Presidential Views: Interview with James Arthur

Every other year, when a new AMS president takes office, the Notices publishes inter- views with the incoming and outgoing president. What follows is an edited version of an interview with James Arthur, whose two-year term as president begins on Febru- ary 1, 2005. The interview was conducted in fall 2004 by Notices senior writer and deputy editor Allyn Jackson. Arthur is a University Professor of Mathematics at the Univer- sity of Toronto. An interview with AMS president David Eisenbud appeared in the February 2005 issue of the Notices.

Notices: When you found out that the Nominat- Notices: The way mathematics is funded by the ing Committee wanted you to run for president, federal government in Canada is very different why did you say yes? from how it’s done in the United States. Can you ex- Arthur: I actually was quite surprised, not being plain the difference? an American and not working in the United States. Arthur: Yes. I don’t know the figures about total I was a little concerned about whether it would be funding per mathematician. I imagine they might a reasonable thing to do. So I made inquiries to both be comparable, or maybe a little higher in Canada. AMS people and also to a number of my colleagues, I think the main difference, as far as mathemati- and I was convinced that it would be viable. I don’t cians are concerned, is that there is no summer believe there has been an AMS president who has money in Canada. The size of the grants is variable, not been actually living in the United States. There and the money is used for postdoctoral fellows and have been other Canadians, such as Cathleen graduate students. Morawetz and Irving Kaplansky. But I cut my math- Notices: Do most Canadian mathematicians have ematical teeth in the United States, and I worked grants? there for twelve years, during graduate school and Arthur: I think most active ones have a grant. afterwards. As it happens I am the only member That suggests there are more grants in Canada per of my family who is not an American citizen. My capita than in the United States. wife is American, and my two sons are American Notices: Are the grants perceived the same way citizens and are both working at this time in the as they are in the US? Here an NSF grant is a big United States. I am very proud to be a member of validation, and mathematics departments take it se- the Canadian mathematical community. I came riously in tenure decisions. Is that also true in back to Canada in 1979, and I am proud to see the Canada? progress that Canadian mathematics has made Arthur: Yes. Of course, the size of the grant is since then. relevant also, because there are some small grants Mathematics is an international enterprise, and in Canada. But it’s taken very seriously. There are the AMS has something like one-third of its mem- of course good sides and bad sides to that. If a per- bers outside the United States. The AMS has some son receives a disappointing decision from the purely American mathematical concerns, but it is granting agency, it can be harmful psychologically. a major force in international mathematics. It is the On the other hand, the work of granting commit- most influential mathematical organization in the tees in both countries is very careful, and I think world and reaches well beyond the boundaries of we would not have that kind of careful, informed the United States. I don’t have a congressperson I analysis of a person’s work and of what a person can write to! But I suppose that one letter from a proposes to do if the analysis were done by uni- president to his local congressperson does not versity administrators who are not mathemati- make that much of a difference. I expect to be able cians. So in that sense I think the granting process to play a significant role in discussions with peo- is on the whole helpful to how mathematics oper- ple in Washington on mathematical questions. ates and how it is organized in universities. The

350 NOTICES OF THE AMS VOLUME 52, NUMBER 3 problem is that in the United States, relatively few At the undergraduate level, mathematicians have people are funded. been criticized for not being good teachers. The cal- Notices: Do you have thoughts on the NSF-funded culus sequence has of course been one of the prime VIGRE program? examples. But we have to remember that a greater Arthur: The idea is very good. It really helped proportion of students are taking calculus now build up graduate programs at some universities. than have done so in the past. In teaching calcu- It must be a little bit capricious as to which de- lus we are being asked to be the gatekeepers for partment gets a VIGRE grant and which one doesn’t. other academic programs. That makes for an ad- And there is always the danger that a department versarial relationship. Probably we as mathemati- might be worse off in the long run if it becomes cians are better teachers than we give ourselves dependent on a program that is not of infinite du- credit for being. We need to remember that, and ration. On the other hand, I think VIGRE probably we need to tell people has been very helpful to departments in attracting in our universities. good graduate students. It’s really hard to get good Notices: People say graduate students. This is something that I would that in recent years hope the AMS tries to affect in one way or another. math departments and We want the people who are best at mathematics mathematicians are as undergraduate or high school students to think much more concerned very seriously about going into a career in mathe- about the quality of their matics. These are talented people, and they might teaching than they were well be good at other things. If society does not im- ten or fifteen years ago. plicitly send them the message that mathematics Is that your sense? is important, for example by providing good fund- Arthur: Oh, ab- ing for graduate school, they might well think of solutely. Part of it is that other things to do. young mathematicians Notices: In your election statement you noted simply cannot survive if that mathematics has been the beneficiary of much they are not competent greater interest on the part of the public in recent teachers. That’s taken years. Why did that happen? very seriously by search Arthur: Well, it is quite remarkable. I am not sure, committees. So most James Arthur but you can point to some obvious things. Andrew young mathematicians Wiles’s proof of Fermat’s Last Theorem, in a way who are hired by universities are pretty good teach- that we would not have expected, caught people’s ers. That puts pressure on everybody to become bet- imagination. Books like the one on John Nash, A ter teachers—if you are an older mathematician, you Beautiful Mind, have also brought a good deal of don’t want to be shown up by the instructor or as- attention to mathematics. And of course in movies, sistant professor you have just hired! mathematics has been chic in the last five or ten Notices: What about minority students in math- years. There is a sympathetic curiosity about math- ematics? There are so few, for example, black peo- ematics. People don’t know what mathematicians ple getting Ph.D.’s in mathematics. What can be do, but they somehow have the feeling that math- done about that? It’s a difficult question. ematics has mystery, power, and beauty. I think peo- Arthur: It is, and I don’t think there is any magic ple who are not mathematicians have a sense of way to do it. It’s the question of role models. As a that. We should stoke their curiosity. We already white male, when I was beginning in mathematics, do so, but I think we can do more. I certainly did not understand the importance that This is probably the most important aspect of role models played for me. When I think back now, strengthening mathematics in the United States it was just something I took for granted. There and around the world. To have public sympathy and were people who were like me but twenty years interest in mathematics would help just about older than me, and they were mathematicians. It’s everything that concerns us as mathematicians. It hard to imagine what it would have been like if no would persuade more talented young people to go such people existed. For black students, there are into mathematics, because mathematics would be few role models as mathematicians. These are ob- regarded with interest, and maybe even awe, by vious things to say, but the AMS should do what it their parents and their friends, and would seem to can to increase the visibility and the prominence be a worthy cause to spend one’s life pursuing. It of mathematicians who belong to minorities. One would help funding for mathematics, because vot- obvious way is through membership on its com- ers would have a sympathy for it. Also, public ap- mittees. The AMS committees do wonderful work preciation of the beauty of mathematics would supporting the many different objectives of the So- help encourage good people to become high school ciety. They also lend a certain prominence to the teachers. people who are on the committees. I think we

