Soap Bubbles Between Art & Science

On 16 March 2019, a large exhibition on soap bubbles in art and science opened in Palazzo dei Priori, home of the National Gallery of Umbria in Perugia, Italy. Marco Pierini, the director of the Galleria Nazionale dell'Umbria and cocurator with me of the exhibition, wrote in the introduction to the catalog that the Soap Bubbles: Forms of Utopia Between Vanitas, Art and Science exhibition was inspired by my book Bolle di sapone. Tra arte e matematica. The exhibition was initially intended to be a kind of mise-en-scène of the volume, physically bringing together the images accompanying the text. However, as organization and research efforts progressed, variations, additions and deviations to the framework were implemented, modifying the guidelines and rendering the initial catalog, which was already abundantly vast and well structured, even richer.

The history of soap bubbles most likely begins with the slow diffusion of soap in Europe; soap bubbles were a side effect of this diffusion. They fascinated children in the northern regions of Europe, especially Holland and Germany. In the sixteenth and even more in the seventeenth century, playing with soap bubbles was likely a popular pastime among children. This is suggested by the hundreds of paintings and engravings on the topic of bubbles. What has inspired artists, however, has been the fragility and vanity of human ambition that the bubble symbolizes. It is probable that the widespread pastime of blowing soap bubbles, on the one hand, and artists' fascination with them, on the other, was what prompted scientists to ask questions about soap film. Color was certainly one of the main reasons.

At the end of the 1660s, Isaac Newton began to study optics. He wrote on colors and on a new theory about light. He published his notes on the theory of colors and light years later in his 1704 work Opticks.

A series of engravings by Hendrick Goltzius is considered to be the beginning of the bubble's thereafter frequent appearance in Dutch art in the sixteenth and seventeenth centuries. Goltzius's most recognized work is called Quis evadet? (Who will be spared?), dated 1594. For artists the sixteenth and seventeenth centuries were the period of greatest interest in soap bubbles; bubbles started to appear constantly in depictions of the broader theme of human frailty and, more generally, of children's games. One of the most famous works was created in different versions by Jean Siméon Chardin in the early eighteenth century and is called Les bulles de savon. Only in the nineteenth century did it become understood that soap films provide an experimental model for mathematics and physics problems, thus fully inserting soap films into the mathematical field of the calculus of variations. Joseph Antoine Ferdinand Plateau was not the first to study soap bubbles and films. However, it was his experimental observations that decisively influenced the work of mathematicians, even though as he was an experimenter, Plateau's work was mainly directed at physicists and chemists. In 1873 he published the result of 15 years of research in two volumes of the treatise Statique expérimentale et théorique des liquides soumis aux seules forces moléculaires. Thanks to Plateau's experiments, it was possible to create surfaces of mean curvature zero, i.e. minimal surfaces, of which either the equations or the geometric generator are known. The idea is to draw a closed contour with the only condition that it contain a limited portion of the surface and that it be compatible with the surface itself; if then a wire identical to the previous contour is constructed, immersed entirely in soapy liquid and then pulled out, a set of soapy films is generated, representing the portion of the area under consideration. While painters like Édouard Manet painted soap bubbles on their canvases in those years, Plateau was not satisfied with their spherical shape and experimented with the physical and chemical properties of soapy water to find completely new forms.

With his experiments, Plateau posed two problems to mathematicians: one that is known as Plateau's problem and the other on the geometry of soap films. In 1931, the...