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Home , Ennio de Giorgi, Enrico Bombieri, Jean Taylor, Leonardo da Vinci, Mathematics and art, Renato Caccioppoli

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pioneers and pathbreakersstatements 184 ABSTRACT LEONARDO, Vol. 52, No.2,pp.184–190, 2019 Started MakingMovies Started How aMathematician that is the year when I started thinking of the project for project the of thinking started I when year the is that The T Itfacts. is my life. the to closer much is ago years 15 than more memory my scientific article but rather the part story of a of my life, and adapted parts of that text because this article is not a strictly deliberately have I [3]. Bruter Claude by organized and 2002,in proceedings the in of conferencea on published was article this of Part filmmaker, too. capable a television. I learned much from my father, and I found myself Art and Mathematics making a film. That was thestart of of the ideaidea of the filmthe series had bubbles—and surfaces—soap minimal on workingmyself found accidentally and 1970 in graduated I participatedof a few father’s I in and my film in ested films. inter was I age, young very a from a be to was I knew I Although 1948. in Festival Film the at andone about da that[2] won Silvera Lion [1] 1954 in Picasso about documentary a example, for art, onmany documentaries butalso moviesonlynot Hemade My father, Luciano Emmer, was a famous Italian filmmaker. filmmaker. tellsoftheauthor’sarticle professionallifeasamathematicianand mathematics, producedbyhisfatherandItalianstatetelevision.This art and ofafilmserieson the ideaofmakingafilm.Itwasstart bubbles—hehad workingonminimalsurfaces—soap and fortuitously would beamathematicianfromyoungage.Aftergraduatingin1970 oncinema,heknew inspired himtowritemanybooksandarticles 2008, oneyearbeforehisdeath.Althoughtheauthor’s interestinfilms fromthe1930sthrough feature moviesanddocumentariesonart The author’s father, LucianoEmmer, wasanItalianfilmmakerwhomade with thisissue. See www.mitpressjournals.org/toc/leon/52/2 forsupplementalfiles­ Email: [email protected]. Sapienza University of , Piazzale A. Moro, 00185 Rome, . Michele Emmer (mathematician), Department of Mathematics, h e S e project started in 1976. Or better,Or 1976. Mathematicsandin Art started project tart i M ing Poin ing H C e l e , produced by my father and Italian state t M M e e r

associated - able to give a rigorous proof of the existence of the solution, be to essential is itmathematician the for kind, this of tion lem. If for the physicist it can be enough to have a demonstra a soapy that is the experimental solution of the prob- soapyitin water andwithdraw it,manyandobtain in cases area. possible It is lowest possible to build the a 3D model has of the curve, and immerse boundary a as curve that has consider a in curve any space and to try findthe surfacethat mathematicsThe problem Plateau’sbears in that to name is T Federer [9] and then by William Allard and Frederick J. Frederick Almgren, Jr. [10],was ableand to prove Plateau’s Allard result. William by then and [9] Federer integralofcurrentsintroduced by Herbert theory the using are only two kinds of angles generated there by soap films. that Taylor, observed experimentally had Plateau [8]. meet they when generate films soap that edges the of gularities raised experimentally over 100 years before: the types of sin- solved a conjecture that the Belgian physicist about developments inItaly. updated be to had research of areas these in working were who mathematiciansworldwide All time. right the at place right the in was I chance, By mathematics.for Prize Nobel a of absence the in math, in prizes distinguished most the ofoneMedal, Fields the receivedBombieri 1976,In . of oped [5–7]—at the Italian Normaleschool Scuola Superiore devel- then Miranda andGiorgi De and 1950s the in duced the perimeter theory—which first intro variations and of the equations, differential partial of investigations the of period the was It Bombieri. Enrico Giustiand Giorgi.Enrico met AtDe Ennio also I thattime, to start working with Mario Miranda, the favorite student of lucky very was I where Ferrara, of University the at career my started and 1970 in Rome of University the from ated andcapillarity surfaces problemsgradu- hadminimal I [4]. ing in an area ofthe calculus variations,called in particular, was at the University of Trento in northern Italy. I was work- essentially two—possibly three—reasons. The first: In 1976 I h Also in 1976, proved a famous result that re- that resultTaylorfamous Jean a proved1976, in Also e Pl e at e a u P u r o b doi:10.1162/LEON_a_01473 le ms ©2019 ISAST - - 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 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 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 , 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 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 . 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 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. I answered that I had been a My son Tommaso had leukemia in 1985, and in 1996 my wife professional swimmer for 10 years, so it was not fair on my Valeria had pancreatic cancer. She died in 1998 [17]. part to participate in the race. Miranda insisted on asking me to swim. Of course I won the race, leaving the other two Möbius Band swimmers many meters behind. A beautiful satisfaction for As for the second reason for starting the Art and Mathemat­ a young assistant! When Almgren and Taylor came to Trento ics project: I was working at the University of Trento while in 1976, the issue of Scientific American with their article had my family—Valeria and sons—lived in Rome. Every Friday just been published. The pictures in the article and the cover I left Trento to go to Rome (seven hours by train), and then were really beautiful and intriguing. I do not remember why, on Monday, I traveled back to Trento. I have always been a but when I looked at the pictures I had the idea of making lover of art, of all kinds, of any culture and period. Of course

