory, the expected theory of everything. Yau's solution to the Calabi conjecture in the 1970's made possible the starting of this story. Twenty years later, the SYZ program made a truly mathematical input to this story again. Mathematics and theoretic physics have influenced each other deeply in this exciting historical moment. Without the tremendous efforts made by Yau and his collaborators the story may not have been as exciting as it is now.

Sincerely yours,

Chin-Lung Wang
Professor of Mathematics
National Central University
Chung-Li 32051, Taiwan
dragon@math.ncu.edu.tw