Soapbox Science is an initiative for female scientists started in the UK, where researchers from all areas of science present their work to the broad public, speaking from a box in a public space to whoever wants to stop and listen.
I participated as a speaker in Belgium's first in-person Soapbox Science event in Brussels on June 26th, 2021.
Communicating pure mathematics research to non-mathematicians – and in 10-15 minutes, no less – is a challenge. Here I want to share what I did and why you should try it, too.

My research is part of the larger areas of Poisson geometry and symplectic geometry. Although this is the mathematical language in which dynamics – "the branch of mechanics concerned with the motion of bodies under the action of forces" (Oxford Languages, via Google) – is written, the central mathematical structures in these fields, symplectic and Poisson structures, are frequently not encountered by students before their Master's degree in Mathematics. And if they do not take a special interest in geometry, they may not encounter these concepts at all.

Given this, how do I explain what I do to non-mathematicians? My family frequently complain that they do not know what I do at work, which was one of my motivations to sign up for Soapbox Science.

Preparation: What to talk about?

While preparing my application to speak at Soapbox Science, I quickly settled on a fairly general educational topic: The history of geometry with a focus on the Parallel Postulate, the 5th postulate in Euclid's Elements. Around the end of the 19th century, it was finally discovered that it was perfectly possible to drop this assumption and still do geometry that makes sense: The 5th postulate is simply the one specifying that you're doing plane geometry. Thus, geometry on curved spaces was born and subsequently developed by mathematicians such as Bernhard Riemann, before being used to formulate the theory of General Relativity by Albert Einstein.

This subject was accessible to most passers-by, starting as it did with Thales' Theorem and Euclidean geometry, the geometry taught in school, before reaching the new and less familiar idea of curved geometry. I drew a series of posters with large illustrations and little writing. As examples of curved spaces, I brought along a 2-sphere and a hyperbolic plane, which I crocheted based on the work of Dr. Daina Taimina, a Cornell mathematician who developed the technique. (Also check out her book, Crocheting Adventures with Hyperbolic Planes!) My final prop was a sheet of foam, which I used to demonstrate how heavy objects bend spacetime, the curvature producing the effect we measure as gravity: Objects follow the geodesics (locally shortest paths) in the curved spacetime. I passed the objects around the audience as well, allowing everyone to see the triangles and geodesics I had drawn on them for illustration up close.

At the end of my short presentation I spent a few minutes talking about studying curved spaces of general dimension in modern geometry research, and how advanced modern mathematics is still used as the language to describe physics, this being one of the motivations for such work.

On the day: The exhilarating experience of loudly advertising Euclid's postulates from a box in the centre of the European capital

Before the event, I was extremely nervous: Not only was I going to give my first-ever talk in Dutch (depending on how you count, my 4th to 6th foreign language), I was going to do it without a dedicated audience, hoping to simply make the spectacle look interesting enough so people would stop to listen.

Luckily, the latter turned out not to be a problem: I had personally invited a few people up front and this small group attracted further spectators. The Soapbox Science organisers also did an excellent job making the event visible among the throng of foot traffic and directly drawing people in to watch.

I also immediately found that speaking in Dutch was precisely the right choice: Not being on the level of a native speaker, I was forced to explain my subject slowly in simple terms. Had I spoken English, not only would I have struggled more to stay away from jargon and complicated sentence structure, but my audience would have had to adapt to a foreign language that they mostly are not used to in their daily lives.

(Of course, the native French speakers, immigrants and foreign visitors in the audience still had to adapt – the nature of a multilingual city like Brussels. But the Soapbox Science event was deliberately organised such that there were always both French and Dutch presentations at any time of the day, with a few English presentations peppered in.)

Overall, the experience was extremely gratifying and enjoyable: The audience was enthusiastic and engaged. In total, I gave my little presentation 4 times, answering questions in between. Participating in Soapbox Science motivated me greatly to engage more seriously and more frequently in science outreach, an effort of which this blog is a part.

But where are the women? And what do I actually do?

Even while preparing my presentation, there was an elephant in the room: Throughout my little history of geometry, all mathematicians I mentioned were male, not a single woman in sight. Soapbox Science being an event about promoting the research of female scientists, I of course recognised the irony in this. It really bothered me: Male scientific discoveries being celebrated, while those of women are quietly ignored, is a common theme in the history of science. I hated contributing to it.

I tried to fix the problem by adding a section on the work of the famous geometer Maryam Mirzakhani, but dropped this idea again quickly: I could hardly do her and her work justice as a footnote to my history of the parallel postulate. Since I could not change the whole concept of my talk at this stage, I decided to instead spend more time at the end of my presentation discussing my own work.

In the end, it seems that this was only partly successful: The most common question I got was to describe a bit more in detail what my own research actually focuses on. I answered in largely conceptual terms: How from the start of my studies (in physics) I was fascinated by how the natural world is quantitatively described in the language of mathematics, specifically geometry, and how I have always been motivated to extend and develop this language of nature.

I still think that I gave an engaging, accessible presentation that illustrated many fundamental principles of how mathematical research works, as well as why it is fascinating and engrossing to solve mathematical riddles. But for the next popular science event I participate in, I will make sure to choose a topic with a significant and visible contribution from female mathematicians. The dilemma of how to talk about my own work in any more than very general terms I have not yet solved, however.

Endnote: Look for a Soapbox Science event in your area right now and bookmark it for the next application round!

Women are still underrepresented in almost all areas of natural sciences research (at least when it comes to senior, permanent positions), but particularly so in pure mathematics. My cursory browse of previous Soapbox Science events, as well the organisers' report on the first 10 years of the initiative also show that mathematics as a discipline is barely represented at Soapbox Science: From 2011-2017, only 1% of Soapbox Science speakers listed "Mathematics" as their field.

This suggests that more public outreach from pure mathematicians, and from female pure mathematicians in particular, is sorely needed, not least to challenge the common mental image that people have when they imagine a mathematician. On top of that, participating in Soapbox Science is great fun! Personally, I found it a very gratifying and enriching experience.

So if you are a female or non-binary mathematician (PhD student or more senior), I strongly encourage you to visit Soapbox Science's page with events for the current year and pick one to apply for in the next round!

(Last edited: 11.10.21)