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Mathematics and non-mathematicians

   

Is mathematics a waste of time? What is it for? Why is it so difficult to explain? How can we make it more attractive? The thoughts and suggestions of British mathematician Timothy Gowers, the winner 1998 of the prestigious Fields Medal.

     
   

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Timothy Gowers - 'Mathematics is a tiny oasis
in a huge desert of unsolved, and mostly insoluble, problems.'

Mr Gowers, do you feel that young people dislike science in general, or maths in particular?
It is hard to generalise. There will always be some young people attracted to science, and others repelled by it. One problem is that people's stereotypical view of a scientist - male, eccentric, unfashionably dressed, obsessed with very abstract problems - is hard to correct.

Mathematics suffers relative to the other sciences from being harder to explain to the general public. A physicist might be able to say that he or she is trying to understand what happened in the first few milliseconds after the Big Bang. Non-scientists, not realising that this actually means playing with equations, studying computer printouts from particle accelerators and so on, will have the illusion of understanding what is being studied. Most mathematicians, on the other hand, work in areas that cannot be explained in a sentence or two, even in a loose way, and most non-scientists start to lose interest after more than this.

How has your vision of mathematics evolved since you were at school?
Perhaps the main difference in my perception now, as a professional mathematician, is an awareness of just how big the subject is, of how much is not known and of what a tiny fraction of mathematics any one person can hope to understand. At school one is given the impression that mathematics is a body of knowledge - addition, multiplication, geometric figures, calculus and so on - which is neatly organised and well understood. It is hard to imagine what research is like since there does not seem to be much scope for unsolved problems. A professional mathematician feels exactly the opposite: mathematics is a tiny oasis in a huge desert of unsolved, and mostly insoluble, problems, and it is almost miraculous that we know as much as we do.

Maths teachers are often asked by their pupils: 'What is this useful for?' How should this be answered?
To summarise a long answer, which I believe to be satisfactory, most mathematical works will never have direct practical applications. However, they contribute to a body of very interlinked knowledge, and this knowledge as a whole has had very important applications; it underpins the whole of science. If the question is asked in a school classroom, then the mathematics being discussed may well have direct applications. It is easy to think of applications of calculus, or matrices, or complex numbers. Teachers should also not be afraid to use the argument that struggling with mathematics is excellent training for the mind, as one learns how to come to grips with difficult concepts.

Is it possible to popularise mathematics? Do you think it is important?
Many areas of current mathematics are almost impossible to convey to a general audience. However, this is certainly not true of all mathematics, and even the more difficult areas tend to have their roots in problems that can be explained more directly. In many ways mathematicians and the general public can happily coexist without communicating with each other. However, it is important that scientists, engineers, economists, computer programmers and others should have some conception of what mathematicians can do. It frequently happens that people in other disciplines come up against mathematical problems that are difficult, but already solved. Good communication can therefore avoid much duplication of effort.

Finally, since most mathematicians depend on public money, they should make some effort to explain why this money is not wasted.

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Genesis - John Robinson

Art and mathematics - Genesis - John Robinson

The sculptor Max Bill was fascinated by the Möbius strip, a surface with only one side formed by joining the ends of a rectangle after twisting one end through 180°. Other artists have been similarly fascinated by other mathematical theories, such as those about knots. One of them is John Robinson, whose work is being followed with interest by researchers at the University of Wales. Where possible, the expression of mathematical concepts in material form can be a major aid to their understanding.

A professor at the University of Wales, Ronnie Brown has designed a CD-Rom on which art comes to the aid of mathematics. It was launched during 'Week 2000' at Obidos (Portugal). A piece of work by John Robinson, entitled Genesis, illustrated on the sleeve, represents the Borromean Rings. 'The Borromean Rings were originally a set of circles which the Borromea family from Italy adopted as their coat of arms. The Borromean Rings occur in subtle ways in mathematics, and also in physics, for describing the interactions of three particles,' explains Ronnie Brown. 'This form illustrates the fact that the whole is not the pure sum of its parts. Robinson shows this by experimenting with squares, triangles and lozenges, as in Genesis. This clearly shows how an artist's imagination can accentuate our perception of a mathematical reality.'


Participants, initiatives

Germany:
In Berlin, the launch of the website 'mathematik.de', a platform for a professional/
public dialogue; various exhibitions, conferences, etc., particularly in Berlin and Munich.

Belgium:
Posters on the Brussels underground

Finland:
Helsinki University presented two exhibitions, one on the visible phenomena in the sky and the other on mathematical modelling. A number of specialised seminars and conferences were also organised during the All Saints' Day long weekend in 2000.

France :
'Maths in everyday life' exhibition at various science centres, universities, schools, etc. Posters on the buses in Pau. A day devoted to the winner of the European Mathematics Society Prize.

Portugal :
Launch of the Genesis CD-Rom by John Robinson in Obidos, 11 November 2000, and an exhibition of posters and CD-Roms at the national history of mathematics seminar (Obidos, 16-18 November).


And on the Net?

The project site
http://www.sees.bangor.ac.uk/public/cpm/rpamath/

Interface platform between the experts and the public
http://www.mathematik.de/

Site of the Centre for the Popularisation of Mathematics
http://www.sees.bangor.ac.uk/public/cpm/

World mathematics year
http://wmy2000.math.jussieu.fr/

       
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