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What if mathematics were the ultimate locus of truth and beauty?

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Before talking about Sylvia Serfaty’s book, Équations Personnelles, I would like to mention two other scientists, Yves Meyer and Celia Pelluet.

In this long video, Yves Meyer addresses the question of his vocation, for the beauty and truth of mathematics from the moment 9 minutes 41 seconds.


I’m going back to my childhood. My childhood was completely ruined, shattered by the Algerian War. I was 15 years old. Especially since I was in Tunisia, which was entirely within a Muslim world. This war seemed absolutely horrific to me. So, I was 15 when it started. In fact, it lasted seven years, and it was truly terrible. And, uh, at that time, we, as children and teenagers, were completely confronted with the fact that the press was entirely censored because you couldn’t say that the war existed, you certainly couldn’t talk about the existence of torture, and so on. And it was either censored or lying. Hence the idea — a rebellious teenager has always existed; even people who wear a tie today, like me, were rebellious teenagers — and it led me to seek the truth for myself, and no longer believing in anyone was, for me, a form of rebellion, a defiance of will. And the charm of mathematics for me was that I was the sole judge of truth. I could prove the teacher wrong. In fact, my teachers were very rarely wrong because they gave excellent lessons. I did occasionally make mistakes while teaching. But you can stop the teacher by telling them they’re wrong, simply that there’s a sign error, or that the argument from authority doesn’t work in mathematics since you can’t say, “You’re going to believe this result, I’m going to prove it to you, and therefore you are the judge of truth.” It’s very strange when you think about it deeply. When I was a child, when physicists told me — my physics teacher — that Michelson and Morley had done such and such an experiment, it was actually, despite the respect I have for physics today, an argument from authority. I was forced to believe that this experiment had been done. I couldn’t possibly verify for myself, through my own intellectual resources, that the result was truly true. Because of my mindset, which was one of rebellion and insubordination, mathematics seemed to me the only discipline where I could control everything myself, and that seemed absolutely essential. So, in my adult life, as an adult mathematician, I first sought truth and beauty. Truth was something I held dear in my childhood because of the political experience of the Algerian War. And beauty, because I was very sensitive to beauty as a resident of Tunis. Beauty was everywhere. The almond trees in bloom in February were breathtakingly beautiful.

I discovered Célia Pelluet at a conference in Angers last week and she made me laugh a lot. She does something unusual: stand-up comedy, through popular science and the position of women in the field, which is as male-dominated as, or even more so than, others. Here’s a great example: “Politics Isn’t Quantum”:

Back to Sylvia Serfaty’s beautiful book. It’s a simple yet subtle book about a vocation for mathematics. “It all started for me at fifteen. […] I proved a more general inequality.” [Page 11] “That day, it suddenly dawned on me that being a mathematician was also a classy, ​​meaningful profession that could make me dream, just as much as being an artist or a writer.” [Page 16] But it’s also about rivalry: One of them had singled me out — I learned it indirectly — as “the girl to beat.” [La fille à abattre][Page 19]

These are shared memories and feelings, often encountered during our studies. Her high school teacher, L. Koechlin, who decided against entering her in the national mathematics competition, said, “Perhaps what he made us give up was the possibility of dreaming a little longer.” [Page 21] She went back to see him during her preparatory school years. “It was a good year, when he passed the agrégation, and I was admitted to the advanced mathematics program M’.” [Page 33]

These are also mixed feelings about those years in preparatory classes. Stéphane Hoguet, looking so much like Dave Gahan, the singer of Depeche Mode [Page 22], was undoubtedly his mentor. “Stéphane Hoguet taught at the Lycée Louis-le-Grand for a grand total of two and a half years (we were his first year). […] I learned of his death. He was 35 years old. […] I have always wondered how many vocations he would have inspired, how many mathematicians he would have launched into the stratosphere, if he had lived longer and taught for another thirty years.” [Pages 36-7]

She is less enthusiastic about her M’ professor. “It was rumored that until a certain time, perhaps ten years earlier, he had refused to have girls in his class. I don’t know if it was true, but there were some telling signs.” [Page 33] or about her physics professor: “An ENS? Well, try ENS Lyon then.” […] When he saw her again, her M’ professor shook her hand courteously and congratulated her. Our physics professor called out to her as a parting gift, “Go ahead and help women advance!” Had she applied this injunction to herself? It was a little late for encouragement. [Page 35] (You may check as a comparison the experience of Malcolm X here.)

But the “crude jokes and dubious traditions” seem to have had a motivating rather than discouraging effect. Sylvia Serfaty entered Ulm among the top students in a class that had never before included so many girls: six out of 42. Of the four who went on to study mathematics, three were daughters of mathematicians. Social mobility and class defectors exist at all levels.

