Caroline Series in conversation with Yu Kiang Leong and Suraj Krishna
In each and every dust mote are infinite bodies With cloudlike transformations pervading everywhere …
– Avataṃsaka Sūtra (The Flower Adornment Sutra)
Volume 7, Book 4 (Buddhist Text Translation Society)
courtesy Caroline Series
Caroline Mary Series has made important contributions to the theory of Kleinian groups, hyperbolic 3-manifolds and dynamical systems.
Educated at Oxford University, Series won a Kennedy Scholarship that took her to Harvard University where she wrote her PhD thesis on Ergodic actions of product groups under the supervision of George W. Mackey. She did short stints at the University of California, Berkeley, and Newnham College, Cambridge, and then moved to the University of Warwick in 1978, where she became a full professor in 1992, and eventually went on to establish a distinguished career.
Series was awarded the Junior Whitehead Prize of the London Mathematical Society in 1987, and in 2014 became the first winner of its Senior Anne Bennett Prize. She has also actively popularized mathematics and promoted mathematical awareness in the UK by giving many public lectures to school students, undergraduates and the general public. She was featured several times on Radio 4 and in the BBC documentary The True Geometry of Nature. In 2016 she was elected a Fellow of the Royal Society, and was the President of the London Mathematical Society between 2017 – 2019.
She is a co-author of the famous book Indra’s Pearls: The Vision of Felix Klein published in 2002 after a 10-year collaboration with David Mumford and David Wright (and a computer).
Series is well-known for her relentless and tireless efforts in promoting the professional interests of women mathematicians around the world, and is a founder member of the organisation `European Women in Mathematics’. More recently, she was Vice-Chair of the International Mathematical Union’s Committee for Women and Mathematics.
Well before the Intergovernmental Panel on Climate Change sounded the alarm on global warming in its by-now famous report of 2007, Series started an initiative for the formation of an environment committee in the University of Warwick in 2000, followed by a climate change seminar and related activities.
During her visit to the Institute for Mathematical Sciences in Singapore, Y.K. Leong interviewed her on 12 August 2010 on behalf of the magazine Imprints. The following is an updated version of the interview in which she talks about her passion for mathematics, her fascination with the beautiful and tantalizing world of fractals, and her personal commitment to women mathematicians and the environment.
Early career
I: At which point in your education did you decide to choose mathematics as a career?
CS: When I was about 14 years old and we had recently studied geometry in high school, we were given a problem for homework. I spent the whole evening trying to solve it. I succeeded and later I discovered that nobody else in the class had done it. From that time I resolved that I would always try to solve every problem which we were given in mathematics. I had a real passion for mathematics. My ambition then was to go to university and study mathematics as an undergraduate. Beyond that, life ended and I never thought about it anymore until I was about to graduate from Oxford University. Then I wondered what to do next. I thought that maybe I would be a schoolteacher. But almost accidentally and not knowing what else to do, I was influenced by a friend to try for a master’s in the US, and perhaps go on to a PhD. Until I had finished my PhD I was uncertain about having a career as an academic mathematician.
Dressed in a `sub fusc’, an academic dress required to be worn during formal University ceremonies in Oxford. A picture from June 1970, before the first-year exams known as `Honour Moderations’ or `Mods’ courtesy Caroline Series
I: You obtained your BA in mathematics at Oxford University but you did your doctorate at Harvard University. Wouldn’t it have been expected for you to continue your postgraduate studies at Oxford? Was there any reason for not doing so?
CS: Actually, I was born and grew up in Oxford. My father [George William Series, FRS (1920-1994)] was a physicist at Oxford University and I had always intended that as an undergraduate I would move to Cambridge. However, for various reasons, I ended up studying at Oxford. After that, I thought it was time I should change and I had a close friend who was recommended to go to Harvard to study for a PhD. So I decided to try to go to the US to study. It was more or less accidental. For my own career, it was an extremely important choice, and I have recommended it to several students since. I just recommended a good undergraduate student to go to the University of Illinois in Chicago. I think it is very good to have international experience.
Somerville College, Oxford. Series was elected an Honorary Fellow in 2017courtesy Caroline Series
I: Were you on a scholarship at Harvard?
