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, 60-70% 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 Taniyama-Shimura 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 anti-Bourbaki, 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.