I don’t know if the book will speak to everyone in the same way — obviously not, that’s a rather silly remark! And on the specific subject of mathematics, it resonates even more when you recognize yourself in the journey. I remember a few teachers’ names: Gérard Falézan, Brigitte Doisneau, Mr. François, Michel Poupaud (Melvil’s father), who also died prematurely, and of course Stephen Boyd. Like Sylvia Serfaty, the non-science teachers were just as important. I only need to think of my French teacher, Yvonne Rollet. And there are even more faces and names that brought so much imagination and inspiration. Not forgetting the friends, sometimes rivals, never enemies! Corinne, Claire, Isabelle, Frédéric, Patrice, Roger, Philippe, Vincent, Peter, Lieven, Laurent… Girls and boys.

Sylvia Serfaty describes the world of research, its grandeur and sometimes its pettiness (as I have also tried to illustrate it here at times). She also mentions the famous Fields medal with a caution I had rarely encountered: “A more accurate comparison would be to say that the Fields Medal is the equivalent of the Oscars, the Palme d’Or at the Cannes Film Festival, or a literary prize. It is awarded by the committee, which chooses based on its own assessment and relying on letters of recommendation solicited from expert and recognized mathematicians, thus striving to also reflect the opinion of the community, where certain groups promote their protégés. […] In other words, it is a scientific choice, but also a political one in the broadest sense, and necessarily subjective. It is therefore clear that the four selected, the only ones who will be remembered, are not necessarily better than the six or eight who are left out. […] Highlighting only them and their work is like only going to see films that have won an Oscar or a Palme d’Or.” [Pages 132-33] One may check about this the article about Perelman (whom you can discover at pages 136-38).

The ending takes a more philosophical turn, mentioning foxes, hedgehogs, birds, and frogs as analogies for the way mathematics is done. It also discusses the revolution that artificial intelligence seems to be bringing to mathematics. When the book was published, I’m not sure that the openAI proof of a mathematical conjecture was known.

Sylvia Serfaty also mentions the recent article “Mathematical Beauty, Truth and Proof in the Age of AI”. Without a doubt, Sylvia Serfaty has written a very beautiful book on the beauty and truth of mathematics.

Of course, there are parallels to beautiful La Voie royale

and as beautiful Le Théorème de Marguerite

Final comeback to Sylvia Serfaty through the France Culture morning program of June 2, 2026:

Testament, Testimony, Street art

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The latin word testamentum (« testament ; testimony ») is itself translated from the Ancient Greek: διαθήκη / diathếkê (« testament, contract, agreement »)

Those two words are curious. This link between testament and testimony. It reminds me of a joke my friend Georges told me. Grün’s eldest son converted to Christianity so he could marry a Catholic. Since nothing worse could happen to a devout Jewish father, Grün sank into a deep depression and locked himself in his room. Then the door opened and an old man with a white beard entered. It was God: “Why are you crying, Grün?” – “Shouldn’t I be crying? My son has been baptized!” – “But Grün, mine too!” – “Yes, and what should I do now?” – “Do as I do: make a new testament!”

More seriously, this is the third time I’ve mentioned these two words in a blog that is primarily a personal account and, after almost 20 years, is undoubtedly becoming something of an intellectual testament. What remains after all these decades?

By the end of the year, I might have compiled over 1,000 startup capitalization tables. About 750 posts ! A passion for mathematics that has never wavered. Not to mention literature and a rather complete failure to get a translation of a beautiful novel published (in my opinion, of course!).

And then there’s Street Art, more or less skillfully published or hidden here. More than 10,000 pieces collected virtually.

Pedicabo ego vos et irrumabo

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All this should have remained in French only, but I felt a need to translate the French post of yesterday… In his latest and more than magnificent novel, Himintungl yfir heimsins ystu brún (“Planets above the World’s Edge”, Benedikt, Reykjavík, 2024) and in French, Corps célestes à la lisière du monde, Jón Kalman Stefánsson writes on page 190 this verse from Catullus “Pedicabo ego vos et irrumabo” hastening to add “a verse that I will not have the audacity to translate here”.

What unites here the tenth novel translated into French by my revered Icelander with the essay Betraying Through Loyalty (Trahir par fidélité), written by Aurélien Barrau and subtitled Against the End of the World with Alexander Grothendieck (more on the 20th-century mathematician here), could well be another quote translated from Icelandic by Eric Boury.

La vérité importe-t-elle plus que l’Amour ?
Voici les questions
Does truth matter more than love?
These are the questions

The two authors share this tragic preoccupation which I found again by a strange coincidence in a third reading in recent days, that of What if Stefan Zweig could speak… by Camille de Toledo (Et si Stefan Zweig pouvait parler… here in pdf) and I could have cited for the umpteenth time that of Wilhelm Reich in Listen Little Man, which you will find without too much difficulty on this blog with its search engine.

