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WMY 2000
Popularizing mathematics

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Mathematics

EXPERIENCES WITH POPULARIZING MATHEMATICS
by Vagn Lundsgaard HANSEN, chair of EMS-Committee on WMY 2000

In a society with an increasing number of superficial distractions and governmental pressure for immediate economical results, it is no longer enough that we mathematicians keep the eternal values of our subject to ourselves.

There are some inherent difficulties. Mathematics contains serious, logical reasoning and cannot be dealt with in 20 seconds ; it needs concentration. Furthermore, although we all have been exposed to mathematics for many years in school, the layman only reluctantly allows the use of the language of mathematics ; it is considered boring. I have been told that the first mathematical equation used in a text reduces the potential number of readers by 50% and that the second one kills it. In general, I oppose this kind of straitjacket put on mathematical writings but you do have to go some way to avoid technical language if you want to present mathematics to a broader audience.

There are many mathematicians who have done much more than I have to popularize mathematics, but given the opportunity, I shall reveal some of my experiences.

In 1982, I was asked to design a shopping bag with a mathematical theme for a major food store chain in the Copenhagen area. (You can read more about this in a forthcoming article in The Mathematical Intelligencer.) It gave me a lot to think about. I wanted to show that mathematics is not only theoretical but that it has something to do with grasping the world in which we live, and that the development of a theory is the result of the combined efforts of mathematicians in many countries over a comparatively long period. I also wanted to show that mathematics interacts with other sciences, and that it has applications. I ended up choosing Dirac's String Problem. The bag was produced in 200,000 copies. I received 25 'reprints'. Surely, I must be the mathematician whose work has been placed in the most wastebaskets in the world. Nevertheless, it was quite entertaining to do the work, and it did generate some interest at the time and also very recently.

The next experience I shall mention came in connection with the publication of the collected mathematical papers of the Danish mathematician Jakob Nielsen. We received a donation from the Carlsberg Foundation to make the publication viable, and I was asked to write an article for their annual report 1983. Since the article was to deal with Jakob Nielsen, and the reason for the donation was his mathematical contributions, I decided to include two short sections on his work in group theory and topology. It was a thoroughly refereed article - every member of the board reading it. They liked it, but as the secretary wrote me : "We do agree with you that there should be some mentioning of the mathematical world of Nielsen, but could we typeset the most 'hefty' mathematical parts with a small font since when it comes to mathematics, there are an awful lot of laymen."

In 1989 I published a book in Danish on the role of geometry in our perception of the world. In 1993 it was translated into English and published by A.K. Peters Ltd. under the title Geometry in Nature. The book is intended for the educated layman and in the preface to the English edition I say : "In fact, I planned the book so that our Danish Minister of Education would be able to read it (if he so wished)." From time to time, people have asked me whether I have tested it out on the Danish Minister of Education. My answer is that I did give him the book, and I can tell you that he remembers me. In a friendly review of the book in the Mathematical Reviews, the reviewer builds up a joke saying : "The reviewer would not be very optimistic on this score in the case of his British counterpart." I have had many delightful experiences in connection with the book including several favourable reviews.

In connection with the publication of the Danish book, I was asked to write an article for a weekly magazine published by the Danish Engineering Society. I put quite a lot of work into preparing an article for them. After submitting the article, I heard nothing from the magazine for a long time. Then one day, a young journalist, with a degree in engineering, wrote to me saying that the "article was too mathematical and dull." I was annoyed but decided to overcome it by writing a new article. And this time I made sure that it was not "dull." It was written in a relaxed style and within a few days I got a letter saying : "Yes, this is much better." The new article was published and, with hindsight, I think the journalist might have been somewhat right about the first version. But not quite!

In the above, it has been my intention to indicate that when you try to present mathematics to a broader audience including nonspecialists you are up against strong prejudices. This includes even many mathematicians who think that one should definitely not try to communicate mathematics to the public. I think this attitude is very wrong. We should in fact encourage people to do it. Mathematics is part of our culture - the most refined product of mankind. And it has important applications as well. We must learn to communicate mathematics and not to be so snobbish that we think it is impossible to tell other people what we are doing.

The public image of mathematics is first of all formed in connection with the teaching of mathematics at all levels. Journalists, politicians and other persons of importance for public opinion all have their own personal experiences with mathematics. And for some reason they most often believe that their own experiences are the general experiences. We must learn to communicate mathematics as a subject very much alive.

My conclusion is that the challenges are so great that for the WMY 2000 project to be successful, all mathematicians must work towards creating awareness about the importance and the great cultural values of our subject. Hence committees should be set up in all countries to work on the project. The EMS Committee on WMY 2000 accordingly sees as one of its important tasks to establish a catalogue of viable ideas on what to do. For that we need the input from local committees and individuals. Everyone is cordially invited to submit proposals to the EMS committee.

Professor, dr. Vagn Lundsgaard HANSEN
Department of Mathematics
Technical University of Denmark
Building 303
DK-2800 Lyngby
Denmark
e-mail : V.L. Hansen@mat.dtu.dk

Spanish translation available:
Gaceta, Academia Colombiana de Ciencias Exactas, Físicas y Naturales: Vol. I, No.5, 1997