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Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/leon_a_01473 by guest on 26 September 2021 there are some whom I prefer more than others. When many illustrations!), including the two volumes of The Visual I was in Trento, I read in a newspaper of an exhibition in Mind: Art and Mathematics in MIT Press’s Leonardo Book Parma, dedicated to one of the most significant artists of the Series [23,24], and even theses for students in mathematics, last century: . I already knew some of the Swiss art- and . Today, more than 45 years

pioneers and pathbreakers ist’s , but I had not visited a large exhibition like later, it is easy to say that the project went far beyond expec- the one in Parma before. As the town of Parma was more tations [25]. or less on my way from Trento to Rome, I decided to stop In 1970 I had started my professional career at the univer- on my way back to Rome to see the exhibition [18]. Bill’s sity, and one of the most difficult things to do at an Italian topological sculptures were a real discovery for me. Years university is to be involved in a field connecting two or more before, I had seen a large exhibition of the works of Henry different areas. During the last 45 years I have been invited to Moore in and of many other artists, but Bill’s works many Italian and foreign universities to show and discuss my almost immediately gave me the inspiration for Visual Art movies. But when I first showed one of my movies in Rome and Mathematics [19]. in 1981 to a wide public audience, in my de- Endless Ribbon—an enormous Möbius band made of gran- partment told me that it was not good for the department’s ite—was a real revelation. Its shape, its physical nature and reputation. This is the main reason why almost all my mov- its tridimensional reality made it live in space. It was a math- ies have been made abroad—in , the United States, ematical form—alive. This was the missing idea: Mathemati- Canada, Japan and even . And the same is true for the cians throughout all historical periods and in all civilizations publication of books and proceedings of congresses orga- have created shapes, forms and relationships. Some of these nized abroad or with the help of non-Italian mathematicians. shapes and relationships are really visual; they can be made This is the reason why it was only possible starting in 1997 visible. This idea is behind the great success of using com- to organize the congress Mathematics and Culture in Venice. puter graphics in some sectors of mathematics. As would be expected from the previous remarks, obtain- Returning from Parma to Rome, I spoke with Valeria. My ing funds and support for the project from Italian institutions project was becoming clearer: to make films, in which to was a desperate feat. Notwithstanding all this, we started the compare the same theme from a mathematical and an artistic project. point of view, asking for the opinion of mathematicians and artists. To make visible the invisible, as the Bris- The Italian State Television son says in the 1982 film Dimensions with Thomas Banchoff During the 1970s, RAI, the Italian public television company, [20]. The themes of the first two films were soap bubbles and had a department specifically dedicated to educational proj- , in particular the Möbius band. To have more visual ects called DSE (Dipartimento Scuola Educazione). They ac- ideas and objects to film, we finally decided to include the cepted the challenge to make a program on mathematics for connections between mathematics and architecture, all the the first time. No one had yet proposed something on these other , in particular biology and , not exclud- topics, except the lessons filmed for strictly educational rea- ing literature and even . And, why not, cinema [21]. sons. They had one condition: that we make a series of films. Series is a magic word for television. If one wants to do some- The Idea for the Film Project thing for Italian television (although I have the impression From the very beginning of the project there was the idea of it is the same everywhere) one has to propose a series, even focusing on the influence and the connections of mathemat- if one only has ideas for one or two episodes and no ideas ics and culture, using the most important visual tool: film. of how to do a series. So they asked me to make eight films. The idea was to show using a single theme, such as soap I said no for the reason that I had no ideas for the other six. bubbles or topology, how the interests of artists and math- Finally we reached an agreement to make four films, with an ematicians are born and to see if it was possible to exchange option to make four more in the following two years. Each ideas between scientists and artists—all this, however, fol- film had to be 27 minutes long. The other topics we were lowing my father’s teachings of expressing ideas using images thinking about were platonic solids (Fig. 2), and alone. I had to build a sequence of images that was first of all . compelling from the point of view of cinema. A film is not In these same years I had already discovered the works of an essay or a picture book. The visual documents fascinate the Dutch graphic artist Maurits Cornelis Escher. From the per se. The idea then is to use few words and many images, first time I saw his engravings, my intention was to make a applying all the possibilities of the language of cinema. The film only on him. My idea was to use the technique of anima- theoretical research on the links between mathematics and tion (no computer graphics, of course) in order to make his art has been amply treated in the books I have written and works really tridimensional—something that Escher himself the volumes of the Proceedings of the Convegno Internazio­ suggested; he personally was involved in a short film with nale di Matematica e cultura (or Mathematics and Culture) in several animations of his works before his in 1972. I Venice [22]. As these were the general outlines of the project, discovered his ideas and the film only a few years later. The it was quite natural to consider as part of it the organization first conference I organized on Escher was held in Rome in of exhibitions (many were presented in subsequent years), 1985 [26], organized together with mathematicians Harold congresses and seminars, and the publishing of books (with Scott MacDonald Coxeter and and Marianne

