Interdisciplinary courses, positions, PhD, in Italy
Dipartimento di Matematica,
Università di Roma “La Sapienza”
The paper elaborates on my experience with interdisciplinary courses between mathematics and a number of subjects (art, architecture,…) over a number of years and discuss some difficulties that have arisen and a few proposal for actions. Some of these themes are general by nature, as well as some of the actions that can be undertaken.
First of all I would like to say that these academic activities started as a personal experience more than 30 years ago. For many years I was (and I still am) officially a full professor in Math and non-officially I worked on the relationships between mathematics, art, architecture, biology, physics, literature, cinema. At a certain point of my activity my work on art and math was recognized as official work in mathematics.
“Changes in education are not going to produce miracles. The division of our culture is making us more obtuse than we need be: … we are not going to turn out men and women who understand as much of our world as Piero della Francesca did of his, or Pascal, or Goethe. With good fortune, however, we can educate a large proportion of our better minds so that they are not ignorant of imaginative experience, both in the arts and in science.”
On October 6th 1956 an article by Charles Percy Snow was published on the New Statesman that discussed a problem that would have been developed in a lecture and a book three years later. The book, entitled The Two Cultures  compared the scientific and humanistic culture, particularly in the Great Britain of that time. The book sparked a long polemic that moved Snow a few years later, in 1963, to publish an appendix to the book that concluded with the words quoted at the beginning. Snow was a chemist who had the misfortune in 1932 to mistake the data in an experiment. The episode determined the end of its scientific career. He became a writer. His novels were published in different countries between 1940 and 1970. With the book The two cultures he became famous all over the world.
In the introduction to the 1993 edition Stefan Collini, professor of English literature at the University in Cambridge wrote: “We need to encourage the growth of the intellectual equivalent of bilingualism, a capacity not only to excercise the language of our respective specialism, but also to attend to, to learn from, and eventually contribute to, wider cultural conversations.” In short we are speaking of interdisciplinarity.
In 1981 the USA art historian Linda D. Henderson published a book destined to change the way in which we look at modern art all the way through, to the artistic avant-garde of the twentieth century “The Fourth Dimension and Not Euclidean Geometry in Modern Art” . The research still continues, (the second edition of the book will be published in 2012, with 200 additional pages, MIT Press). Linda Henderson reconstructed the ways through which the new ideas of geometry of the second half of nineteenth century, particularly non Euclidean geometries and the idea of the fourth dimension, (before the theory of the relativity and the space-time), have influenced the art of the XXth Century, including through the literature inspired in mathematical research, in particular the novel Flatland of Edwin Abbott, published in 1884. 
Linda Henderson used almost the entire scientific and mathematical researches of the period. She obviously does not affirm that these were the only sources of inspiration for the artists. She identifies complex and fascinating Arianna’s threads that form new ideas in science and in art.
In 1982 I realized with Linda Henderson one of my films of the series Art and Mathematics. Since then we have collaborated in different conferences and in the project of a large exhibition on Mathematics, Modern and Contemporary Art. It is not clear if the exhibition will be realized due to Italy’s financial problems.
In the same years I discovered the Journal Leonardo and I started a collaboration on art and science that is still ongoing. I have had the great pleasure of being in the board together with Max Bill, one of the great artists of the XXth Century, with whom I realized two films of the series Art and mathematics. 
The situation in Italy
After many years in 2012 a huge operation of evaluation of Italian Universities, professors and researchers took place. Around 50.000 people and hundreds of thousand of articles and scientific books are being appraised. The magic answer to this problem was finally found. If numerical objective indicators existed, numerical (and what can be more objective than numbers!) to identify best candidates, the problem would be solved. These indicators have existed for a few years. They serve to measure the number of published articles, the quality of the journals in which they are published (international journals obviously), the number of citations of the articles showing the interest and the seriousness of the researches.
The ANVUR, the National Agency for the Evaluation of the Research was created. Scopus indicators of the publishing house Elsevier and those of Web of Science of Thomson Reuters ere chosen, with all the problems of objectivity that these choices involve. It is important to clarify that these indicators work only for the scientific sectors, for the humanistic and artistic sectors, they don’t exist. Then the way to appraise had to be divided in two. Selected journals were selected for the non-scientific sectors, sectors in which obviously the published books are considered essential to appraise in this discipline. Some of these journals were really peculiar and not really scientific, their titles were even published in the Italian newspapers. So the scientific researches have they the indexes, the not scientific have theirs peculiar methods. And more, scientific evaluation methods based on h-index or similar do not exist for books.
