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.



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.