CS: Yes. I won a very nice scholarship for the first two years, called the Kennedy Scholarship. It was a fund set up in memory of President John F Kennedy to allow some British students to go to either Harvard or MIT. After a couple of years, I was given a teaching assistant position. By the end of my PhD, I had no money left.
I: How did you choose your supervisor at Harvard?
CS: When I arrived at Harvard, I hadn’t really done enough research on the type of mathematics done there. I had imagined that because it was in the US, the graduate school would be enormous, but the mathematics department was actually quite small. Most of the professors were doing either algebraic geometry or number theory, and I was more interested in analysis at that time. So there were really not many professors to choose from. One was about to retire, and another, I felt, was too intimidating. I chose George Mackey because I thought he was more geometrical, more analytical than others.
Harvard — The then new brand new Science Centre, taken through the gate of Harvard Yardcourtesy Caroline Series
I: I notice that the topic of your PhD thesis is something about ergodic theory. Isn’t it a bit probabilistic?
CS: Yes, it is a bit probabilistic. George Mackey was, of course, a great expert on representation theory of Lie groups. But at that time, he was very interested in groups acting on measure spaces because this gives good examples of group representations. He had rather interesting and very original ideas. His other students at that time, including Bob Zimmer, worked on his ideas about what he called virtual groups, which turned out to have relations with many other topics. Also, early on, I was very uncertain if I could complete my PhD. I thought that I could perhaps instead get a master’s degree in statistics and become a statistician. I didn’t quite do that, but I did take some statistics courses. Studying ergodic theory fit in and would have made it easier to switch.
During graduate schoolcourtesy Caroline Series
B: In another interview of yours that appeared in Mathematics Today, the description of your time at Harvard is so graphic that we are compelled to recall here: “Being at Harvard had an enormous effect on my life afterwards because you get to know people so well at that time in your life. You saw all the top mathematicians in the world – many were on the faculty and other great people came to give colloquia. Mathematics was passing by in front of you and you were drawn into its orbit.’’ Was there any particular moment that left you with a lasting impact and drew you into choosing ergodic theory?
CS: I am afraid not, it was as I just described: I was working on statistics in the hopes of getting a Master’s degree and my supervisor Mackey was interested in ergodic theory which is very closely related mathematically. Besides which, it didn’t seem too overwhelming a subject to learn the basics of and get involved in, unlike some of the other topics I might have turned to.
George Mackey George M. Bergman, Archives of the MFO
I: You taught at the University of California, Berkeley, for only one year immediately after your PhD, before you returned to England to pursue and develop your academic career. Was this due to some kind of cultural pull?
CS: I always had the intention of returning to the UK in the long term. After I finished my PhD, I was in a fortunate position. I was offered a temporary lectureship in Berkeley which academically was my first choice. But I was also offered a position in Newnham College, a women’s college in Cambridge (UK). It was a research fellowship but it was pretty certain it would become a permanent college teaching job. I thought I couldn’t give up the opportunity of a likely permanent job in a Cambridge college. So it was agreed that I would go to Berkeley for one year and then go back to England. In fact, I only stayed in Cambridge for one year. At that time there were very few people there who had related mathematical interests. I was very lucky I got a job in Warwick, where there was a big group in ergodic theory.
Mathematics was passing by in front of you and you were drawn into its orbit
I: If I’m not mistaken, Cambridge was rather male-dominated at that time.
CS: At that time, it was exceedingly [male-oriented], socially and academically. But I did make a few good acquaintances, particularly S.J. Patterson; we found our work had an unexpected scientific overlap and our connection has continued over the years.
Indra’s Pearls and writing
I: According to David Mumford, the book Indra’s Pearls: The Vision of Felix Klein which you wrote with him and David Wright took 20 years {in the making. Mumford and Wright were in the US while you were in England. How did this collaboration come about?
