Tangente: a catalyst for mathematical culture | Tangente

The pairing of the words "culture" and "mathematics" may strike many people as incongruous. Yet discovering Tangente was a revelation for some, including Fabien Durand, president of the Société mathématique de France, who puts it this way:

"I discovered Tangente at the beginning of 1988, when issue 2 came out. I was then a student at the Université de Reims, preparing for something entirely different from studying mathematics. Mathematics did not frighten me, although I felt I had not fully mastered it. Around the time I was reading that second issue, I happened upon Douglas Hofstadter's book Gödel, Escher, Bach: An Eternal Golden Braid (InterÉditions, 1987). Reading the two at the same time sparked a powerful enthusiasm and a total commitment on my part to studying mathematics at university."

Fabien Durand proudly displaying his copy of issue 2 of Tangente.

An encounter, an adventure, a passion ----------------------------------------

For Fabien Durand, as for others, this marked the beginning of an adventure that continues to this day. Have you noticed that "The Mathematical Adventure" is Tangente's subtitle? It truly was an adventure for the famous and unsung alike who chose to devote their lives to mathematics, whether studying it or bringing it to a wider audience. They include the many authors who regularly put pen to paper—or rather, fingers to keyboard—to write articles for our pages, much to our readers' delight, and even books that are reaching an ever-wider readership through bookshops.

For them, it became a passion, as it did for Stella Baruk, whose passion predated the founding of Tangente but who was delighted to join our team.

"When you own issue 1 of Tangente, bought one day in the autumn of 1987—for 25 francs, ah, the nostalgia—a magazine bold enough to advertise the risk it was taking with the subtitle L'aventure mathématique*, seeing its 200^th issue arrive cannot help but stir both emotion and admiration. Mathematics, on glossy paper, presented differently from the way it appears in mathematics books—but mathematics all the same! It could only arouse my curiosity, along with the hope that, besides the discoveries I was bound to make, I might find answers to my students' perennial "What's it for?" —a question that had received only rather inadequate answers. A few issues later, I could venture a conjecture; today, on the threshold of the 200^th, I can state the answer even more succinctly: "Everything!" "*

In these words, Stella Baruk describes how Tangente accompanied her for a third of a century in her unending quest to answer the question "How can we make people love mathematics?" (see her account in the box).

Stella Baruk's emotions ----------------------------

For Stella Baruk, the adventure created by Tangente *is a cultural as well as an emotional one. Here is what she says about it.*

Stella Baruk with Martine Brilleaud (editorial director) and Bertrand Hauchecorne (editor-in-chief).

The "Tangente galaxy" mentioned in issue 179—the phrase could hardly be more apt. Painters, writers and even a psychoanalyst have explored it—Lacan et les maths, étrange ou démon? With its themed special issues and its Bibliothèque series, offering a wealth of original reference material close at hand rather than scattered across one's desk—ah, Le who's who du cercle; ah, Les découpages et pavages, delighting the eye and firing the imagination—the galaxy expanded in 2000 with the quarterly Tangente Éducation.

The joy of reading ------------------------

Each richly varied issue of Tangente captures both the promise it showed from the beginning and the possibilities still ahead. It keeps pace with the times, presenting the subjects and people shaping contemporary mathematics—inevitably challenging—while also celebrating the mathematics of the past: ideas from every age and place that have endured and been revisited over the centuries. Egyptian mathematics, with its fractions and its Heron, can appear alongside the "Fête à Fermat" in the same issue (see Tangente 127); conjectures can await their elevation to theorems, while theorems that have endured for centuries live on.

But sometimes it also revives fragments of memory that upheavals or innovations had seemingly sought to erase forever. How moving it was to turn a page and suddenly encounter "my" Bouvart et Ratinet (see Tangente 163), or to see "my" loci as the headline of an issue (Tangente 176 and 177). The delight they brought after sometimes lengthy investigations had, for a time, become almost shameful to admit. Now they had been restored, and the wounds soothed.

Women in Tangente ------------------------

But of course there are not only male mathematicians, grey-haired or otherwise: there is Sophie Germain! With numbers all her own! And many other women mathematicians to whom Tangente pays tribute: Maryam Mirzakhani, the first woman to win the Fields Medal, taken from us too soon; young women members of the Académie des sciences who are still little known; and the far too little-known Katherine Johnson, who, despite being both a woman and Black, became the first woman mathematician admitted to NASA meetings (see Tangente 193).

Mathematics competitions for women (see Tangente 167)? A matter for debate. It took far less to stir and inspire two women whom I am pleased to bring together here. The first, who died recently, was Marjorie Rice (see Tangente 163 and HS 64). A homemaker with no particular mathematical training, she had five children and was over fifty when, secretly working in her kitchen, she tackled the difficult problem of pentagons that tile the plane. Beyond the types already known, the problem had fascinated and even thwarted Martin Gardner; she discovered four new types!