The criteria adopted in Italy (index, etc.) create some problems. All those areas that are and want to be interdisciplinary are virtually eliminated. Would the books of Linda Henderson and Snow be taken into consideration? In which sector? For example, historians of mathematics as mathematicians are in the scientific sector but they edit and write books and therefore are not considered by the humanistic criteria of evaluation, nor by the scientific ones since books are nor considered. So forget to study art and science! This is the general situation in Italian universities. And so it is impossible to ask any young researchers to take courses that are interdisciplinary in nature. There is no future for them.
Some positive signs
I was very proud when I received as national coordinator two grants in 2007 and 2009 (the rules exclude applying for a grant every year) for research on mathematics and modern art. These grants were assigned by the Italian Committee for National Funds (PRIN) for mathematics. So the math researchers decided to support my research on art and math. Due to the economic crisis in Italy and in the funds for the Universities a choice like this means that other research, strictly math research, did not receive a grant. This was unthinkable 30 years ago, even 20 years ago.
Due to the change in the attitude of the Math community it was possible to undertake several projects:
Conferences and books
The “Mathematics and Culture” international yearly conference in Venice starting in 1998. Part of the conference is dedicated to art and math. Proceedings in Italian and in English by Springer verlag, more than 25 volumes. From 2012 a new series “Imagine Math: math and culture”  always published by Springer verlag. The next conference in 2013 will be particularly interesting because speakers will include Linda D. Henderson on a project for an important exhibition on art and math in Italy.
The series of books “The Visual Mind: Art and Mathematics”,  published as Leonardo books by MIT Press, the first in 1993, the second in 2004, with several editions.
A first traveling exhibition in Bologna, Parma, Milano and Rome on “The Eye of Horus: itinerari nell’immaginario matematico” in cooperation with the Istituto Italiano of the Enciclopedia Italiana, the Isttituto di Studi Filosofici of Napoli and the Citè des Science de la Villette de Paris, in 1989/99.
A session of the Biennale of Art in Venice in 1986 dedicated to the theme of Art and Science. Including a part on art and mathematics.
Smaller exhibitions related to art and science and the annual meeting in Venice with artist like Peter Greenaway, Achille Perilli, George Hart, Heleman Ferguson, Bradley Miller and others.
A large project of an exhibition on Mathematics and Modern and contemporary Art, to take place in novemebr 2012, postponed due to financial problems.
20 films of the series “Art and Mathematics”  produced in several languages, shown in the Italian State Television and other TV channels, including the film on Soap Bubbles, featuring the well known mathematicians at Princeton University Fred Almgren and Jean Taylor.
A film on Escher with Roger Penrose and Donald Coxeter, distributed in USA for 20 years, a film based on the book Flatland all in animation, original music by Ennio Morricone. All films were produced in French for the Citè des Sciences de la Villette in Paris. Most of the films produced also in English and Spanish versions.
Courses at the University
In 2004 I launched a completely new course, existing only at the University of Rome, called “Space and Form”,  an interdisciplinary insight of the relationships between mathematics, art, architecture, biology, literature, theatre, cinema with a myriad of applications in all these fields during the XIX and XX century. It involves students of the last years in math, design and architecture, including a small group of ERASMUS students from several European Countries.
The number of students is usually every year between 50 and 60, adding to more than 450 in seven years. There is a project to write in English a text book of the course to be used of course not only in Italy, but I hope in Europe and elsewhere.
Soap bubbles are part of the topics of the course on “Space and form”. There is the project to publish an English version of the book.
Architects, Like Massimiliano Fuksas, artists, writers, filmmakers like Gustavo Mosquera, came to present their works to the students for the course “Space and Form”
One important result of this activity was:
– The Literary Viareggio Award 2010 (Best Italian essay 2010) for the book on “Soap Bubbles” I wrote in Italian. The same year the International Viareggio Award was given to Vargas Llosa. A short abstract of the motivation of the Jury, most of them university professors):
“Emmer wrote an extraordinary book in which mathematics and science, analytical rigor and artistic sensibility is a perfect match, …a real adventure of intelligence, which he reconstructs in masterly fashion by giving us a book not only interesting, but rare.”
The same book also received the Premio Capalbio Scienza 2010 (Best science book)
The real problem
– There is an interesting discussion developing in Italy and Europe on the possibility to introduce interdisciplinary curriculum, master, PhD in art and science. The real problem is to obtain positions for researchers in this area. In Italy in particular there is a major problem: in which discipline can we insert an interdisciplinary course? Can you ask a math department for a position for a young researcher on art, math and architecture? In Italy it is impossible for the time being. As it is impossible to obtain any dedicated PhD program or any contract for lectures. I cannot recommend my students to continue to study art, math, architecture, as there will be no future for them.