David Mumford George M. Bergman, Archives of the MFO
Series in 1981courtesy Caroline Series
David Wrightcourtesy David Wright
CS: Of course, I knew Mumford when I was a student at Harvard, but this has nothing to do with our book. What happened was that some years after I left, Mumford became interested in making computer-generated pictures of limit sets of Kleinian groups, which are rather like Julia sets. David Wright was at that time a graduate student at Harvard, and very interested in computing. Together they made a large number of astonishingly beautiful pictures. They wanted to create an elegant coffee table type book of the pictures but it never took off because every time they met, they would spend the time creating more pictures. I saw some of their pictures and they fascinated me. I began trying to prove some facts about them. Mumford came across a popular article I had written about the pictures and he asked me to join them in writing the book. It took a long time, a full 10 years, but we finally succeeded. It was difficult partly because we didn’t very often have the opportunity to meet. One of us would write a long piece and send it to the others. The others, of course, wouldn’t answer because they were busy with other things. Finally, we would meet and decide we didn’t like what had been done and we would start all over again. This went on for years. It was really our publisher, David Tranah at Cambridge University Press, who had faith in the project and wanted it to succeed. He began to give us more and more pressing deadlines and finally, the book took shape. Without him, it would never have been written.
I: The patience paid off.
CS: Yes, I’m very happy with it. David Tranah gave us constant encouragement and support.
I: I must say that the pictures are really very nice. How did you do the colours?
CS: David Wright did the colours. It’s not hard to add colours; for example, you are plotting things at different levels, level n, level n+1, and so on, and you can cycle the colours. David Wright enjoyed playing with it. Since then some people have taken it up as a much more artistic enterprise, particularly Jos Leys, who is a wonderful mathematical graphics artist. He modified our programs to create very beautiful pictures; one has to pay attention to colour, arrangement and background. It’s a great skill.
A Schottky group is generated by transformations which map the outside of one sphere onto the inside of another. Normally all the spheres defining the generators should be disjoint from one another. The adjoining picture shows an arrangement of nested spheres for a particularly symmetric Schottky group where the generating spheres touch, which means that strictly speaking they are limits of Schottky groups. David Wright
I: The book Indra’s Pearls is largely computational in approach. Does this represent an alternative, if not new, approach to research in geometry? Has this approach contributed significantly to research in geometry?
CS: It’s not just our book. Computational pictures have made very important contributions to geometry in recent years. The whole theory of complex dynamics has been inspired by the computational aspect. The pictures Mumford originally liked actually had a lot of influence because when you see them, you understand that something that is conjectured to occur, really does. You begin to see intricate structures, and this inspires people to go and try to prove things. It’s a two-way thing. The computer-generated pictures have inspired a lot of research, and then the research suggests we make further pictures. They go hand-in-hand.
I: Did any of those pictures suggest new theorems?
CS: Yes. They suggested theorems of mine. I believe they also contributed to a very important result proved by Yair N. Minsky called the Ending Lamination Conjecture. Perhaps you have a theorem in mind, but seeing the pictures makes you feel more certain that there must be something in it, and you, therefore, become even more determined to prove it.
I find it astonishing that so many natural objects have outlines or structures that are fractal-like
I: Did it suggest any counterexamples?
With Mumford in 1983 when he was being given an honorary degree at Warwick courtesy Caroline Series
CS: I think it showed unexpected phenomena. You see something that you don’t understand fully and you realise you have to pay attention. The pictures in our book are 2-dimensional. Eventually, I learnt that in order to prove results about them one needs to use 3-dimensional hyperbolic geometry. It took me a long time to understand this. 3-dimensional geometry is very important.
I: It must be hard to imagine 3-dimensional space.
CS: It’s hard to draw pictures in 3-dimensional space. Now I’m looking at parameter spaces in higher dimensions. One difficulty is how to present computations; all you can do is to show two-dimensional slices, but you really want to see the full picture.
I: In the Avataṃsaka Sūtra, which you quoted in several places in your book, there is mention of an infinite web of pearls which mutually reflect each other and all the reflections in each pearl. This is an amazing analogy with a religious world view of the mutual interconnectedness and dependence of all things. Do you see any parallels in such viewpoints and your own mathematical viewpoints? For example, do you have a Platonist viewpoint that fractals exist “out there” and not just as mental constructs.