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of Escher and inserted them in the pioneers and pathbreakers film Möbius Band. It would take me more than 10 years to complete the film on Escher in 1990 (Fig. 3). What we needed for the project was a title; it was quite nat- ural to choose the general title Math­ ematics and Art (although the title was changed for RAI because Italian television, like Italian universities, cannot consider the idea of treating two topics at the same time; the prob- lem is to have a precise target!). This added months to the process, but at Fig. 2. Still from the filmPlatonic Solids by Michele Emmer, 1979. (© Michele Emmer) the end of 1979 I was able to show a preliminary version of Soap Bubbles at a scientific film festival at the Na- tional Center for Scientific Research (CNRS) in Paris. The second movie, on the Möbius band, was also almost ready. In 2003 I edited a new transla- tion of Edwin Abbott Abbott’s novel Flatland, including the DVD of my animated film, with original by Ennio Morricone, a friend of my father [29].

Max Bill I contacted Max Bill by writing him a letter. He was very kind; he invited me with my troupe to his house in Zurich, and he gave me permission to film whatever interested me, includ- ing his fabulous collection of contem- porary art. There was one exception. It was strictly forbidden to film a little window in which he had his collection of topological forms made of paper—very small objects—that

Fig. 3. Still from the filmM.C. Escher: Symmetry and Space by Michele Emmer, 1982. (© Michele Emmer) were his database for future works. He was afraid that someone might see his projects and copy them. We Teuber, and a second one in 1998, in Rome again, with Doris became friends and made two exhibitions and another film, Schattschneider [27]. The film was made with Coxeter and Ars Combinatoria, together [30]. We were both on the edito- Penrose [28]. rial board of Leonardo, at that time published by Pergamon The financial support of RAI was not sufficient to make Press. We met several times. For my book The Visual Mind: my first four movies; it was out of the question to make a Art and Mathematics (MIT Press, 1993) (Fig. 4), Bill rewrote film on Escher using animations, as this technique is very the title and made some changes to his famous paper origi- expensive. Financial support from RAI was just enough to nally written in 1949 on a mathematical approach to art [31]. make a film, entirely in a studio, consisting of a person talk- Two of Bill’s works are reproduced on the front and back ing throughout—their idea of an educational TV series. My cover of the book. The volumeThe Visual Mind IIis dedicated idea was to film all over the world, where the artists and to Valeria and Max Bill. mathematicians involved in the film were working. My father In my annual congress in Venice I dedicated a special

