SPEECH AT
THE FORUM IN MAUBEUGE

by Michele
Emmer

When, in
1977, I began my "Art and Mathematics" project (and it is

unimportant
which word comes first), I had something that was very clear in

mind, I was
not at all interested in making "educational" films like the

ones being
produced at that time, which tried to explain what a result, a

theorem, in
mathematics was. Films that were very boring, and essentially

very short,
and in my opinion completely useless. I was not convinced, and

I am still
not convinced today, that a film, a video, a software can act as

a
substitute in teaching, and in particular in the case of mathematics, to

a direct
contact with the teacher.

One of the
things that the media will never be able to do, is to react to

the faces of
the persons that are listening to what you are saying. Anyone

who has
ever taught knows that the faces of the students are a very

important
thing.

A film
therefore cannot be used for this, it cannot be used to replace

studies
that must be individual, with books, exercises software
or

CD-roms,
that can always and only be used as a material support to the

"physical"
contact with the person who is teaching, with the one who

suggests,
informs, explains, clarifies. Besides, there is also another very

important
aspect, a famous Italian mathematician, who died a few years ago,

said a
number of times that teaching is the best way to learn deeply.

However I
was convinced that a film, a video, could be very useful to

strike
one's fantasy, to stimulate imagination, in other words to make one

feel the
need to understand, to study further. And not only a film, but

also an
exhibition, a book, a show.

From the
very beginning of the project I thought of making films,

exhibitions,
books, meetings, all these things together, and after a number

of years I
can say that the project has worked. It has worked because one

of the
great fortunes of art and mathematics is that of being universal. If

one speaks
of mathematicians or artists from any part of the world, one

can be
understood if he succeeds in finding the right interpretation key.

Why am I
speaking of art? Because from the very beginning, as the first

idea was
that of realising videos, "visual" images had to be used. And

therefore
why not also ask the collaboration of artists, besides

mathematicians?
I am also convinced that it is not possible to speak of

"Visual
Mathematics", in all the sectors of mathematics, just as it
would

be absurd
and ridiculous to make art seem to be always tied to scientific

or
mathematical ideas. Just like it would be absurd , today , to privilege

the
computer, the Internet, and make art seem to be "new" because it

utilises new technologies.

In
mathematics and in science, perhaps, we can speak of progress, in art

it is
totally absurd. Technology serves art in the same way as it serves

mathematics,
but neither art nor mathematics are pure technology, pure

method,
pure calculation. Creativity, invention, are essential both in art

and in
mathematics.

Which
surely does not mean that the task of "showing" the ties between art

and
mathematics is a desperate one.

So the idea
from which I started was to realise videos (and then

exhibitions,
books, meetings), in which the "visual ideas" that artists and

mathematicians
(and not only them, architects, biologists, musicians) used,

would be
highlighted. Ideas that can be compared, "described" in some
way,

always
trying to use mostly a visual language.

And so,
beside a number of mathematicians, from D. Coxeter to Roger

Penrose,
from T. Banchoff to De Giorgi, I asked the collaboration of many

artists,
from Max Bill to Luigi Veronesi, to De Rivera, to Bruno Munari and

many
others.

2.

In order to
privilege the images, the spoken part, the explanations were

cut down to
minimum, and these are not even "real" explanations. A typical

example is
the film "Soap Bubbles" in which Jean Taylor and Fred Almgren

speak of
the theory of minimal surfaces, in particular, of the result on

the
singularities of minimal surfaces, but the video can be seen by

children, even
if they are very small, and they will interpret it

differently
from, for example, the students of the University of Princeton,

where the
same film was shown.

Therefore
art, artists, can be very useful to mathematics, as, in a certain

sense also
mathematics, the images of mathematicians can be very useful to

art, to
artists. Always bearing in mind that each one is doing his own job,

that even
if creativity seems to have some features that are common in all

man's
activities, however each discipline, both artistic and scientific,

has its own language, its own technical means of expression. Otherwise, one

risks
making people believe that anyone can be an artist, anyone can be a

mathematician.
It is not sufficient to know how to "play" with a computer

in order to
become an artist, it is not sufficient to invent a new

technique.
As in mathematics, there certainly must be intuition, creative

capacity,
but there also must be the capacity to prove, to explain what

one is
doing, right to the end. Given the above, I believe that artists

can be very
useful in teaching mathematics, and also in making people

understand
how mathematics is a discipline with its history, with its

evolution,
with its mistakes and its successes, in conclusion, that

mathematics
have given and continue to give a great contribution to Culture.

Without
expecting, as faculty members always do, to teach the

school-teachers,
from kindergarten to the high schools, what they must

teach and
how. Those who do not have an experience in teaching in a

school, and
I do not have it, should be very cautious in suggesting

solutions
that seem to be the panacea for all the troubles of teaching.

Undoubtedly
most faculty members always look from above, downwards upon the

teachers,
and this attitude is not helpful. Also from this point of view,

artists can
teach mathematicians a lot of things.