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