Emmer, How a Mathematician Started Making Movies 187

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Fig. 5. Unknown artist, Dutch school, untitled, oil on canvas, 26 × 20 cm, sixteenth century, collection of the author. (Photo © Michele Emmer)

ics in Barcelona [36] in 2000. And in 1986 it was shown at the Venice Biennale of Art [37,38]. The movie is still circulating. In 2009 I wrote a 400-page book on soap bubbles in art and that received one of the most important awards for an Italian essay, the Premio Letterario Viareggio Rèpaci [39] (Fig. 5). And almost every year there is a session on soap films or soap bubbles in the annualMathematics and Culture conference in Venice. Fig. 4. Cover of The Visual Mind: Art and Mathematics by Michele Emmer. (© MIT Press) I organized the first large traveling exhibition in Italy on Art and Math, The Eye of Horus, in Bologna, , Parma and Rome in 1989 [40,41]. All my films were part of the ex- ­session to Bill in 2014, 20 years after his death. The session hibitions. In April 2016 in Florence there was a three-week included papers by Armanda Quintavalle, Cornelie Leo­pold festival on art and math [42] at which I was invited to give and myself [32]. In my paper [33], I show pictures of the mak- a talk, and my films were shown during the festival—some ing of a large by Bill, starting from the choice of the made over 40 years ago. marble in Carrara and the transportation to Germany [34]. And the story is still going on. . . . A large exhibition of Bill’s work was organized in Milan’s Palazzo Reale in 2008 [35]. There was a part dedicated to his The Art and Mathematics Film Project topological sculptures, not including the largest and the most M. Emmer, Art and Mathematics: my films, produced by Film well-known, Endless Ribbon. It was his dream to have a large 7 International and L. Emmer prod., Rome (1979–2013). All exhibition of his topological works. films are in color, (most are) 27 min and available in DVD in various languages. A Short Conclusion A film is not the best tool for explanation or learning. A film Möbius Band (1979) can, in a short amount of time, provide ideas and suggestions Soap Bubbles (1979) and create stimuli and emotions. A film can generate inter- Platonic Solids (1979) est, even enthusiasm. Looking at an engaging, pleasant film Symmetry and Tessellations (1979) can stimulate the audience to learn more, both in the artistic Dimensions (1982) and the mathematics fields. In this sense I consider my films M.C. Escher: Symmetry and Space (1982) educational, but only with this meaning. This was also the (1982) reason why RAI originally refused the films. Helices (1982) This, on the contrary, is the secret of their success, as with Ars Combinatoria (1984) the movie Soap Bubbles, even after 40 years. In fact the most M.C. Escher: and Impossible Worlds (1984) beautiful sequences I have ever made—the soap films danc- (1984) ing to Invitation to the (Le Spectre de la Rose) by Carl Geometry (1984) Maria von Weber—were included in the VideoMath festival Labyrinths (1987) selection for the International Congress of Mathematicians Computers (1987) in Berlin in 1998 and in the European Congress of Mathemat- Avventura del quadrato (1987)

188 Emmer, How a Mathematician Started Making Movies

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/leon_a_01473 by guest on 26 September 2021 Figure geometriche (1987) F. Armati and M. Emmer, eds., Ricordando Fabrizio L’occhio di Horus, 35 min, RAI prod. (1989) Clerici, AICS prod. (1994) Metamorfosi di Fabrizio Clerici, 7 min, animated (1991) Matematici part 1, part 2, 60 min, Città della Scienza, Venezia perfetta, 20 min (1993) , (1996)

The Fantastic World of M.C. Escher, 50 min, produced by , video interview, 75 min, UMI (1997) pioneers and pathbreakers Emmer and distributed in the U.S. by Acorn (1998) Venice 2008, Emmer and Villarreal prod., Rome (2008) Flatland, 23 min, in animation, music by Ennio Mor- Il Leon musica fa le bolle, 35 min, La Biennale di Venezia ricone (1999) (2013)

References and Notes 18 A. Quintavalle, ed., Max Bill (Parma: Università Comune Provincia di Parma, 1977). 1 L. Emmer, Picasso with , script by L. Emmer and S. Amidei (Rome: Rizzoli Film, 1954). 19 M. Emmer, “Visual Art and Mathematics: The Möbius Band,” Leo­ nardo 13, No. 2, 108–111 (Spring 1980). 2 M. Emmer, “A Film on Leonardo by Luciano Emmer,” Leo­ nardo 42, No. 5, 449–453 (2009). 20 M. Emmer, Dimensions, color, 25 min, DVD (Rome: RAI and Emmer prod., 1982). 3 M. Emmer, “: The Film Series,” in C. Bruter, ed., Mathematics and Art: Mathematical Visualization in Art and 21 M. Emmer, Numeri immaginari: Cinema e matematica (: Bol- (Berlin: Springer, 2002) pp. 119–133. lati Boringhieri, 2013).

