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Q : How does IMU feel, and more precisely, what do you think about the WMY 2000 initiative?
D.M. : I think it is an excellent initiative and I think it offers a great opportunity to try and improve the image of mathematics and to try and give some inspiration to the mathematical community. This should be done in terms of several factors like Hilbert looking ahead to where we stand in mathematics and what the major challenges are and, at the same time, looking at our relations with the applications of mathematics, looking at the issues in mathematical instruction and looking at the hopes of involving the Third World more intensely in mathematical activities.
Q : Specifically on these three topics which have been defined for the WMY, have you a personal view on what the challenging problems in mathematics will be in the 21st century ?
D.M. : Ah! That is really a great question ; one would want to sit down and think about it much longer! I personally feel that a very important issue is to restore the free interchange of ideas between pure mathematicians and applied mathematicians. During the 19th century, you see that most mathematicians were both. Fourier series, for instance, were inspired by applications. But there has been a divergence, especially in the US, although I think to some extent in other countries too. I hope that the present emphasis on the usefulness of science in general (if the public is going to put money into scientific research, then it will be useful), will not lead simply to pushing applied subjects at the expense of work on pure subjects, but rather to a sense of common purpose where pure researchers can find inspiration in applications and use their theoretical ideas to grapple more effectively with applied problems. I think there has always been an interchange, but that will really be a major challenge.
Q. : What is your involvement in mathematical education ?
D.M. : It is a vast question. I'm involved in a particular project in the US, called "The Calculus Reform movement", where the goals have been to make instruction in Calculus more relevant to people who are specialized in all kinds of science and engineering and financial professions. Specifically, there is a group lead by Deborah Hughes-Hallet and Andrew Gleason which has written a series of texts now. They have what they call rule three : instead of simply teaching formulas and algebraic manipulations which are often the hardest things for people to apply, to understand their relevance, they are putting equal stress on numerical work and stating every general concept in terms of "How actually do you compute it on a calculator, how can you approximate when you have the data in front of you ?". That's one thing. Secondly, there is the visualisation approach that seeks to make effective use of graphical techniques to see the geometrical side of concepts. Finally, one must not forget algebraic manipulation. I should add that with these three technical methods of tackling the subjects, they also combine the idea of always including meaning for applications at every stage, so drawing applications from physics and chemistry, from economics. For instance, teaching multivariable calculus, when they start with integration. They start off with a graph representing the fox population in South West England which comes from this bible book of mathematical biology by Murray. And the question is : "How do we estimate from this graph giving the density of fox presence, the entire fox population?". So, this, of course, leads to and motivates integral calculus. I strongly believe that mathematical instruction should make a very serious effort to try to have real applications in mind. If you go back to the 19th century, you will find that almost all elementary school teachers often used examples with money : lending money and borrowing money, and so on, and every child understands money. This is concrete. I think statistics is a very important subject to bring into the school curriculum, because the kind of errors that schoolchildren are apt to make are very often errors in numerical judgement ; if you introduce the subject in schools, they will be better prepared.
Q. : What would you like to see in the Newsletter WMY 2000?
D.M. : What I hope will happen is that more concrete activities will gradually be formulated, with concrete plans for involving different groups, and so I think the Newsletter will evolve around these initiatives. We talked in the Executive Committee of IMU about the issue of the image of mathematics and tried to identify methods for explaining what mathematics is to the general public. I think there is no simple answer to this question. I think it is a very difficult challenge, I believe the most important thing is to find some individuals who are highly motivated and have the ability to put themselves in the place of the scientific public. Some people have this skill, and some don't. I think we have to resist a strong tendency to give lectures that are always more and more specialized.
Q. : Have you projects to change a bit the way IMU is organized?
D.M. : I have had two projects that I felt to be very important since people asked me to be President, that we are moving ahead on. One of these concerns the perception from the point of view of the US that the Union is some mysterious rather secret organization that is never clearly understood. Maybe one goal is to publicize what the Union is and what it does: we hope to have next April in New York City a meeting in connection with the meeting of the Executive Committee, to have a public forum, a round table discussion on Union activities, so the general public will see the valuable things it does. The other issue that I have been involved with is trying to increase the participation of applied mathematicians in the congresses and the method for doing this that we want to explore is to have joint activities with applied mathematical organizations. So we are not just talking about a subcommittee of the Union itself, but about involving groups like ICIAM, computer scientists, statisticians, mathematical physicists.