The second was a fifth-grader, scissors in hand, carefully following the instructions for cutting a Möbius strip (see Tangente 185, page 24). I will never forget how her face lit up when she saw the result: two interlocking hearts. Both were moving, weren't they? For those moments of emotion, thank you, Tangente. S.B.

Manu Houdart during one of his performances. If you are going to the Avignon Theatre Festival, you can see Very Math Trip at the Théâtre des Lucioles

from July 7 to 31 at 5:30 p.m.

Manu Houdart, now famous for his breathtaking show "Very Math Trip," recalls the moment he fell in love:

"I remember the first time I came across the magazine Tangente very clearly: it was... in a black-and-white photocopy. My mathematics teacher wanted to share an article on conic sections with us! I was 17, and I thought it was brilliantly put together. Later, while studying for a mathematics degree, I could read the magazine in the university library, and as soon as I began teaching, I subscribed!

Today, it is an important source of information for me, and I often draw inspiration from it for my shows or my YouTube channel. In turn, the magazine helps people discover my work: audience members often tell me they came after seeing me listed in its events calendar. When I began writing my book, I definitely sometimes found myself—at the back of my mind—dreaming of the Prix Tangente! Today, that trophy, which I won in 2020, adorns my mantelpiece. Thank you, Tangente !"

A flowering of initiatives ---------------------------

From its very first issue, Tangente attracted many subscribers, showing that by the late 1980s there was a real appetite for a different approach to mathematics—one rooted in culture, history and games: in short, for enjoying oneself while doing mathematics.

There was also a need to dispel the disastrous image of mathematics left by the period known as "modern mathematics" (see Gilles Cohen's article on page 14).

In the years that followed, right up to the present day, many initiatives appeared with the same aim. Would they have come about if Tangente had never existed? If its team had not taken the risk of putting it on newsstands in 2000? Probably—but they would have developed more slowly and been fewer in number. The magazine regularly reported on all these events, often partnered with them and publicized them through its events calendar.

Conversely, many advocates of mathematical culture found not only inspiration but also the motivation to organize their own activities. In the last century, could anyone have imagined people enjoying themselves at mathematics festivals such as the "Culture et jeux mathématiques" fair; the "Maths en ville" and "Maths en scène" festivals; the "Fête à Fermat" in Beaumont-de-Lomagne; "Math'Gic" in Gennevilliers; "La Nuit des maths"; or the Grand Forum des mathématiques vivantes?

Mathematics rallies have also flourished, culminating in the creation of the Kangourou des mathématiques, which brings together hundreds of thousands of participants.

Gaël Octavia's account* --------------------------------

September 2002. Wanting to become a science journalist, I resigned from my job as a telecommunications engineer. "I want every science magazine you have!" I told my newsagent. Amid the enormous pile he gave me was the wonderful little magazine that would change my life: Tangente. I sent my résumé to its publishing director, Gilles Cohen, who decided to give me a chance. I remember my five years on the editorial staff of Tangente as a time of perpetual discovery. They gave me an opportunity to see mathematics differently: as an essential part of a well-rounded person's cultural education, alongside literature, art and history.

Gaël Octavia is a writer (La Fin de Mame Baby*, Gallimard, 2017) and head of communications at the Fondation Sciences Mathématiques de Paris.

Every year, some thirty books related to mathematics—but neither textbooks nor specialist works—are published. Despite the difficulties of getting them into bookshops—independent booksellers are not always well informed—some have enjoyed considerable success. Examples include Le Théorème du perroquet by Denis Guedj (Le Seuil, 1998) and Le Grand Roman des maths by Mickaël Launay (Flammarion, 2016).

The creation of the Prix Tangente du livre in 2009, followed by the Prix Tangente des lycéens, helped showcase this literature and promote a different approach to mathematics. Authors and publishers alike now watch closely, since winning one of these awards can make a book's sales soar. Another ongoing initiative, Litteramath, jointly organized by Tangente and the APMEP, recommends books, classified by level, for school libraries to make available to students.

Let us leave the final word to Charles Torossian:

" Tangente is a model of bottom-up thinking. It shows that modern organizations are not merely top-down structures in which a few people isolated in a ministry provide the impetus and direction—although this is absolutely necessary when seeking to launch ambitious national policies, such as raising standards in mathematics. They must also know how to listen, bring grassroots initiatives together and enable them to be rolled out on a large scale."

Our thanks to all the prominent figures who contributed their accounts and are quoted in this article and the next.