Étienne Ghys: A Life Less Ordinary
Throughout his career, renowned French mathematician Étienne Ghys has ventured off the beaten path for the benefit of the subject he has devoted his life to.
By Jimmy Fryers
Etienne Ghys recently completed a three-day tour of Vancouver, delivering PIMS-sponsored lectures around the city and giving a public talk on the beauty and mystery of the geometry of snowflakes at Science World.
These events were organized as part of his role as the Permanent Secretary of the Académie des sciences in France — an institute that can trace its origins back to 1666, and PIMS’ efforts to bring high-quality mathematical events to Canada.
PIMS has a longstanding relationship with French mathematics through its partnership with the CNRS (Centre National de la Recherche Scientifique). This relationship has been integral to facilitate and encourage research collaborations between mathematical scientists at PIMS member universities in North America and researchers across France, as well as hosting events such as Étienne’s Vancouver Tour.
As a career mathematician, Etienne has spent decades advancing the subject but has also strived to make his knowledge more accessible to fellow mathematicians and the general public.
He took time out of his packed schedule to sit down with PIMS and discuss his life and work.
The Brazil Connection
Étienne’s mathematical journey started out as few others have. In 1970’s France all men were obligated to serve in the army for one year; however, as Étienne explains, there were a few exceptions:
“At the time the military service was compulsory in France and there was an option of joining a scientific corporation to teach in a foreign country for two years rather than being a soldier for one. In 95% of cases, the young French men in this corporation would go to former French colonies such as Algeria, Marocco and even Tunisia.
“In my case, I was lucky enough that my advisor had a relationship with Brazil and I received notification that I had to go to Rio de Janeiro and teach.
“For me, it was probably the most significant moment in my life. I completely changed my point of view on everything; I loved it there — I loved the language, I loved the climate, and I loved the mathematics.
“The relationship between people in Brazil is very open-minded and they were very kind to me. When I arrived they told me I had to teach and when I told them I don’t speak Portuguese they encouraged me and said: “Go on — you can do it!”
“So,” Étienne said in a cheerful and matter-of-fact way, “I taught in Portuguese!”
“It was a challenge but the students, who were almost the same age as me, were very nice. It was a great moment for me. A big part of my way of thinking about mathematics comes from Brazil.”
The fondness Étienne has for Brazil and meaningful international travel has been an everpresent part of his life and continues to this day.
The Road Less Traveled
Once his service to his country came to an end and as his career and reputation as a mathematician developed, Étienne continued to journey overseas, which included visiting complex locations across the world.
Asked why he visited these places, he replied, “Because I like diversity. I do like to visit places like Los Angeles, Vancouver and I’m very happy in these locations but I don’t feel as useful as when I visit places like Mauritania. Very few mathematicians go to these places so I feel that I can make a positive difference in some way.”
But his desire to be useful mathematically is not his only reason to travel: Étienne is a friendly conversationalist and clearly enjoys the company of others:
“I love the warmth of human connection. When I was leaving Mauritania my host wanted to offer me a gift to remember his country. When we arrived at the airport he opened the trunk and there was a suitcase weighing 23kgs, which was full of fresh fish. I understood it as a really friendly gift. It is an example of human relationship — he was offering me something heartfelt and sincere — showing the best of his country.
As well as Africa, Étienne spent time in the Middle East and recalls his time there fondly:
“In Palestine, I was at a summer school, and an interesting fact about visiting places like this in the Middle East is that it is one of the very few opportunities mathematicians get to lecture in front of an audience made up almost entirely of women.
“During the half-day break in the summer school, two French mathematicians and I had the idea of visiting Jericho.
“When we mentioned our trip to the students, they mistakenly thought we meant all of us were going and got very excited about it. We ended up renting a 50-seater bus and went to Jericho together. I wanted to visit the biblical places but the students, they wanted to go to the fairground.” Étienne says with a smile.
When I asked him if he ended up visiting the places he wanted, he laughed and said enthusiastically, “No, no, no, but we had a great time!”
Connection Through Travel
It’s obvious that Étienne is passionate about bringing math to the masses but acknowledges the difficulty of doing so. When asked if his travel and public events are a way of bridging the disconnect between mathematics and society, he agrees:
“It is a challenge — it’s difficult to attract the general public to math events, which is very important to me.”
“To give a talk is easy, to give a good talk is also easy, but to be able to catch the attention of the public, who have no prior connection to mathematics, is much more difficult.”
The Beautiful World of Snowflakes
What better way to attract the public to a math event than discussing the mysterious world of snowflakes — a topic Étienne has given much thought to over the years and a topic he still works on:
“My dream would be to prove that the dynamics of snowflakes, moving in time according to physics, converge on a two-dimensional attractor.”
When asked if he thought he’d ever get to a point where he could prove this hypothesis, Étienne laughs and says “I hope so. I have some ideas. I’m convinced that there should be something behind the observations of physicists and this something should be mathematical.”
Sadly, Étienne believes we’ll never get to a point where we can predict the shape of a snowflake, “It’s not my dream to predict how a snowflake will converge into a specific shape — it is impossible; my dream, and what I one day hope to prove, is that they converge on a specific attractor, and that attractor, hopefully, will be two-dimensional.”