But before returning to Grothendieck (I will not write anything more about the Icelandic novel which can be read without any hesitation), I will add some visual memories of this break away from work.

El Greco à Tolède

Plus à Tolède

Plus à Cadix

It’s very difficult to give an overview of Aurélien Barrau’s excellent essay, written in such a distinctive style. I wrote (in French only) about this author last year regarding his vision of scientific research as a poetic and revolutionary act. He revisits similar themes in his analysis of Alexander Grothendieck’s choices, leading one to wonder if he wasn’t not only the greatest mathematician of the 20th century, but rather the greatest mathematician in the history of the discipline. In the introduction, page 16:

“Grothendieck is a lord in rags. A prince in tatters. Poor by choice and alone by necessity. Modest by inclination but misunderstood by obligation.
Perhaps he was a genius in spite of himself, thanks to a deep and persistent wound.
Touched by grace and faithful to beauty, whatever the cost.

Angel and poet. Saint and martyr. Revolutionary and scholar.”

Page 29: “Normal mathematicians can sometimes painfully reach the summit of a mountain, thanks to superhuman efforts from the valley floor, but Grothendieck flew from one peak to another.”

Page 19: “Grothendieck not only saw from a higher vantage point, he saw different colors, he heard different melodies, he discerned the elsewhere in the here that no one had yet been able to imagine.”

Page 27: “Grothendieck publicly improvising a demonstration much shorter and distinctly more elegant than the speaker’s, before a stunned audience. Grothendieck understood that this gesture was undoubtedly humiliating for his colleague and bitterly regretted it.”

Stefansson, Zweig and Grothendieck are brought together here in the fundamental and ultimately tragic idea that truth, beauty and love are inseparable and perhaps too often irreconcilable…

Stefansson, Zweig et Grothendieck sont réunis ici dans l’idée fondamentale et finalement tragique que vérité, beauté et amour sont indissociables et peut-être trop souvent inconciliables…

One can also delve deeper into Grothendieck’s work with the lecture “Grothendieck’s Thousand and One Mathematical Pages” by Bertrand Toen (in French):


or by listening to Alain Connes:
– on France Culture in the Scientific Conversation: What kind of man was Alexandre Grothendieck? Quel homme fut donc Alexandre Grothendieck ?
– The legacy of Alexandre Grothendieck. With Alain Connes.

Post-Scriptum of the next day : The reader who has arrived here might wonder why such recent posts about topics that have little to do with technological innovation and startups. For twenty or even thirty years, I tried to remain a technician, not to say an expert, on these subjects. But I am forced to acknowledge that this topic touches on many others, from sociology to psychology, including politics, the arts, and the sciences. I cannot escape them. This latest post is perhaps even more mysterious because of its title. It also reminds me, in a completely different vein, of Maurice Pialat’s famous remark, “If you don’t like me, I can tell you that I don’t like you either.”

Montaigne has become my guide, my compass. In these extraordinary times, there is no better source of inspiration and reflection. I would be curious to know if Jón Kalman Stefánsson counts him among his influences. Reverend Pétur, the main character in *Celestial Bodies at the Edge of the World*, is too close to Montaigne for the question not to arise quickly.

For the past few days, I have been reading one of the last Essays, De la physionomie (Book III, Essay 12). Here is the note from the edition prepared by Bernard Combeaud: “This essay revolves entirely around the problematic relationship between appearance and being. Most of the places where we can display or disguise what we value, what we think we are worth, what we think as well as what we disguise: our words, our customs, our gestures, our actions, our physionomie, our writings, but also clothing, haughtiness, ostentation, culture, or philosophy, which we flaunt at will in one’s speeches or books, in the form of quotations, will be successively invoked here. The emblem of this chapter is the figure of Socrates, with his outwardly “vile form” and his inwardly beautiful soul. But no less emblematic here are the peasants bent over after their work, who know how to die so simply, they whom philosophy has never prepared for such a moment. Or even the author’s own good looks, which saved his life on two occasions when he fell victim to trickery amidst the turmoil of the Wars of Religion. Monstrous civil wars, where injustice appears as justice, where values ​​are overturned, for then appearances can only deceive universally. Thus, it appears that none of the artifices we rely on can guide us as surely as nature. This is somewhat like Montaigne’s philosophical testament.”