One of the first pictures of a limit set made by David Mumford and David Wright David Mumford and David Wright
CS: The last part is a very fascinating question. Mathematics exists in our minds and yet it gives us such a powerful way of dealing with the external world. One reason I like working with these computer-generated pictures is that you start with an abstract mathematical construct, but as you plot it by computer the reality seems to grow. All the things that you have proved, you see vividly in front of your eyes. And somehow one can’t argue with the pictures; they are so concrete. As for fractals, I find it astonishing that so many natural objects have outlines or structures that are fractal-like. It seems to me that the concept of fractals captures something very important in nature. I imagine that fractal geometry and its applications will become more and more important as time goes on.
I’m not sure about the religious part. But one thing that strikes me is that different cultures have different concepts of infinity. In the western tradition, we think of infinity as counting: 1, 2, 3, 4, going on forever in a linear way. The concept of infinity in Buddhist and Hindu writings is much more to do with objects subdividing into parts and then each part subdividing again and again forever. This leads to an uncountable infinity of limit parts. It’s a very different way of thinking. I think it must really colour the world view of these cultures. Western culture is very goal-oriented and likes to measure everything, whereas Eastern culture is more about inner structures and realities. Another example is the Maya in South America – their calendar worked in cycles. That is another idea of infinity. I suspect these different viewpoints profoundly affect people’s attitudes toward life. If I were more of a philosopher or an ethnologist, I would have liked to study this more.
I: Can I ask you if you have read the Avataṃsaka Sūtra?
CS: I can’t say I have read the whole thing. I bought a translation (it’s translated into English now) and I did read a considerable part of it while we were writing the book. I was always looking for suitable quotations. The book is extremely long. One thing is amazing. At various points are descriptions of large numbers of things: buddhas, jewels, worlds within worlds, and so on. The numbers described are huge, gigantic numbers. The people who were writing this ancient text must have had the concept that infinity was truly unimaginably huge. (Of course, I am speaking here about what I found in the English translation, not the Sanskrit or the Chinese versions.)
Concept of infinity in Buddhist and Hindu writings is much more to do with objects subdividing into parts leading to an uncountable infinity of limit parts
I: Now that Thurston’s Geometrization Conjecture has been recently solved by Perelman [Grigori Perelman (Fields Medal 2006)] and others, is it fair to say that everything of importance is now known about hyperbolic 3-dimensional manifolds?
CS: It is true that the Geometrization Conjecture has been solved by Perelman and others. But actually, there has been another extremely important development that happened more or less at the same time, done by Yair N. Minsky and his co-workers. This is the Ending Lamination Theorem I mentioned above. They managed to carry out a program initiated by Thurston [William Thurston (1946-2012), Fields Medal 1982] to classify infinite volume hyperbolic 3-manifolds using some rather simple invariants associated with their ends. From the knowledge of the end invariants, they show that it is possible to reconstruct the entire geometry of the manifold. This transformed the subject. Previously people were always trying to understand whether there could be any “wild” hyperbolic manifold lurking around somewhere. Now we know that in a precise sense they are all “tame”. We know how to handle all the infinite geometry. In that sense, the big questions were indeed solved within the recent past. I think it is true that the field has changed since this happened. But there are still many things to do, which one can now tackle using the manifold structure. I’m currently thinking about how limit sets evolve as the manifold is deformed. Minsky’s theory is just what is needed. People in the hyperbolic geometry community are also now looking at different kinds of geometry and geometric structures, some of them even related to physics. Our current program [Aug 2010] at NUS brings together different kinds of geometries in a broad way.
B: Could you explain the concept of limit sets in hyperbolic geometry for our readers, and tell us about their significance in the subject?
CS: This is rather complicated, but I will try.
Imagine a tiling of the ordinary Euclidean plane by rectangles. Any horizontal or vertical movement of the plane which moves these rectangles onto themselves is called a symmetry of the tiling, and the collection of all such movements is called a symmetry group. Now colour the top left corner of one rectangle with, say red, and label it {\rm P}. The symmetries move {\rm P} around so that we get a whole lattice of red points in the plane, one for the top left corner of each rectangle. This is called the orbit of {\rm P}, the original red dot.
Western culture is very goal-oriented and likes to measure everything, whereas Eastern culture is more about inner structures and realities
In a similar way, a Kleinian group is a collection of symmetries of three-dimensional hyperbolic space. If you choose a point {\rm P} in hyperbolic space, it gets moved around everywhere by the group, forming its orbit.