– At a European level however, there is a new PhD in France and Switzerland on art and science for artists and designers, as well as interdisciplinary seminars on art and science proposed for 2013 in Paris. While at the European level it is possible to ask a grant to organize an exhibition on art and math this is out of the question in Italy.
– In 2008 we started an important project of a large exhibition on math and modern and contemporary art to make visible all the work that has been done in the last years. This year there was the exhibition on art and math at the Cartier Foundation in Paris (nor really satisfactory) and the small exhibition on Henry Moore and math at the Royal Society in London. This exhibition will probably move to Venice in 2013.
Suggestions and actions
I can suggest the following actions:
– Action #1: Web site and Visibility
I agree with the proposed Action #1 of K. Evans  that cross-disciplinary art- science humanities researchers are isolated and have no knowledge of what is going on in the world. So the first thing is to create a well done website so to maximize the diffusion of all possible information’s, on interdisciplinary courses, masters, degrees, on the curricula, on books (with possible reviews), articles, journals, conferences, meetings, novels, films, plays in theatre.
It will be essential to have a website where it is possible to exchange ideas, experiences.
– Action #2: exchange of experience
To encourage the exchange of professors and students to participate in interdisciplinary experiences in different countries. It is clear that it is easier among European countries using the program ERASMUS, more complicated between Europe and non-European states for obvious reasons of cost. In the website an essential part must be dedicated to all possible opportunities of exchange of professors and students.
– Action #3 promote new interdisciplinary researches
To use Leonardo and a new website for suggestions for new interdisciplinary courses and researches. I believe that the contact between different universities and research teams in order to obtain funds from ESF (European Science Foundation) and similar institutions in other countries is essential. A program of research to be presented by researchers and artists who are linked to the network of Leonardo for proposals for new research and exhibitions to be presented in conjunction with the European community, the NSF and other similar bodies.
Interdisciplinary projects that will lead to the realization of exhibitions, interdisciplinary conferences, screenings of films that have interdisciplinary interest to motivate younger students to learn in an interdisciplinary way.
Ask all researchers and artists involved in the SEAD to start a formal request to initiate exchanges of students and researchers for short periods. With regard to mathematics and art, there are various associations, various annual conferences, that can be contacted.
– Action #4 new book series
Start creating interdisciplinary series of publications not only at a research level but also for graduate and undergraduate courses. Not only the Leonardo book series. For mathematics and art and architecture there are already the series by Springer verlag “Mathematics and Culture”, “Imagine Math”, and by Birkhäuser “Mathematics and architecture”
Due to my personal experience and my knowledge it will be easier to organize interdisciplinary courses, masters, perhaps PhD, at the European level. It will be probably easy if the different European countries put their experience together to ask for an international and interdisciplinary important Grant for the next years. It will be probably more complicated to cooperate also with USA. But Leonardo is a good way to cooperate.
 C. P. Snow, The Two Cultures, Cambridge University Press, Cambridge, 1993.
 L. D. Henderson, The Fourth Dimesion and non Euclidean geometry in Modern Art, Princeton University Press, 1981; second ed. MIT Press, to be published.
 E. A. Abbott, Flatland, London, 1884; M.Emmer, ed, Flatland, Italian & English, with DVD of the film by M. Emmer, Bollati Boringhieri, Torino, 2008.
 M. Emmer, film maker, Dimensions, series Art and Mathematics, DVD, 25 m., english, french, italian. Prod. Film 7 International & M. Emmer, Rome.
 M. Emmer, film maker, Moebius Band, Ars Combinatoria, series Art and Mathematics, DVD, each 25 m., english, french, italian, spanish. Prod. Film 7 International & M. Emmer, Rome.
 M. Emmer, ed. Mathematics and Culture, volume I, II, III, IV, V, VI, Springer verlag, Heidelberg, 2005- 2012. Italian version Matematica e cultura, Springer Italia, Milano, 14 volumes, 1998-2011.
Website of the annual congress: http://www.mat.uniroma1.it/venezia2013
 M. Emmer, ed. Imagine Math, Sprigner verlag, Milano, 2012. Imagine Math 2, to appear march 2013.
 M. Emmer, ed. The Visual Mind, MIT Press, Boston, 1993; The Visual Mind 2, MIT Press, Boston , 2004.
 M. Emmer, film maker, series Art and Mathematics, 18 films in DVD, each 25 m., english, french, italian, spanish. Prod. Film 7 International & M. Emmer, Rome.
 K. Evans, Breaking down the Silos: curriculum development as a tool for crossing disciplines in the arts, sciences and humanities, SEAD white paper, preprint.