4 R. Finn, Equilibrium Capillary Surfaces (Berlin: Springer, 1986). See 22 M. Emmer, ed., Mathematics and Culture, series of Proceedings of Emmer’s results. the International Conference in Venice (1997–2011), 20 vols.; Imag­ ine Math, new series of the proceedings (Milan: Springer-Verlag & 5 E. De Giorgi, F. Colombini and L.C. Piccinini, Frontiere orientate IVSLA-UMI, 2011–2018), 6 vols. di misura minima e questioni collegate, Publication of the Class of Sciences of the Scuola Normale Superiore (Pisa: Editrice tecnico 23 M. Emmer, ed., The Visual Mind: Art and Mathematics (Cambridge, scientifica, 1972). MA: MIT Press, 1993).

6 M. Miranda, Superficie Minime e il problema di Plateau, quaderni 24 M. Emmer, ed., The Visual Mind II: Art and Mathematics (Cam- Università di Lecce, 1/2006 (2006). bridge, MA: MIT Press, 2004).

7 E. Giusti, Minimal Surfaces and Functions of 25 M. Emmer, Visibili Armonie: Arte, cinema, teatro e matematica (Tu- ­(Basel: Birkhäuser, 1984). rin: Bollati Boringhieri, 2006).

8 J.E. Taylor, “The Structure of Singularities in Soap-Bubble-Like and 26 H.S.M. Coxeter et al., eds., M.C. Escher: Art and Science (Amster- Soap-Film-Like Minimal Surfaces,” Annals of Mathematics, Second dam: North-Holland Elsevier, 1986). Series 103, No. 3, 489–539 (1976). 27 M. Emmer and D. Schattschneider, eds., M.C. Escher’s Legacy: 9 H. Federer, “Geometric Theory,” in Die Grundlehren der A Centennial Celebration (Berlin: Springer-Verlag, 2003). Mathematischen Wissenschaften 153 (Berlin: Springer-Verlag, 1969). 28 M. Emmer, The Fantastic World of M.C. Escher (Rome: RAI, Film 7 10 F.J. Almgren Jr., “Geometric Measure Theory and Elliptic Variational International, Emmer prod., 1998). Problems,” in Geometric Measure Theory and Minimal Surfaces, 29 M. Emmer, ed., Flatland by E.A. Abbott, English & Italian version E. Bombieri, ed., C.I.M.E. Lecture, III Ciclo, Varenna C.I.M.E. Sum- (Turin: Bollati Boringieri, 2008) including DVD by M. Emmer, film- mer School 61 (Berlin: Springer-Verlag, 2010); reprinted, 1st Ed. maker, Flatland (Rome: Film 7 International, Emmer prod.), all in (Rome: Cremonese, 1972) pp. 31–117. animation. 11 J. Plateau, Statique expérimentale et théorique des liquides soumis aux 30 M. Emmer, Ars Combinatoria, color, 25 min, DVD (Rome: RAI and seules forces moléculaires (Paris: Gauthier-Villars, 1873). Film 7 International, Emmer prod., 1984). 12 E.R. Reifenberg, “Solution of the Plateau Problem for m–Dimen- 31 M. Bill, “The Mathematical Way of Thinking in the Visual Art of Our sional Surfaces of Varying Topological Type,” Bulletin of the Ameri­ Time,” originally published in German in Werk 3 (Winterthur: 1949); can Mathematical Society 66, No. 4, 312–313 (1960). reprinted by the author with changes to the title: “The Mathematical 13 F.J. Almgren Jr. and J. Taylor, “The Geometry of Soap Films and Soap Approach in Contemporary Art” in Emmer [23] pp. 5–9. Bubbles,” Scientific American 235, No. 1, 82–93 (July 1976). 32 M. Emmer, M. Abate and M. Villareal, eds., Imagine Maths 4: 14 Papers by W.K. Allard, F.J. Almgren Jr., E. Giusti, J. Taylor, M. Miranda ­Between Culture and Mathematics (Bologna: Unione Matematica and L.C. Piccinini in E. Bombieri, ed., Geometric Measure Theory Italiana and Istituto Veneto di Scienze, Lettere ed Arti, 2015). and Minimal Surfaces, C.I.M.E. (Centro Internazionale Matematico 33 M. Emmer, “Max Bill: A Journey through Memories,” in Emmer [23] Estivo), Varenna, August 24–September 2, 1972, C.I.M.E. Summer pp. 29–41. School 61 (Berlin: Springer-Verlag, 2010); reprinted, 1st Ed. (Rome: Cremonese, 1972). 34 W. Spiess, Kontinuität. Granit-Monolith von Max Bill (Dortmund: Deutsche Bank, 1986). 15 L. Emmer, Domenica d’agosto, story by S. Amidei, screenplay by F. Brusati, L. Emmer, G. Macchi and C. Zavattini (Rome: Colonna 35 T. Buchsteiner and O. Letze, Bill (Milan: Electa, 2006). Film Prod., 1950). 36 M. Emmer, Soap Bubbles & Platonic Solids, in S.X. Descamps and 16 L. Emmer, Camilla, story and screenplay by L. Emmer, E. Flaiano S. Zarzuela, eds., Video and Multimedia at 3ecm: Barcelona, July 10– and R. Sonego (Rome: video production and Paris: Cormoran Films, 14, 2000, Springer VideoMATH series, T. Apostol et al., eds. (2000). 1954). 37 M. Emmer, “Lo spazio tra matematica ed arte,” in G. Macchi, ed., 17 M. Emmer, Lo specchio della felicità (Milan: ebook, VandA ePublish- Arte e Scienza: Spazio Colore, Catalog of the exhibition, La Biennale ing, 2015). di Venezia, Biennale Venezia ed. Venice (1986) p. 3,739, 72.

