On “The Discrete Charm of Geometry”

by Carl Pierer

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As in any other academic field, outsiders as well as insiders often ask what do pure mathematicians actually do? What do they work on and how do they work? It probably does not help that whether the objects of study actually exist, or rather, what it would mean to say that they exist, is unclear. Who, then are the people who are drawn to this field?

It is notoriously difficult to make a film on intellectual work. Yet, there has recently been a surge in this kind of films: from Margarethe von Trotta's Hannah Arendt (2012) and Maria Schrader's Stefan Zweig: A Farewell to Europe (2016) to the more Hollywoodian Morten Tyldum's The Imitation Game (2014) and Matt Brown's The Man Who Knew Infinity (2015). The difficulty is really rather trivial: there is not very much to show about intellectual work. Somebody sitting at a desk, tearing her hair out? Typing a couple of words, only to delete three more sentences? Or the theatrical stare into the distance while chewing on her glasses? That hardly makes for a feature-length film. But the protagonists of these films are famous beyond their respective field. As some kind of ‘intellectual celebrity', their lives and characters have a special sort of attraction. There is a natural interest in their persona, maybe because of their work's status in general culture. To tell their story, then, is sure to attract interest, because their names have become a sort of institution. It is quite a different task to shoot a film on current, less glamorous and perhaps more ‘ordinary' research: the ongoing work of academics.

After the very well-received Colors of Math, Ekaterina Eremenko has recently come to Edinburgh to screen her most recent film The Discrete Charm of Geometry. Eremenko graduated with a masters degree in mathematics from Moscow State University in 1990, but later obtained a second masters degree in Film Directing from the Gerasimov Institute of Cinematography. She has directed a few documentaries before turning to films about mathematics.

In just 66 minutes, this documentary follows a team of algebraic geometers in Berlin as they come together to unite forces. It opens with shots of the mathematicians, as they try to get their heads around a problem given to them by Eremenko. Each one of them seems to approach the problem similarly, yet the beauty of this opening scene is that already the different characters of the mathematicians break through. Some hesitate, some mumble to themselves, others chew on their pen. Throughout the film, this theme of individuality, the person behind the idea of ‘the mathematician', is explored.

The three variations of the theme are: passion, doubt, and private life. Firstly, the people in the film are mostly passionate about the subject. Even if the mathematics behind it remains unclear to the viewer, the fervour with which the mathematicians discuss, the curiosity they show, is captivating. Their inquiry, their search is thrilling even without understanding very well what is difficult about it. In addition, the cooperation, the discussions and the misunderstandings, also through language barriers, gives a very accurate portrait of the delights of mathematical group work. It is shown how, from the debates and confrontations in the group, every participant takes away something different, still all of them are inspired in one way or another. And yet, their passion is not that simple love for mathematics. It is more complex, and for each mathematician it has a personal meaning and weight.

Another aspect that adds much to the humane perspective is the depiction of doubt. Doubt comes in many shades. There is the constant doubt about who is correct. Despite the cliché of the one correct answer in mathematics, it is not easy to decide who is correct when two views clash. Another beautiful scene shows a disagreement between one mathematician and the rest of the group. Everyone is convinced of this approach, except for one person. Later, even the person who has been suggesting the approach and defending it, turns sceptical, for who knows? The former has been right before. A way out of the clashes between two ideas, which happens several times during this film, is suggested: to look for a framework in which both are correct. But there is also more personal doubt: the PhD students are doubting whether they wish to pursue an academic career, the professors are reflecting on the impact they have made and their (un)willingness to sacrifice personal life for scientific achievement, and even Nobel and Abel prize laureate John Nash says: “I'm not even sure that I'm a real mathematician”. The different people have different ways of coping with these doubts, but for everyone, it seems, doubt is an integral aspect of their life with mathematics. Perhaps this has to do with the fact that nobody is ever quite sure what is right. At any moment, someone might be proven right, who was previously been thought wrong, or vice-versa.

Thirdly, there is the private life of the mathematicians. The film gives much room to this factor and uses it to underline the individual and different characters of the mathematicians. Some of them are shown spending time with their children. At many instances there are beautiful shots of the pursuit of hobbies: the throwing of knives, the making of music, climbing and running. All these activities seem to play an important role in the lives of the mathematicians, perhaps just as important as the mathematics. The question of sacrifice for the field does crop up at several instances throughout the film: how much time are they willing to spend on doing mathematics over other things they love? It seems that academic fame does not outweigh family life, sport or music. This maybe allows a new perspective on the role of doubt as well. If the time spend on doing mathematics is proportional to the advances made (as one professor suggests), then the decision to not work any longer on a particular problem, to be satisfied with the work produced, already entails doubt. For it always remains open to question whether the problem is really solved, and if – had the person spend more time on it – they might not have found a better solution. This aspect is certainly not unique to mathematics, yet it is perhaps reinforced by the idea that there is a single right answer.

What remains problematic about this film is its depiction of women. Only three women make appearances on screen: there is the little girl who tries to get her dad's attention, while he is busy talking about mathematics, there is a shy postdoc who interrupts a meeting and discreetly leaves the room again, and lastly there is the only woman on a team of roughly 10 mathematician, a female PhD student, who does not figure as prominently as her male counterparts. Surely enough, the film shows a sad reality about the mathematical academia and academia in general. Yet, to feign ignorance or plainly ignore the issue of how women in research are represented seems outdated. While the little girl and the postdoc are shown to interrupt the heavy intellectual work of the men, the female PhD student is never seen thinking, reflecting or chewing on her glasses. The impression that is given is that this is not really a field for women. The failure to render this problematic is a sad lacuna to what is otherwise an original and delightful film about mathematics.

Nonetheless, perhaps the greatest merit of this beautiful film is to show the human side of mathematics. Too often, a mathematician is rendered as an eccentric, autistic genius, lacking in personal or emotional qualities and impassioned by a love for numbers and abstraction. The picture painted here is much more nuanced, much more subtle. In this film, the captivating thrill of intellectual inquiry is blended with the life of ‘normal people' – as one mathematician says about people sleeping in tents in a park: “They are normal people, just like us”.

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