Assoc. Prof. Christina Sormani, C.U.N.Y. Graduate Center, responds to the New Yorker article
Oct. 6, 2006
To Whom it May Concern:
I am writing on behalf of Professor Yau from the perspective of a young mathematician whose career he has supported.
S. T. Yau was not my adviser but took an interest in my work after hearing me present a theorem of mine at MIT. It was a partial solution to one of over a hundred problems he has published that have given young mathematicians a place to look for new questions.
I am eternally greatful to Professor Tian for inviting me to give the talk at MIT and then introducing me to Prof. Yau, and I am eternally grateful to Prof. Yau because I was offered a position as a Harvard postdoc two weeks later. At the time I had no job offers despite finishing my doctorate at a top university with NSF funding.
Mathematics is a very competitive field, with a seriously bad job market and very little NSF funding. Naturally there will be people who resent Professor Yau for the choices he has made. Keep in mind that all of us have had our papers rejected, our NSF proposals turned down and our job applications pushed to the bottom of the pile. Some people choose to blame S. T. Yau when things do not go well for their students or their proposals.
Professor Yau is not “determined to retain control over his field”. I give an example from my experience as his postdoc. He recommended that I read and present some very exciting papers by Gromov which have shaped my future research considerably. I would like to remark here that Gromov has a very different style of mathematics than Yau and, by encouraging me to read Gromov’s work, Yau was not promoting his own agenda in any way. He recognized that I had a metric geometric approach to mathematics rather than an analytic one and advised me accordingly. By presenting the work to his students, they learned Gromov’s methods and ideas as well.
While S. T. Yau first gained an interest in my research because of a partial solution of one of his many conjectures, Yau has shown sincere interest in my other work entirely unrelated to his lists: like a partial solution of a conjecture by Milnor, a paper on spectral theory suggested by Gordon and an application of Gromov’s techniques to study the stability of the classical Friedmann model of the universe not mirror symmetry. S. T. Yau writes the lists to provide a guide to those looking for interesting problems, not a prescription for all future mathematics.
Professor Yau “pushed his students to tackle big problems” because his students and postdocs are ready to meet the challenge. S. T. Yau met with his students and postdocs “three days a week for three hours a day” so we could present papers to each other. This is the best possible way for the presenter to truly understand a paper: presenting every step in full detail rather than just giving a one hour overview. Often a paper would need to be presented for a week or two. It is also an excellent way for the students to learn more mathematics than they have time to read on their own: they were welcome to ask questions and to listen to Yau’s insights as well as that of the presenter.
Professor Yau’s students do work on hard problems. They are very intelligent people: Harvard graduate students. If you aren’t going to push the best of the best to do more than their best, how does one end up creating a top notch mathematician like Tian or Cao? Great mathematicians work hard. If you don’t want to be a great mathematician, you don’t have to choose a top notch math program like Harvard. Any Harvard graduate student has their choice of doctoral programs not to mention plenty of opportunity for excellent jobs outside of academia. But a Harvard doctorate without a top notch thesis will not get them the academic job of their dreams.
Professor Yau has a Fields Medal and as such has acted as a leader in our community. According to the Fields Institute website, Fields stated that “while [the medal] was in recognition of work already done, it was at the same time intended to be an encouragement for further achievement on the part of the recipients and a stimulus to renewed effort on the part of others”, that the committee should “make the awards along certain lines not alone because of the outstanding character of the achievement but also with a view to encouraging further development along these lines”. This is supposedly the justification of the age limit, that the Fields is given at the beginning of an excellent career rather than as a lifetime achievement award because the recipient’s direction of research is meant to be continued.
Thus it is natural for Professor Yau, as a Fields Medalist, to suggest further directions of study in mathematics. It has been very generous of him not only to donate such time and energy to his students, pushing their success, but to publish problems lists and write textbooks which are easily read by any graduate student around the world. Should one say he has cowritten a textbook on harmonic maps to control the mathematics world? Of course not, his Fields Medal called for the advancement of mathematics related to his research and disseminating it in a textbook himself is generous. It is not easy to make profound new ideas accessible, but S. T. Yau has put in the effort to do so both through his texts and with his well written, detailed, correct and profound articles.
Perelman was never interested in the Fields Medal. Prof. Perelman has been well known in the geometry community for many years as a quiet intelligent mathematician with no interest in material wealth, prestige or leadership. It was not a suprise to any of us that Prof. Perelman should turn down the Fields Medal for this reason. Any implication that Prof. Perelman turned it down because of Prof. Yau’s promotion of the capstone paper by Cao-Zhu, needs to be supported with significant evidence. Personally I would like to see a publication of the full interview with Grisha Perelman. I am sure that, in the interest of truth, Prof. Perelman would grant permission for this unveiling.
Finally, I would like to close with the statement that young mathematicians need more professors like Shing-Tung Yau to guide them with open problem lists, textbooks and encouragement. He has been more than a great mathematician. He has been a leader.
Christina Sormani, PhD
Dept of Math and Comp Sci
C.U.N.Y. Graduate Center