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2 according to class standing. I was ranked first in my high school. I had my college education in Taiwan National University in Taipei. In high school, I liked both Chinese literature and mathematics. In college, I decided to major in mathematics. I: You started as an analyst but you are now interested in problems about geometry. Do you consider yourself to be an analyst first and then a geometer, or the other way around? C: I consider myself to be an analyst first and a geometer second because of my background and the way I think about mathematics. So basically I am an analyst and now I am working on problems which are very geometric in nature. Fortunately, I have other co-authors who are more of a geometer than an analyst. So we cooperate with each other. I always think of myself as an analyst. I: There have been many recent developments at the interface between geometry and partial differential equations. When and how did the interaction start? C: It has a long history. The interaction between geometry and partial differential equations (or between geometry and analysis in general) is most natural. I would say it started even in the 19th century. Geometers like [Henri] Poincaré already used the analytic approach to study problems in geometry in the late 1890s. There are also the geometers of the previous generation, like S S Chern, [Michael] Atiyah and [I M] Singer, who laid the foundations for approaching problems in geometry using analytic methods. There has also been pioneering work by contemporary people like [Louis] Nirenberg, [Karen] Uhlenbeck, [Richard] Schoen and [Shing-Tung] Yau. I: Partial differential equations are analytic in nature. C: Yes. You first study the problem in the plane domain and then you study the problem in Euclidean 3-space and it is most natural to study it in higher dimensional space. There the curvature and the geometry come in. I: It seems that geometry is becoming very analytical in nature. Is there any intrinsic geometry that is involved or is it just a matter of using the language of geometry? Does it involve any geometric intuition per se? C: I wouldn t put it that way. I think that analysis is a tool in studying geometric problems. Geometry provides concrete examples for studying some problems at the interface between geometry and analysis. The geometric objects are concrete examples for problems in analysis. For example, you want to know what happens on the sphere that is a concrete model. You have the analysis which is abstract analysis convergence, weak convergence. To apply the abstract theory you need concrete examples. Geometric objects provide those examples. Of course, it is intrinsic geometry that is involved. And geometric intuition plays an important role in the approach. Analysis is sometimes a tool. I: Geometric intuition is not something that everyone has. Is that so? C: That is true, but on the other hand, I think that everybody has some type of geometric intuition. A problem would not be natural without the geometric intuition. I: There are some famous mathematicians who are able to look at geometric problems and see the results even before they can prove them. This must have involved a lot of geometric intuition. C: Yeah, yeah. If you are talking about 2-dimensional problems, maybe some people have more intuition than other people. It could also be a way of training, from their background, from the way they see things. It is true that some people have more intuition than others. I: Is it possible to develop such geometric intuition? C: I think so. For example, a lot of analysis problems need a lot of intuition. It s not just geometric problems that need intuition. I: But analysis is more axiomatic. C: Yes, it is more structured and more systematic. You are trying to derive formulas to solve a problem. However in the direction of approach to the problem in most times, you also need intuition. You need to have some picture in your mind in both geometry and analysis. Maybe more so in geometry. I: Have you applied your mathematical ideas to problems in physics or other scientific areas? C: I hope to do so in the future. At the moment, no. Some of the problems I am working on are related to 26 July 2012, Volume 2 No 3

4 and conferences and so on. Maybe it s more difficult for young people to really quiet down and think through a subject more deeply the fundamentals, the basic background. I think young people should not be pushed by fashion and should not be forced to be very quick and have a lot of publications. They should instead think more quietly and think through the foundations of the subject. I: Of course, mathematics has a lot of competition from more lucrative subjects like economics, computer science, financial mathematics. C: The competition is always there, of course. First, you must have a real love for the subject, so you really want to understand something. So you are willing to devote your time and take the long-term approach. I: Also, mathematics is a very demanding subject. C: I think if you want to do well in any subject, it is demanding. If you want to be a good musician, a good painter, a good economist or to know your subject well, it takes a lot of devotion. I: Can you tell us something about the latest work you are working on? C: I m working in a field called conformal geometry. Recently we are trying to use fully nonlinear partial differential equations to study patterns in geometry; in particular, the latest project I m involved in is to classify a certain type of 4-manifolds up to diffeomorphism using the analytic approach. I: Do you think collaboration is very important for mathematical research? C: It is. You learn much faster by talking to other people. For me, I m an analyst and, in my project, it s important for me to talk to geometers. In this case, fortunately for me, one of my main collaborators is my husband, Paul Yang, who is a geometer. I think it s very important to collaborate and talk to other people. I: Papers written by single authors and papers written with other authors are often given different weights. What is your view on this? C: For papers written by yourself and papers written with others, the weights should be a little different. If you have to do everything by yourself, the weight should be heavier because the speed will be slower. If you have collaborators, you could have more papers. When you work alone, you may have only one paper. If you have collaborators, you may have two or three. Even if you count it as one-half, it s still fair. However, the quality of a person s papers is more important than their quantity. I: Knowledge is now so broad that it is quite natural for research to become more like a collective activity. C: But I also want to say that in the evaluation system, we should leave room for people to work alone. Some of the fundamental work requires deep thinking and a long-term commitment. Some people may want to work on their own project rather than in collaboration with others and be obliged to listen to other people s opinions and be influenced by them. In the mathematical community, we should leave room for people who want to do work in their own way. Mathematical research is not just a scientific approach; the nature of mathematics is sometimes close to that of art. Some people want individual character and an individual way of working things out. They should be appreciated too. There should be room for single research and collaborative research. The following two questions were sent to Professor Chang as an update of the 2004 interview and her responses are given below. Q: An International Congress for Women Mathematicians was held before the International Congress of Mathematicians in August 2010 in Hyderabad. What do you think are the main issues confronting women mathematicians in the United States? A: The main issues confronting women mathematicians in the United States are probably not so different from the main issues confronting women mathematicians in the rest of the world. Basically and traditionally, mathematics is considered to be a field of interest for men ; many girls and women are not encouraged, or do not know the possibility, to pursue interest in this direction. The other issue is the conflict between career and family during the child-bearing years but this is a common issue for women in any profession, not just restricted to being mathematicians. Especially in the academic world, the tenure system is very unfavourable to women, as normally the critical time period 28 July 2012, Volume 2 No 3

5 in which tenure is decided coincides with the time period one would consider to raise a family. Q: Princeton University started something called the Noetherian Ring. Please tell us something about it. A: Noetherian Ring is a nation wide club for women mathematicians. The branch at Princeton started around the year 2000 and was formed by a group of women graduate students. As for references, there is a university news article from 2008, when it was run by Lillian Pierce: pwb/08/0310/math/ and the web page math.princeton.edu/noetherian/events.html has a partial listing of events since Y K Leong National University of Singapore Y K Leong is an Associate Professorial Fellow in the Department of Mathematics of the National University of Singapore (NUS). He obtained his BSc (Honours) from the University of Singapore and his PhD (in group theory) from the Australian National University. He has taught in University of Singapore and its successor NUS since He was an academic advisor to the Open University Degree Programmes (Singapore Institute of Management). He has held offices in the Singapore Mathematical Society. He has been an editor in the Singapore Chess Federation and the Institute for Mathematical Sciences, NUS. His research interest is in algebra. July 2012, Volume 2 No 3 29

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