Sentimental mathematical education
A cartoon review of "Le théorème de Marguerite"
We take a break this week from our usual concern with mechanization to review a French film that may or may not be making the case for a vision of mathematicians as ripe for replacement by a more reliable technological substrate. The occasion is my recent viewing of Le théorème de Marguerite on an Air France flight, which coincidentally arrived in New York City a few days before the film was shown as part of the 29th edition of the “Rendezvous with French cinema” at the Film Society of Lincoln Center. “Marguerite’s Theorem” was not listed among this year’s award winners. Let’s see why.
That headline caught my attention about a year ago in the monthly bulletin from the INSMI, with the title of the film and the news that it was created in consultation with my former colleague, the indispensable Ariane Mézard. She immediately confirmed, in response to my inquiry, that she had climbed the steps at Cannes along with the rest of the cast and crew. Then I forgot about the film until February, when it appeared on the screen of my flight to Paris. Before the show was interrupted for explanation of emergency procedures I managed to watch the first 15 minutes. That was enough1 to anticipate the outline of the plot — as an excessively unkind reviewer wrote
— and I preferred to spend the overnight flight sleeping, but I vowed to finish the film on the return flight.
Here is my synopsis of the opening:
The film is about a talented young female mathematician named Marguerite. She announces a great breakthrough in her thesis defense. But a young male mathematician in the audience named Lucas asks a question that shows her idea is fatally flawed. Her thesis advisor tells Marguerite to start over with a different advisor; meanwhile he will now be Lucas's thesis advisor. Instead, Marguerite tells her advisor that she will quit mathematics. All this happens in the first 15 minutes.
Can you fill in what will happen in the rest of the film?
In her interview that accompanied the film’s official selection at the 2023 Cannes Festival, director Anna Novion “evokes the burden that weighs on the shoulders of women who are immersed in a masculine world.” The tone is set early on when Marguerite crosses the École Normale Supérieure cafeteria to the sound of the male students pounding the tables and chanting Marguerite! au séminaire! in the purest French tradition of chahut. Viewers are supposed to understand that French women are never expected to speak in seminars; in the interview Novion refers to Mézard as “one of the rare French women mathematicians.”
There’s no doubt that women in France, like elsewhere, are subject to abuse and degrading behavior on the part of some male colleagues, and the proportion of women professors in France, as in mathematics nearly everywhere, is disgracefully low.2 But it’s hardly unusual for a woman to speak at a French mathematical seminar. Claire Voisin, for example, has won most of the prizes the profession has to offer, is universally respected as one of her generation’s leaders in algebraic geometry, and is in constant demand as a seminar speaker.
This interview with Voisin in Quanta, published after she was awarded the Crafoord Prize, is a reminder that not all mathematicians are ready to join Kevin Buzzard in viewing “[m]athematics …as a game with precise rules”:
…I am absolutely not interested in games. It’s not for me. And in high school, mathematics felt like a game. It was hard for me to take it seriously.
Voisin, who “spent a lot of time painting” as a student at the ENS and “was very fond of poetry,” is inclined rather to
…compare a mathematical theorem to a poem. It is written in words. It’s a product of language. We only have our mathematical objects because we use language, because we use everyday words and give them a specific meaning. So you can compare poetry and mathematics… they both completely rely on the language but still create something new.
Marguerite, unlike the real women of French mathematics like Voisin and Mézard, is “tacitly spectrum-coded” and not at all poetic.3 Like Star Trek’s Mr. Spock, she is quick to point out (but with more irritation than Spock) that what you are saying is illogical.
A film about formulas, or a formulaic film?
If Claire Voisin is the poster woman for “Women in Science” in the vision promoted by L’Oréal, Marguerite is the poster child for mathematicians on the verge of being replaced by machines. By sheer coincidence Voisin was awarded the Crafoord prize the same month Ella Rumpf won a French equivalent of the Oscars — the César de la meilleure révélation féminine — for her performance as Marguerite. No less coincidentally, Voisin’s Quanta interview aligns perfectly with the message of Le théorème de Marguerite, namely that mathematics is not about formulas alone; that becoming a mathematician requires a sentimental as well as a technical education.