In one of the common models of hyperbolic space, the space is represented as the region above a base horizontal plane {\rm C} in three dimensional Euclidean (ordinary) space. However, distances are distorted (in fact as you go towards the base plane, distances look exponentially smaller than they really are) so that the distance from {\rm P} to {\rm C} is infinite.
As you move further away from the original point {\rm P}, even though orbit points remain hyperbolically equally spaced, they appear to pile up towards the bounding plane {\rm C}. In the limit, this creates patterns on {\rm C}. These patterns are the limit set. The original symmetries can also be represented as symmetries of the plane {\rm C}. In Indra’s Pearls, we don’t mention hyperbolic space and think of {\rm C} as the complex plane. There are very nice formulae in terms of complex numbers which represent how the symmetries act on {\rm C}. Moving {\rm P} around in hyperbolic space is echoed via repeated applications or iterations of these formulae on {\rm C}. This is what we have implemented on a computer, and explored in the book.
Limit sets are intimately related to the nature of the associated tilings and manifolds in hyperbolic space, but that would take too long to explain here.
I: Is it possible for one single person to read through the proofs of the classification results? (I’m thinking of the situation in the classification of finite simple groups.)
CS: It’s not as bad as that. There is a group of people who understand in principle how it [the proof] works. I can’t say that I have read it all. I think it is perhaps more conceptual. There are some very important geometrical and topological principles, and once you understand the principle and the outline structure of the proof then you can go and check the details. It is a reasonable thing to hold in your mind. I doubt that there are many people who have gone through everything but it is feasible. There have been some simplifications and no doubt it will be cleaned up further – it’s a matter of time.
I: Is the next step in geometric research on manifolds to go on to dimension 4?
CS: There is a community of people who work on dimension 4, but it has a very different flavour. For hyperbolic geometers, it’s not so much dimension 4, but investigating different kinds of geometric structures. This could be in dimension 4, but it could be much broader.
B: You have given many popular talks to a general audience based on your work on Indra’s Pearls, the most recent one being the online public lecture in January 2021.1 How do you assess the public response, in the sense that, were there any interesting incidents to recall? Or has it been mostly mathematicians who ask questions?
CS: People are fascinated by the pictures at many different levels. Many people say how beautiful they are and some want to experiment for themselves. Some people got a little more involved, and even used them as a basis for design, creating even more elaborate pictures.
I also get questions from mathematicians, ranging from quite elementary school-level questions to people asking me real research-level technical questions. Sometimes it can be quite hard to field all these different kinds of questions at the same time.
The people who were writing this ancient text must have had the concept that infinity was truly unimaginably huge
>B: One can imagine that engaging in writing books like Indra’s Pearls, with an outreach intent, and giving public lectures on the same topic, must be quite different experiences. What has been your experience, and which one of these has been more satisfying for you?
CS: It was a deeper experience to actually write the book. I greatly enjoyed working with the two Davids. It was a massive effort and I learned a lot about writing. It has influenced all my writing since, be it of mathematics or other things. I learned when writing mathematics always to try to keep the symbols and notation to a minimum, and to try to present things in a way that I hope the reader will find both inviting and clear. On the other hand, in giving public lectures, it is very satisfying to get feedback and general appreciation and to be able to share this beautiful bit of mathematics with a wide audience. Every audience is different. Giving lectures by Zoom is another matter which I haven’t yet really mastered. One thing which is sadly lost is that one can’t judge people’s reactions, and I miss the `buzz’ of having an audience I can see. And I still have to learn how to time myself better.
B: Imaginative titles do indeed play significant roles in the success of a book. Whose idea was it basically to come up with this fascinating title for the book, and how did it come about?
CS: The idea of the title was mine, and it came to me quite suddenly one day in the common room at Warwick when I was talking to David Mumford. Since I was a teenager, I had an interest in `Eastern’ religions and I had read quite a lot of books on the subject. One, in particular, was Fritjof Capra’s The Tao of Physics. The myth of Indra’s Pearls is mentioned there, and it had even been picked up by the brilliant physicist Mike Berry and quoted in a paper he wrote: I think it was about patterns formed by distortions caused by refraction through fractal surfaces. Somehow those words had always stuck in my mind, and came to me at that moment as a possible title. Luckily, when I explained, the others agreed.