MARCH 2005 NOTICES OF THE AMS 351 already work very hard on this, and when I am session, in which the speaker is given friendly ad- president, I hope we can find overlooked minority vice: “No, this is not going to work, you will have mathematicians and women mathematicians and to polish up on that.” I don’t know if we mathe- make them more visible as role models. My pre- maticians would stand for it! decessor David Eisenbud has done a very good job In September I went to a Congressional briefing on this. organized by the AMS Washington Office. Fred It’s a little sobering to be taking over this pres- Roberts [director of DIMACS] spoke on how math- idency! I look back at the past four or five presi- ematics can help with emergency preparedness, dents, and while they perhaps had different inter- disaster prevention, and related security matters. ests, they were all very impressive in the things they I don’t think Fred would mind me saying that he did. The AMS, in its professional operations, does didn’t speak about anything particularly deep in many different things. From the executive director mathematics on this occasion. It was a very charm- down, it’s an extraordinary organization. The AMS ing talk, and there were all kinds of questions at publication operation is really very important. I the end. One person, who appeared to be a Con- don’t want to get into trouble with commercial gressional aide, asked “What’s it like to be a math- publishers, but they are making it difficult for ematician? What does a mathematician’s typical mathematics and other subjects because the fees day consist of?” It was quite amazing, they were that they charge are enormous. Just look at what really curious. There was something about the way the AMS does. We have the Journal of the AMS, and Fred talked that invited this—you felt that he was it’s one of the best three or four journals in math- conversing with you. ematics. I doubt that other professional societies In calculus courses, we have the potential to in- have such outstanding journals. Mathematicians fluence a huge number of university students, look forward with anticipation to the monthly No- some of whom are going to be the leaders of to- tices of the AMS. We also have MathSciNet, with its morrow. And we somehow forget that. We can’t unequaled mathematical database. make every calculus student happy, but neverthe- One thing we have to be concerned about is the less we can try to communicate to them that math- lack of AMS membership among younger mathe- ematics is interesting, even if they themselves don’t maticians. I think that’s extremely important, and want to do it in the long term. I hope to try to think of ways in which we can in- About ten years ago, a former University of crease membership. It is not a question of the Toronto student endowed a chair in mathematics. dues—dues are not a large part of our budget. He was a person who had gone to New York and What is much more important is to have as many had done very well in investment banking. He took people participating in the AMS as possible. It in- first-year calculus in 1980 or 1981 at the Univer- creases our strength as a community. We need to sity of Toronto, and then did not continue in math- emphasize that we are part of a common enterprise ematics. He so liked his experience in calculus that that is a source of strength and energy for all of ten years later he came back to the university and us. endowed a chair in mathematics. This is really Notices: Are there other things that you want to quite scary, when you think of all those students try to address as president? in your calculus classes! Calculus is very pretty, and Arthur: I haven’t completely formulated in my we forget how remarkable it is. Perhaps we can own mind what things I will try to do. So many sometimes try to indicate to students that calcu- things are working well in the AMS that one has to lus is the starting point for much of mathematics. be a little bit conservative. But I will try to change I think there is a lot of good will that we don’t tend or add to things where I think I can accomplish to see on the part of the students. What we see per- something. Perhaps the area where one could try haps is their resentment at having to take calcu- to make the greatest difference is in, as I already lus when they don’t want to take it, and also the said, the public understanding of mathematics. I stress they have in learning and passing the exams think we should consider sponsoring more public in what is quite frankly a difficult subject, compared lectures and more publications that are directed at to the other first-year courses that they might take. the general public. But we forget that, underneath, a lot of them have For public lectures, there are two aspects. We a good will towards mathematics. Not all of them, would first of all have to do the mechanics of ad- but a significant number have an interest and an vertising it, getting people to come to it—then we’ve appreciation, even if they are not going to go on in got to deliver the goods! We would not regard giv- the subject. We need to stimulate it. ing a public lecture as a reward for being a good I am very honored to be president of the Soci- mathematician. We would instead have to make ety. It has had a wonderful history, and I have sure we find the people who do it best. I am told some very distinguished predecessors that I can try that other organizations actually script their pub- to live up to! I am very much looking forward to lic lectures. Before the talk they have a practice starting my term.

352 NOTICES OF THE AMS VOLUME 52, NUMBER 3