That says it all…

Testament or Testimony ? Lessing, Reich, Grothendieck, Jobs, Arles

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August is a good time to look back at things. It’s when I was thinking of this, that I wondered if there was a common etymology to Testament & Testimony. Apparently, there is not. Whatever… 1370 posts since July 2007 (in fact close to 700 as the blog is bilingual French-English, that’s about one per week), about 600 comments (ah ah!) and a lot of lessons.

August was also special on different sides, particularly cultural… I’ve been reading The Golden Notebook by Doris Lessing, a remarkable novel. Here is an extract: The Communist Party, like any other institution, continues to exist by a process of absorbing its critics into itself. It either absorbs them or destroys them. I think: I’ve always seen society, societies, organized like this: a ruling section or government with other sections in opposition; the stronger section either ultimately being changed by the opposing section or being supplanted by it. But it’s not like that at all: suddenly I see it differently. No, there’s a group of hardened, fossilized men opposed by fresh young revolutionaries as John Butte once was, forming between them a whole, a balance. And then a group of fossilized hardened men like John Butte, opposed by a group of fresh and lively-minded and critical people. But the core of deadness, of dry thought, could not exist without lively shoots of fresh life, to be turned so fast, in their turn, into dead sapless wood. In other words, I, ‘Comrade Anna’ — and the ironical tone of Comrade Butte’s voice now frightens me when I remember it — keep Comrade Butte in existence, feed him, and in due course will become him. And as I think this, that there is no right, no wrong, simply a process, a wheel turning, I become frightened, because everything in me cries out against such a view of life

This reminded me another post dated May 2009 about innovation and revolution which I found a little similar. “Entrepreneurs are the revolutionaries of our time.” And he had added: “Democracy works best when there is this kind of turbulence in the society, when those not well-off have a chance to climb the economic ladder by using brains, energy and skills to create new markets or serve existing markets better then their old competitors” You’ll find it here, Entrepreneurs and Revolution. And also a quote from the autobiography of Malcolm Little , which I had copied in my book. “When he was still at school, he wrote, his teacher asked him what he would like to become as an adult. A lawyer, he answered. Uncomfortable with his answer, she told him he’d rather think about becoming a carpenter thanks to his manual skills, but also because of his status. From that day on, he decided not to listen to such advice”.

August was also the opportunity to see some of the Rencontre photographiques in Arles.

A few exhibitions, from left to right and top to bottom: Masculinities, Pieter Hugo, Jazz Power!, Sabine Weiss, The New Black Vanguard, Thawra! ثورة Revolution!, Desideration (Anamanda Sîn)

Street artists have also been active in August. Just have a look at Banksy or Invader. Artists show the world as it is, the crises, more and more of its diversity, its uncertainties too. Transmission, accepting to disappear have been recurrent topics here, a rather darwinian view of the world. And that’s why I would just like to mention again a few other important quotes to me:

Reich_Listen_little_man

“I want to tell you something, Little Man; you lost the meaning of what is best inside yourself. You strangled it. You kill it wherever you find it inside others, inside your children, inside your wife, inside your husband, inside your father and inside your mother. You are little and you want to remain little.” The Little Man, it’s you, it’s me. The Little Man is afraid, he only dreams of normality; it is inside all of us. We hide under the umbrella of authority and do not see our freedom anymore. Nothing comes without effort, without risk, without failure sometimes. “You look for happiness, but you prefer security, even at the cost of your spinal cord, even at the cost of your life”. Wilhelm Reich already posted in March 2010.

sjobs

No one wants to die. Even people who want to go to heaven don’t want to die to get there. And yet death is the destination we all share. No one has ever escaped it. And that is as it should be, because Death is very likely the single best invention of Life. It is Life’s change agent. It clears out the old to make way for the new. Right now the new is you, but someday not too long from now, you will gradually become the old and be cleared away. Sorry to be so dramatic, but it is quite true. Your time is limited, so don’t waste it living someone else’s life. Don’t be trapped by dogma — which is living with the results of other people’s thinking. Don’t let the noise of others’ opinions drown out your own inner voice. And most important, have the courage to follow your heart and intuition. They somehow already know what you truly want to become. Everything else is secondary. Steve Jobs already posted in July 2007.

Finally, not a quote but an extract from a text about how Alexandre Grothendieck also discovered this painful passage from youth to future disappearance: In May 1968, the machine goes wrong. Shourik, as his relatives call him, goes to Orsay to dialogue with the “protesters”. The anar is scolded by the “enraged”. The outcast discovers he is a Mandarin. “After that, he was not the same” […] “It was a terrible slap, it was incredibly violent”. I spoke about this math genius in March 2016 and August 2020.

I finish this post which may look a little gloomy with a link to a very good article about trusting science: How to make the future more rational. It is optimitic, enthusiastic and shows that we can be realistic about the world, and our limits and still be positive and happy. Just a testimony or small, fragile testament.