Open Science
Throughout the interview, Étienne affectionately refers to the work and of bygone mathematicians. When asked if why it’s so important for him to be involved in public outreach, he responds by referencing Prof. Hilbert:
“Professor Hilbert is one of the most famous mathematicians and he wrote a wonderful paper proposing 23 questions that should be solved in the 20th Century. In the introduction of the paper, there is a discussion about what is a good problem and what is a good proof. Hilbert says the proof is good only if it can be explained to the man in the street. This is remarkable. Of course, it’s a dream — in many cases it’s impossible, nevertheless, it’s a direction.”
This idea of being able to explain something complicated to a non-expert is an approach that Étienne follows:
“I understand better when I explain things. It’s at all levels: the only way for me to make sure that I’ve understood a theorem is to explain it to someone else. While I’m explaining it, I can discover if I did not understand it or what I need to understand better.”
“12 years ago I was preparing a talk for the general public and I wanted to use some images I’d found online. I contacted the owner, who was a chemical engineer in Belgium, and he allowed me to use the pictures. After the talk, we decided to collaborate and he produced more images and asked me for an explanation about what they were.
Instead of explaining to him we decided to make a movie: ‘Dimension.’ It was a great moment in my mathematical life because I had to produce a movie explaining difficult topics an audience who knows very little about mathematics.
Open Science
Etienne’s effort to make mathematics more accessible is not confined to public appearances — he made his most famous book, “A Singular Mathematical Promenade,” freely available and removed all copyright restrictions on its use. Étienne spoke passionately about why he made the decision to do so:
“I did it for many reasons. I think mathematical books are too expensive. Most publishers make a lot of money, too much money, from the sale of books. They steal money from us. We produce everything — these days most mathematicians write everything and produce a document, which in many cases is completely finished. So the work of the publisher has been cut in half during the last 20 years, yet the prices of the books are ridiculous, which can easily be over $100 — I think it’s nonsense.
“Another reason is that I am a civil servant, I receive a salary from my country. If I write a book during my work-time I don’t see any reason why I should make any money from it. If I were a poet or a novelist, then I would understand — it’s their occupation.
“My view is that mathematics, science and cultural objects produced by professionals paid for doing that work, should be free. This is the open science movement where everything should be freely available. So for this book, I made it free for these reasons. If you look at page 2 you will see that I make that very clear, even to the point of stating that the material is freely available and can be used even for financial gain. I did this on purpose — to make it clear that a mathematician should not make money from a book that was his duty to produce.
“There were two positive consequences of doing this. I received an email from a colleague I knew a little bit, who was from Turkey. She asked me if she could translate the book into Turkish. I’m so happy that my book is now available in Turkish — could I dream of anything better? Maybe this situation wouldn’t have happened if there were restrictions placed on the material.
“Perhaps a teacher or professor takes an extract from the book and uses it in their own way in the classroom. This, for me, adds to the pleasure of doing my work” Étienne said with a warm smile.
There are over 400 diagrams and pictures in the book, nearly all of which Étienne created himself. When asked him why he went to such great lengths to illustrate the book he laughs, “Because I enjoy drawing. But this is also a philosophical and mathematical question — traditionally, mathematics is transmitted through letters. Why should that be so? Music is music, it’s not written in letters. Mathematics is mathematics, why should it pass through the written language?
“If you go back in history, for example, you look at the Greek Euclid or Archimedes, unfortunately, we don’t have the original texts, but it’s quite clear that they contained a lot of pictures. Historians of mathematics are discussing whether or not a picture illustrates the text or whether the text illustrates the picture. It’s a fascinating question. When you study geometry, you have the picture and the text, and for me, I always look to the picture first. I try to see what I can understand from the picture and then if I don’t understand, I read the text.
“If you look at the history of mathematics, in some periods, pictures were somehow forbidden. If you look at French mathematics of the twentieth century up until the 1970’s it was a sin — it was against the ‘rigour’ of mathematics.
“Hibert once said, one of the duties of mathematicians of the future is to master pictures, symbols and diagrams in such a way that they can be used in a rigorous way — he’s asking us to use pictures to convey mathematics. For me, for my own perceptions of mathematics, it goes through pictures. Pictures are my main internal word. I need pictures and when I made the 546 pictures for the book, it was a way for me to check whether or not I understood what I was trying to explain. For me, it’s part of the book — it’s not a bonus, it’s like a comic book. A picture is worth a thousand words.
“In some ways the book is unusual — I’m trying to express feelings but many traditional mathematicians try to hide them,” Étienne said.
The Next Chapter
Étienne has been busy for decades and that doesn’t look like it’s about to change anytime soon:
“Now I’ve started a new challenge in my life. I’ve been an elected member of the French Academy of Science for some time now, but last summer I was elected as the Permanent Secretary. My new duty is to go outside of mathematics and somehow deal with scientific problems like climate change, biological questions, ethical questions, and so on.
So now I’ve started a new life, where I will probably do less mathematics but I try to be active in the dissemination of science among the general population. For me, it's a new life with new colleagues.
“I am now more involved with politicians, two weeks ago I had lunch with Macron. I’ve moved to Paris. I now have the opportunity to try to influence politicians, including on topics like free access to science and international collaborations, so maybe I can be more useful.”
For Étienne, in his quest to be useful, to make a positive difference, and to bring math to the masses, he may have found the perfect role.
This interview was conducted as part of the Étienne Ghys 2019 Vancouver Tour, proudly sponsored by the Pacific Institute for the Mathematical Sciences.