>B: Do you look at it now as a thing of the past, or is there something that is yet brewing in your minds?
CS: The book is of the past but I am still proud of it, and I am still working on a similar part of mathematics. And I still love the pictures.
B: Do you do other creative writing, like poetry, apart from writing on mathematics?
CS: I used to write poetry although only one or two have ever been made public. I wrote a poem titled `Cornish Dawn’ a long time ago when my parents had a small holiday house in Cornwall.
With parents George and Annette Series in Cornwall in the 1980’s. George (G.W. Series) was also an FRS (a physicist) courtesy Caroline Series
Cornish Dawn
Come to the light, stand soft at the turning,
The dawn wind breaks low on the eastern moor.
Watch with the elm on the edge of the sunrise,
Cradled by gorse in the primrose-damp hollow,
Heart sunken deep in the bracken-ribbed earth.
Wheel with the seagulls high on the morning,
Crying to foxes far down the marshes,
Wandering wild in the echoing dawn.
Let your pain sink in the pool by the ash root,
Soft, that the kingcups may bury your hurt.
Bending to reed banks bowed by the alder,
Swaying in grasses tall by the water,
Watching your thought in the ebb of the stream,
Secretly cleave to the oak in his standing,
Steadfastly bound at the womb of the world.
Caroline Series. Cornwall, April 1978.
I like writing but usually, if it is not mathematical it is short articles. I was rather proud that part of a piece I wrote about fractals and chaos found its way into the Faber Book of Science, an anthology of popular science writing chosen by John Carey, professor of literature at Oxford University, for its clarity and literary value. One article that I co-wrote with David Wright for Plus magazine on Non-Euclidean geometry and Indra’s pearls might interest your readers.2
Service and outreach activities
I: Picking up another thread, you have been very active in promoting and supporting opportunities for women pursuing careers in mathematics for many years. What have been the achievements of the organization European Women in Mathematics [EWM] of which you are a founder member?
CS: When we set this up, it was not really [meant] to be a campaigning organization. Rather, we wanted to create a network of women to exchange ideas, share problems, encourage each other, meet at conferences and so on. I believe we have had some influence. It was set up almost 30 years ago now, and there have been a considerable number of programs in different countries and different institutions to encourage and give more recognition to women. This could be inviting women to give prestigious lectures, or special meetings or grants. Some universities have made it a point to make sure that they have women on committees. Particularly in Germanic countries, it used to be very difficult for women, but now the climate has become quite favourable. We were a group of women from many different countries and this gave us a wide perspective. We gathered some statistics and it was very noticeable that there are a lot more women mathematicians in some countries than others; it is partly a cultural issue. I think we probably encouraged a number of young women, who without us would have taken up some other job. Women usually have to carry the burden of family life. We had some successful older members who could say, “Well, it’s difficult but I’ve managed to succeed and this is how I did it.” This has been encouraging to other women.
I: Is this organization centred in England?
CS: No, it is pan-European. There was already a big organization in the United States. Our idea was that we should have a counterpart in Europe. We have a main meeting once every two years somewhere in Europe, which attracts 70 to 80 people. We also have a number of members from outside Europe. Our structure is set up so that women anywhere in the world can come along and say they want to establish a group in their country.
B: I understand that more recently you have been involved in another international organisation for women mathematicians?
CS: Yes, around 2013 the then President of the International Mathematical Union (IMU), Ingrid Daubechies, had the idea of creating a part of the IMU website as a resource for female mathematicians internationally.3
I got very involved in making the website and this led to the IMU setting up a new committee, the Committee for Women Mathematicians (CWM), in 2015. I became CWM’s Vice President. Aided by generous funding from the IMU, I am proud that we were able to help numerous groups, largely in developing countries, to get themselves organised and start having meetings for women mathematicians. Everything came together in a big conference called the World Meeting of Women Mathematicians just before the 2018 ICM in Rio de Janeiro. CWM is still doing great work although I am no longer very involved. I was involved in writing a history of both EWM and CWM which are to appear in a book called Association for Women in Mathematics: the First Fifty Years, to be published by Springer later this year.