Is there an algorithm for that? To test whether the film can actually be mapped by a formula, I used the synopsis of the first 15 minutes that you read at the beginning of this post — changing Marguerite’s name to Margaret and Lucas to Simon — as a ChatGPT prompt, ending with: How does the film continue? Here’s the answer:
ChatGPT: After Margaret's devastating encounter at the thesis presentation, the film continues to explore her journey outside of the mathematical realm. Here's a possible direction for the screenplay:
Act 2: Finding Purpose
Margaret's Struggle: Margaret struggles to come to terms with her shattered dreams. She grapples with feelings of failure and self-doubt, questioning her worth beyond mathematics.
Exploring New Paths: With the support of her friends and family, Margaret begins exploring different career options. She tries her hand at various fields, from teaching to data analysis, but nothing seems to ignite the same passion she felt for mathematics.
Encountering Simon Again: Margaret unexpectedly crosses paths with Simon, who expresses remorse for his role in her downfall. Their interactions are tense at first, but as they spend more time together, they develop a begrudging respect for each other's intellect.
Rediscovering Mathematics: Despite her initial reluctance, Margaret finds herself drawn back to mathematics in small ways. She starts attending lectures and workshops, realizing that her love for the subject hasn't entirely faded.
Act 3: Redemption
A New Perspective: Margaret's time away from mathematics gives her a fresh perspective on her previous work. She begins to see flaws in her thesis that she hadn't noticed before, realizing that Simon's critique was a blessing in disguise.
Reconciliation: Margaret reaches out to her former advisor, expressing her desire to return to mathematics. Although initially hesitant, her advisor sees her newfound determination and agrees to support her once again.
Collaboration with Simon: Margaret and Simon form an unlikely partnership, combining their unique insights to tackle a new mathematical problem. Their collaboration is fraught with challenges and disagreements, but ultimately leads to groundbreaking discoveries.
The Triumph: Margaret's perseverance pays off as she presents her new findings to the mathematical community. This time, her work is met with admiration and acclaim, cementing her reputation as a brilliant mathematician.
Conclusion:
The film concludes with Margaret reflecting on her journey, acknowledging the setbacks and failures that ultimately led her to success. She embraces her identity as a mathematician once again, but with a newfound humility and appreciation for the challenges of the field. As the credits roll, we see Margaret mentoring a new generation of aspiring mathematicians, passing on the lessons she's learned along the way.
Last year Hollywood screenwriters went on strike for nearly 5 months in an ultimately successful effort to guarantee that
Mathematicians who wish to study the screenwriters’ tactics are probably wondering — when can we strike? and against whom? But if the above draft is the best ChatGPT can do, Hollywood screenwriters need not have worried. I immediately saw that something essential is missing, and I suspected I knew what it was:
MH: I forgot to mention that Simon, as seen in the first scenes, is very handsome. Would you make any changes?
ChatGPT: Certainly! Adding the element of Simon's attractiveness can add another layer to the dynamics between him and Margaret. Here's how the screenplay might be adjusted:
Act 2: Finding Purpose
Margaret's Struggle: Margaret not only grapples with the failure of her thesis but also with the undeniable attraction she feels towards Simon. His devastating critique only amplifies her conflicting emotions.
Exploring New Paths: Despite her feelings for Simon, Margaret tries to move on and explore different career paths. However, his presence lingers in her mind, making it difficult for her to fully commit to anything else.
Encountering Simon Again: Margaret's encounters with Simon become more frequent, and the tension between them grows palpable. Despite their intellectual clashes, there's an undeniable chemistry simmering beneath the surface.
Rediscovering Mathematics: Simon's presence reignites Margaret's passion for mathematics, but she struggles to reconcile her feelings for him with her desire to succeed on her own terms.
Act 3: Redemption
A New Perspective: Margaret's renewed interest in mathematics leads her to reassess her previous work. With Simon's help, she begins to see the flaws in her thesis and the potential for a fresh start.
Reconciliation: Margaret and Simon's relationship evolves as they work together to rectify her mistakes. Their collaboration forces them to confront their feelings for each other, leading to moments of tension and vulnerability.
Collaboration and Triumph: Margaret and Simon's combined efforts lead to a breakthrough in their research, earning them recognition in the mathematical community. Despite the challenges they faced, their partnership proves to be mutually beneficial and transformative.
Conclusion:
The film concludes with Margaret and Simon standing side by side, their differences reconciled and their bond stronger than ever. As they continue their work together, they find solace and fulfillment in each other's company, proving that even the most unexpected partnerships can lead to greatness.
