I heard a famous French illustrator on the radio this morning and one of the thing he said strongly resonated with me. There were several versions of his background circulating in the press, publisher blurbs, web pages. In some of them he was an alumni of a famous Art School and in some of them he never had any formal training in drawing or painting. When asked by the interviewer about it, he simply said he did not go to an art school. He remarked he was often asked about his training, for instance: “When did you start drawing ?” He usually turns that around:
“You see, most children start expressing themselves through drawings, from a very early age, at home, in kindergarten. I did that, too, that’s nothing remarkable. Usually during primary school, they don’t do it anymore. I just didn’t stop. I never stopped. I kept drawing every day, every kind of things, and it happened partly because my parents did not block me or frown upon this activity. And I still do it. So when people ask me that kind of question, I ask them back: when did you stop drawing?”
Hearing him, I recalled my own frequent feeling of powerlessness when I try do draw something or see the kind of work I would like to produce myself. I told a friend who was listening with me to the radio program: “I think that’s what I did with mathematics. I started early playing with numbers, object combinations, dots, lines, a compass, gridded paper, I never stopped, and I never asked for permission.”
That’s probably what I should have done with drawing. Thinking about my terrible mandatory middle-school art hours may give me an insight into what people experience in the ordinary math classes — and what disgusts them.
To all those people feeling bad about mathematics,
we could ask : when did you stop doing “it”?
I write “it”, because many activities that are profoundly mathematical are not recognized as such by teachers and family of young children, while art is more commonly seen as a continuum. Parents are more open to their child expressing themselves in pre-art activities, to the point it becomes a nuisance to everyone else.
If I follow the analogy with early childhood drawings, it suggests that when helping people who have a failed or non-existent relation with mathematics, most approaches start with an excessive level of sophistication, preconception and structuration. We take for granted cognitive processes, standard viewpoints, rhetorics and expectations most mathematicians have acquired unknowingly from many clues. We are the ones who “got it”. We expect to bring people to reconciliation and insight within a few hours of structured exposure, we do not help them practice some accessible, spontaneous, “proto”-mathematics that could be formative, nor do we really prepare and aim for life-long practice, enjoyment and learning.
I hope I could “restart” drawing, as if I was 3 years old, discovering the fun of playing with color pens and sheets of paper.
There are many entry points for mathematics, many of them we have yet to find.
There are several ways to relate to mathematics, many ways to excel at it. This is not so widely known. Alexander Borovik, in several of his books, describes people warming to mathematics very early or others in their late adolescence or young adulthood (entering the University). I am rather of the first kind. Furthermore, I tend to quickly identify and entertain ancient connections between what I am studying and doing now and what I felt and longed for when I was in my school years, even as a very young child. Part of it is probably a self-serving fabrication: I take pleasure into the sense of cognitive continuity it offers. Genealogy conforts me and provides valuable analogies and insights.
But another part is linked to the fact that academic published mathematics has always been to me an extensive, wonderful and bewildering area of mathematics, not the whole. Before I was initiated to the global mathematical culture, I accumulated a store of pre-mathematical facts, experiences, tastes, concerns, implicit problems and naïve research programs that are still nagging me today. The corresponding perspective in art is very common: art is not restricted to what you can see in museums or what is labelled or publicized as such. You grow a sense of aesthetics, you look at some art and you see something that you always wanted to see or feel that something is missing. You know that art can be found almost anywhere, with various degree of sophistication, and that many starting points exist, many of them we have yet to find. I wish it were a more widespread opinion about mathematics too, especially among mathematicians.