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Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/leon_a_01473 by guest on 26 September 2021 38 M. Emmer, “Soap Bubbles in Art and Science: From the Past to the Manuscript received 2 February 2016. Future of Math Art,” in Emmer [23] pp. 135–142. 39 M. Emmer, Bolle di sapone. Tra arte e matematica (Turin: Bollati Michele Emmer was full professor of mathematics at the Boringhieri, 2009), The Best Italian Essay, Premio Letterario Viareg- University of Rome “La Sapienza” to 2015, as well as a , gio Rèpaci 2010. journalist and filmmaker. He is a member of the Istituto Veneto pioneers and pathbreakers 40 M. Emmer, ed., L’occhio di Horus: Itinerari nell’immaginario Scienze Lettere Arti (IVSLA), Venice. His area of interests are matematico (Rome: Istituto della Enciclopedia Italiana, 1989). PDE and minimal surfaces; relationships between mathemat­ 41 M. Emmer, script and final editing, L’occhio di Horus, RAI Italian ics and the ; and architecture, cinema and culture. He has state television series The Most Important Exhibitions of the Year, been a member of the Leonardo Editorial Board since 1992. 35 min (1989). 42 http://php.math.unifi.it/archimede/archimede/festadellamatemat ica16.php, 2016.

CALL FOR PAPERS

Science and Art: Understanding the Cross-Disciplinary Dialogue Leonardo Special Section

Guest Co-Editors: Catherine Baker (Birmingham City University) and Iain Gilchrist (University of Bristol)

This call seeks to highlight projects in which the technological aspects of interdisciplinarity do not dominate the conversation but in which the relationship between the two disciplines is, rather, at the of the conversation. Most importantly this section will seek to question the relationship between practitioners and provide a roadmap for such relationships into the future.

We encourage submissions exploring the full breadth of interdisciplinary partnership across art, science and the humanities, presenting the candid voices of those whose ongoing activities reside at this key interface. Submissions can be considered from artist–scientist collaborators whose experiences of interdisciplinary exchange prompt reflection on the conditions of collaboration. We welcome submissions from artists and scientists who found value in the journey and not only the output, as well as submissions that take a historical on such relationships.

PROPOSALS AND INQUIRIES Interested authors should submit inquiries to Catherine Baker [email protected] and Iain Gilchrist [email protected].

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190 Emmer, How a Mathematician Started Making Movies

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color Color Plate D: HOW A MATHEMATICIAN STARTED MAKING MOVIES

Still from the film Soap Bubbles by Michele Emmer, 1979. (© Michele Emmer.) (See article in this issue by Michele Emmer.)

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