How to fill 97 minutes of a feature film
ChatGPT’s second attempt is still pretty awful but it did get the general idea. Note that ChatGPT figured out without my help that Marguerite would return to mathematics! Taking the two drafts together confirms that if you have read my synopsis of the first 15 minutes, along with the detail I added for the second draft, you have no right to complain about the spoilers that you will see if you continue to the end of this post. The review in Variety of the Cannes screening observes that
all the expected beats arrive with the punctuality of a German train schedule4, and about as much excitement.
and Screendaily’s review is even more precise:
about half an hour in it’s possible to accurately forecast nearly every significant narrative beat.
I already cut the half hour down to 15 minutes, but of course a 112-minute film can’t be built by beats alone. Lines have to be written for those “friends and family” required to “support” Margaret’s exploration of alternative “career options.” “Family” stands on the right in the frame copied above, and this next frame
tells you everything you need to know about “friend.” The Variety review calls the woman on the right “Black Best Friend Archetype Noa,” but my sense is that French cinematic efforts at multiculturalism are still stuck at an earlier stage. When I added “reserved” to my prompt about Margaret, ChatGPT calculated that “friend” would be “outgoing and extroverted,” Margaret’s “polar opposite.” Is that not clear enough in the above still? Or in the sequence where Noa magically initiates Marguerite into life in the material world?
Digression on the Erdős-Bacon number
Marguerite, Lucas, and their shared advisor are all on the trail of “Goldbach,” of which the audience gets a metaphoric glimpse in this shot5:
so it’s not altogether disconcerting to see, not only big O’s and other tools of the trade
but also familiar names, like those listed in Marguerite’s “Triumph” scene (to borrow from ChatGPT).6
Can Goldston et al. claim the coveted Erdős-Bacon numbers on the basis of the appearance of their names in the film? Jean-Pierre Darroussin, who plays the advisor, has 2 degrees of separation from Kevin Bacon, so János Pintz, for example, would win an impressive Erdős-Bacon number of 5, low enough to be listed on the Wikipedia page, if mention of the name meets the threshold for “appearing” in a film.7
“Passion, necessity, difficulty, tenacity, relentlessness”
Although director Anna Novion — the title of this section comes from her Cannes interview — broke no new cinematic ground with Marguerite’s Theorem, I still think anyone interested in the representation of mathematics in popular culture should see it. If you have ever tried to motivate mathematical research to a skeptical outsider you can appreciate Novion’s (and Mézard’s) accomplishment. The film is no more clichéd or formulaic than The Imitation Game or The Man Who Knew Infinity, and it’s incomparably more authentic than A Beautiful Mind, which managed to win four Oscars by playing on the most insidious stereotypes of mathematics.8
This “Featured Review” on IMDB (rated 9/10) gets it right:
as a movie - there's nothing out of the ordinary with it. …But … one point … for me made it all worth my while. It's a story about a brilliant mathematician that manages to really reach her potential only when she comes to accept her emotional relation to math. We're all used to hear how science must be rational and detached from any sort of emotion. In fact, the idea is repeated a few times in the movie itself. Thing is, Marguerite sees math as the thing that keeps her world together, and as such she's very emotional about it. Without accepting that fact she can't really reach her potential, no matter how brilliant she is. … For that reason alone, I rated it as I did, and for that reason I think it's a movie worth seeing.
Will machine learning reach its potential only when it accepts its emotional relation to math?
There was, however, an astonishing cameo in those first minutes. Two cameos, actually: the amphithéâtre Hermite at the Institut Henri Poincaré, where Marguerite gave her ill-fated thesis defense, site of some of the most important mathematical lectures (but rarely, if ever, thesis defenses); and the very familiar face of a long-time colleague, sitting in the front row.
I call 22% (in 2022) disgracefully low, but not “rare.”
This contrast with Claire Voisin can be taken as a hint if you haven’t yet figured out where the film is headed.
Variety’s reviewers clearly haven’t taken German trains recently.
Since her mother lives conveniently in the mountains, Marguerite can reach Lausanne in time for the climax.
The colleague mentioned in footnote 1 should insist on being listed on IMDB to claim his Erdős-Bacon number of 6.
Diving into Math with Emmy Noether, created by Portraittheater Vienna and taken on the road, proves that it is possible to bring mathematics to life for a general audience without clichés or misrepresentations. As a a one-woman show it may not be ready for Cannes, perhaps, but it’s much better than any popular film I’ve seen about mathematics.
Ooh I look forward to see this. Not coincidentally, I assume, Marguerite is the name of the beautiful woman Faust sells his soul for. I've long had an idea to write a novel about what She might sell Her soul for - my idea is it would not be a beautiful man but a beautiful theory.