statements pioneers and pathbreakers How a Mathematician Started Making Movies M i ch e l e e M M e R The author’s father, Luciano Emmer, was an Italian filmmaker who made essentially two—possibly three—reasons. The first: In 1976 I feature movies and documentaries on art from the 1930s through was at the University of Trento in northern Italy. I was work- 2008, one year before his death. Although the author’s interest in films ing in an area called the calculus of variations, in particular, inspired him to write many books and articles on cinema, he knew he ABSTRACT would be a mathematician from a young age. After graduating in 1970 minimal surfaces and capillarity problems [4]. I had gradu- and fortuitously working on minimal surfaces—soap bubbles—he had ated from the University of Rome in 1970 and started my the idea of making a film. It was the start of a film series on art and career at the University of Ferrara, where I was very lucky mathematics, produced by his father and Italian state television. This to start working with Mario Miranda, the favorite student of article tells of the author’s professional life as a mathematician and a Ennio De Giorgi. At that time, I also met Enrico Giusti and filmmaker. Enrico Bombieri. It was the period of the investigations of partial differential equations, the calculus of variations and My father, Luciano Emmer, was a famous Italian filmmaker. the perimeter theory—which Renato Caccioppoli first intro- He made not only movies but also many documentaries on duced in the 1950s and De Giorgi and Miranda then devel- art, for example, a documentary about Picasso in 1954 [1] oped [5–7]—at the Italian school Scuola Normale Superiore and one about Leonardo da Vinci [2] that won a Silver Lion of Pisa. In 1976, Bombieri received the Fields Medal, one of at the Venice Film Festival in 1948. Although I knew I was the most distinguished prizes in math, in the absence of a to be a mathematician from a very young age, I was inter- Nobel Prize for mathematics. By chance, I was in the right ested in film and I participated in a few of my father’s films. place at the right time. All mathematicians worldwide who I graduated in 1970 and accidentally found myself working were working in these areas of research had to be updated on minimal surfaces—soap bubbles—and had the idea of about developments in Italy. making a film. That was the start of the idea of the film series Also in 1976, Jean Taylor proved a famous result that re- Art and Mathematics, produced by my father and Italian state solved a conjecture that the Belgian physicist Joseph Plateau television. I learned much from my father, and I found myself raised experimentally over 100 years before: the types of sin- a capable filmmaker, too. Part of this article was published gularities of the edges that soap films generate when they in 2002, in the proceedings of a conference on mathematics meet [8]. Plateau had experimentally observed that there and art organized by Claude Bruter [3]. I have deliberately are only two kinds of angles generated by soap films. Taylor, adapted parts of that text because this article is not a strictly using the theory of integral currents introduced by Herbert scientific article but rather the story of a part of my life, and Federer [9] and then by William Allard and Frederick J. my memory more than 15 years ago is much closer to the Almgren, Jr. [10], was able to prove Plateau’s result. facts. It is my life. THe PlateAu PRoBlems THe Starting PoinT The problem in mathematics that bears Plateau’s name is to The Art and Mathematics project started in 1976. Or better, consider a curve in any space and try to find the surface that that is the year when I started thinking of the project for has that curve as a boundary and has the lowest possible area. It is possible to build a 3D model of the curve, immerse it in soapy water and withdraw it, and obtain in many cases Michele Emmer (mathematician), Department of Mathematics, Sapienza University of Rome, Piazzale A. Moro, 00185 Rome, Italy. a soapy surface that is the experimental solution of the prob- Email: [email protected]. lem. If for the physicist it can be enough to have a demonstra- See www.mitpressjournals.org/toc/leon/52/2 for supplemental files associated tion of this kind, for the mathematician it is essential to be with this issue. able to give a rigorous proof of the existence of the solution, 184 LEONARDO, Vol. 52, No. 2, pp. 184–190, 2019 doi:10.1162/LEON_a_01473 ©2019 ISAST Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/leon_a_01473 by guest on 26 September 2021 to determine, if possible, if it is in agreement with the physi- cal experience. It is clear that to prove the existence of the solution in a fairly general way is commensurate to obtain solutions to similar problems, even with very complex curves for which it is impossible to build a model and simulate its pioneers and pathbreakers behavior using soap films. The general mathematical solution to the problem of Plateau was difficult to obtain. Joseph Antoine Ferdinand Plateau (1801–1883) began his scientific career in the field of astronomy. During an experi- ment in 1829, he exposed his eyes to sunlight for too long, causing irreversible damage to his sight. By 1843, completely blind, he started to take an interest in the nature of forces in molecular fluids to discover the forms generated by soap films contained in metal wires immersed in soapy water. In 1873 he published the result of 15 years of research in two vol- Fig. 1. The author in a still from the filmCamilla by Luciano Emmer, 1954. (© Michele Emmer) umes: Statique expérimentale et théorique des liquides soumis aux seules forces moléculaires [11]. In the early 1960s De Giorgi and Ernst Reifenberg in- a film on soap films to show their shapes and geometry in troduced a completely new approach to Plateau’s problem. the greatest possible detail, using the rallenti film technique. The idea was to generalize the concept of surface, area and I must say that for me, thinking of making a film was quite boundary, looking for a general solution. The method used natural. Marcello Mastroianni made his first film with my was that of the calculus of variations, that is to say: Look, father, Domenica d’agosto, in 1949 [15]. When I was a child I in the class of admissible surfaces, for that minimizing the was involved in filmmaking—as collaborator, organizer and system energy, in this case surface tension, proportional to even actor—in several of my father’s movies [16] (Fig. 1). the area of the surface. By using different methods and work- Both Almgren and Taylor were very interested in my proj- ing independently, Reifenberg and De Giorgi solved Plateau’s ect. My idea was not to make a small scientific film, a sort of problem in its generality [12]. scientific commercial showing some small experiments with soap bubbles and soap films (Color Plate D). I was attracted FRed AlMgRen by the phenomena of soap films because they were visu- Again in 1976 the journal Scientific American asked Tay- ally interesting, and I thought that the technique of filming lor and Almgren (they had married a few months before) them would increase general interest and fascination about to write a paper on the more recent results on the topic of them. I was not at all interested in merely filming a lesson by minimal surfaces and soap bubbles [13]. A professional pho- Almgren and Taylor, inserting a few images of soap bubbles tographer was asked to take the pictures for the paper. The and soap films here and there. Almgren and Taylor shared same year, the University of Trento in Italy invited Taylor my opinion. and Almgren to be visiting professors. During that year I was In 1982 Almgren invited me to Princeton University. I associate professor in Trento. I already knew both of them— showed the preliminary version of the film in his Calculus Almgren, who, in his Swedish manner, was always very kind of Variation course. Bombieri also invited me to present the with me, perhaps a little better. movie at the Institute for Advanced Study in Princeton. I A few years earlier, in 1972 in Varenna, on Lake Como visited Almgren several times. I remember one night in a (north of Italy), the summer school of the Centro Internazio- Jacuzzi in the garden of his house we discussed our lives and nale Matematico Estivo (C.I.M.E.) held a summer course on our interests for many hours. He asked me if my idea was to minimal surfaces [14]. It was the year of the Olympic Games continue to be a mathematician or to become a filmmaker. and the feats of the U.S. swimmer Mark Spitz. Miranda was Almgren died in 1997 of leukemia. Frank Morgan, one of his carried away with enthusiasm and proposed a swimming PhD students (now editor-in-chief of Notices of the AMS, race in the lake. The only participant who accepted was American Mathematical Society; we met several times in Almgren. Miranda (at that time I was his assistant) asked Trento), sent me all the letters we exchanged over the years. me to join the two swimmers.