B: In the recent past, you held the office of the President of the revered London Mathematical Society (LMS). What was your experience? Do you think the particular stint also helped further your own interests and activities to meaningfully engage with the larger mathematical community? Were there any novel ideas that you were able to initiate?
CS: It was a great honour to be the LMS President. I had the chance to meet all sorts of people and travel to different places, including the ICM in Rio and the Abel Prize celebrations in Oslo. I enjoyed learning from the inside how an organisation really works and dealing with all the many things which came up. It was also very hard work, especially since I have a long train journey to get to London. I was able to set up several initiatives. One was that we moved a large part of our electronic systems online, which as it turned out was just in time as it has meant that all staff could easily work from home during the Covid pandemic. I also initiated some actions to commemorate Sir Michael Atiyah who died during my time in office, and I commissioned an environmental audit of the LMS Buildings in London which has since been developed further into a proper Environmental Policy. I have written more about my experiences in the May 2020 LMS Newsletter.4
I: Could you tell us something about your interest and involvement in activities concerning environmental issues and climate change?
CS: This is something I have become increasingly concerned about in recent years. It began when I became involved in our university’s recycling. We were not recycling anything very successfully. The system was reliant on charitable and voluntary actions, and it didn’t really work. Eventually, I came to realise that you needed something in the infrastructure of the University to take care of environmental issues. It’s no good just relying on people’s goodwill. So around the year 2000, I managed to set up a committee in the university. I made contact with a professor from the Business School and together we approached the university administration. We set up an informal group of some academics and some administrators. For several years we were not very successful because we had no proper resources. Finally, the university decided to hire an environmental officer whose job was to be a focal point for environmental issues within the university. He was responsible for handling issues like recycling, energy consumption, water consumption, and transport problems. Now we have an official university committee with an environmental officer, transport officer, recycling officer, energy officer, and the university is making very substantial efforts to reduce its carbon footprint. We have a cost-effective recycling scheme. I’m very happy with it.
B: No doubt these things have moved on since 2010?
CS: Yes indeed. The operation at Warwick University has become fully professional and has been broadened to include the difficult issue of travel. This confirms my vision that environmental issues need to be handled on an institutional or `official’ level. Of course, concern about the environment has finally become entirely mainstream. I am so relieved that President Biden seems to be taking climate change very seriously indeed.
On a personal level, I had already put solar panels on my house in Warwick and when I retired in 2015 and moved house, putting up both solar electric and solar hot water was almost the first thing I did.
Recently I have become very concerned about the rise of the global population. We are now nearing 7.8 billion people on earth compared to only about 2.3 billion when I was born. In many countries, the birth rate is falling, but not fast enough, and our population has already outstripped the capacity of the earth to allow everyone to have a reasonable standard of life. Once you think about it, it becomes obvious that the huge global population is behind so many of our environmental problems. The global population is projected to get to 11 billion by the end of the century. I have read that if every other couple had one less child this would mean 4 billion fewer people in 2100. Surely this would be a good thing.
I: What advice would you give to students, especially women students, who would like to pursue a research career in mathematics?
CS: My advice is that first of all, you must really like doing mathematics. It may not be a glamorous career. But if you really want to do it and love mathematics, and you are persistent, then you will find a way to succeed. What I did and what worked for me is, at the beginning of your career, try to go to the best places you can and meet the leading people in the field. That way you get a good grounding. Later on, when you have to find a permanent job and you perhaps have family constraints, then you have already got a good basis and good contacts, and so wherever you settle, you are still able to continue research. For me, it has been a wonderful career and I would recommend it.
Thank you very much, Professor Series, on behalf of Bhāvanā, for consenting to do this updated version of your ten-year-old interview. It has been a great pleasure.\blacksquare
The IMU is the main international body that coordinates all national mathematical societies and has been likened to the `United Nations of Mathematics’. It organises a major international conference, the ICM, once every four years. ↩
Yu Kiang Leong is a retired Associate Professor in the Department of Mathematics of the National University of Singapore. He was the founding editor of Imprints from 2002 to 2006.
Suraj Krishna is a Visiting Fellow at the Tata Institute of Fundamental Research and a contributing editor of Bhāvanā.
