STORYTELLING AND MATHEMATICS: THE CHALLENGE FOR EDUCATION
 TRANSCRIPTION OF DOXIADIS CONFERENCE*

Buonasera and thank you for being here.
I admire you for being here: you must be very special people. If this
conference was kept in Athens in Greece on Saturday no one would have
come. So it's an honour for me to be here, thank you.
I come here from a strange world: people, not too many of us, not yet
anyway, who have thought of combining story telling and
mathematics. This is a very new thing, as you all know, especially at
the scale in which it is occurring now When I was studying mathematics, 30 years ago, you could really read
nothing about mathematics, except mathematical textbooks.
There were one or two good or less good mathematical biographies; the
book "Men of mathematics", a very politically incorrect title
for these days, which inspired generations of mathematicians and
biographies on mathematicians, usually focused on mathematics. But
there was no film starring a mathematician, Russell Crowe
would have not dreamt to play a mathematician, he would have
disappeared from Hollywood; there was no play as "Proof",
no novel with the words "conjecture" or "theorem" in its
title: this was strictly unthinkable.
Of course the rest of the world did not know what it was missing; I
mean the literary world, the world of story telling, the world of
people who like stories, which is the world of all people, because
people love stories, live with stories, grow up with stories, teach
with stories and learn from stories.
But someday something happened, no one could understand exactly what;
there are many theories on this: for example people suddenly started
studying mathematics, people had some good ideas about enriching the
world of story telling and I use the word story telling and not
fiction because I don't want to distinguish very much real
stories, as biographies, and fictional stories because in many points
the intersection in very interesting and I think is this that we are
talking about.
Some people say that mathematics has become fashionable and this
really shocks the mathematicians, of course. So we have the birth of
a new term, "mathploitation", as "exploitation", because suddenly as we
put a mathematician into a film or a novel it becomes commercial.
Anyway, I come here to talk from this world, small world, that's
just becoming bigger and to address the question to education, but in
a very general sense; I am talking about school, culture and about
how mathematics has become something that all of us can talk about,
mathematicians and non mathematicians, in different kind of ways and
in different kind of languages.
Giancarlo Rota, a great Italian mathematician, said in one of his lectures:
"A lecture audience is like a herd of cows, moving
slowly in the direction in which the lecturer leads it; if he
makes one point, there is a good chance that the audience will take
the right direction; if he makes several points then cows will go all
over the field and get lost"
which is not very complimentary to a lecture audience.
So I will make one point only in the remaining half hour, that is:
stories are interesting and they are a good way to enrich the
mathematical experience, a non trivial way, as a mathematicians would
say.
And the obvious way is that stories make subjects more likeable. Of
course, if you read a good novel or a biography on a mathematician
suddenly you might be tempted to look in this field.
But I want to show you the non trivial point in which mathematics and
story telling are related.
Today there are people, for example in literature, that can be
nothing in mathematics and that is fine: they are however very
intellectual people. To give another example, I have three
children:
my daughter is completely unmathematics, but she's a great story teller and
a great painter; she just doesn't love mathematics and that is
completely understandable.
Her brother who's six years old solves sums and
subtractions before going to bed to relax.
Some people are born mathematicians, like Gauss, Riemann, Galois, and
some are not, but that is also fine because they can become
mathematicians.
Sometimes when I have talked because of my book "Uncle Petros and
Goldbach's Conjecture" I have explained my theory that most
people like mathematics or don't hate it.
Usually I do a test. My first question is: "How many people here
actually hate mathematics?"
As I usually don't speak to mathematicians, 6070%
of the people answer yes and I ask them to keep their hands
up.
Then I say: "Now all of those among you who loves murder histories
please lower your hand" and someone does it.
Then I say: "Now those among you who plays chess, or draughts or
any game like that at any level of sophistication and enjoys it
please lower your hand.
Now all of you who like puzzles or enigmas or who are fascinated by
mysteries of any kind, lower your hand".
At the end no one still has his hand up.
So I say: "Then you see that no one really hates mathematics,
because mathematics is not just equations, but all of the other
things as well and all of us have had some experience in
mathematics".
Only one lady, in a small Greek town, did not low her hand till the
end, so I said to her:
"Congratulation madam. You are the only person I've ever known
who really hates mathematics!".
However people who are not close to mathematics can be approached in
other ways.
A great American educational psychologist, Bruner, wrote "Two
modes of knowing", in which he studies how we know and
understand.
He says that there are two ways of knowing the world: the one way,
call it classificatory, taxonomic way, is the way of science; we
apply it in history, grammar, philosophy, nature: any subject is full
of taxonomic or inductive type arguments.
But we also know the world in the way of story telling.
What is important is that he uses the word knowing, because usually
when we talk of stories we stress the emotional or aesthetical
aspect, but stories also teach us things about the world, give us
instructions. If you go in a traditional society, as a village, the
way they know world is through stories. Stories like Odyssey, or the
epic of Gilgamesh, show how people live, with complex problems and
situations and they are different from mathematical arguments because
they operate with variables too complex to be formalised. Stories are
complex algorithms: the logic is part of them, but is not everything
in them. So story telling is a very complex environment.
I have studied the exact structure of story telling: there
are similarities between a mathematical proof and the way the hero
solves the story's problem in traditional stories and they come
very close to having the same structure.
In mathematics we have intermediates goals, like intermediate
results, and the way of reaching a result is very similar in
structure to the way the hero acts.
I will show you an example of this. From the website of the
department of mathematics of Bologna I read this paragraph:
"The Department of Mathematics at the University of Bologna is
located at the end of Via Zamboni (the street where most of the
University administrative offices are located) in Piazza Porta San
Donato (one of the old city gates on the ring road called the "Viali"
around the historic centre)".
Any mathematician can see that this can be a very good algorithm to
solve a certain problem.
If I translate this into:
Once upon a time there was a little boy that went to the old man
of the village and asked: "how can I reach the department of
mathematics?" And the old wise man said: "You have to go
through via Zamboni and reach Piazza San Donato were the old gate is and
then fight the dragon" and you can imagine wonderful stories
with this.
As Wiles solved Fermat's last theorem, through Ken
Ribet's result, solving the TaniyamaShimura Conjecture, this
little boy acts with a similar structure.
Furthermore as stories can enrich mathematics, mathematicians
are lovable characters and heroes for stories (e.g. Galois: every
book of mathematics has a chapter on Galois because his life makes
him more attractive).
Moreover mathematical theories are ideal stories because they have
all the characteristics of a quest, a search, in the most pure
form.
I like to say that the story of a proof is the proof: if you try to
build the story of a proof of many years of collaborations, the more
you make it detailed the more you describe the proof itself.
What I am saying is really antiBourbaki, that is formal and clean,
when mathematical research is very informal and unclean.
What is new is that through stories mathematicians can talk about
mathematics, in a non classical way.
A story's problem can be trivial (we saw it in school), but also
non trivial (e.g. all the problems of logic,...).
More interesting are stories of problems: a mathematical history or
biography which doesn't explain only facts.
Finally I want to reflect on the fact that we have so many good books
of mathematics in the last years: probably one reason is that, as we
saw, mathematics make such good stories for many reasons and probably
because any mathematical quest is a great mystery.
(*)Transcription not reviewed by the author, edited by Sara Ceccoli.
