Moebius Strip, with the artist Max Bill Soap Bubbles, with the mathematicians Fred Almgren and Jean Taylor Platonic Solids, with the mathematician Donald Coxeter Symmetry and tessellations, with the mathematician Roger Penrose Dimensions, with the mathematician Thomas Banchoff and art historian Linda Henderson

Helices, with the mathematician White

Spirals, with the mathematician André Deledicq Geometry, with the japanese architect Koji Miyazaki Ars Combinatoria, with the mathematician David Singmaster and the artist Max Bill

Labyrinths, with the matheamtician Anthony Phillips Computers, with the mathematician Thomas Banchoff Knots, with the mathematician Lee Neuwirth -Flatland, all in animation with real objects. The Eye of Horus, an exhibtion on art and math"

2) Conferences and exhibitions organized:

"M.C.Escher: Art and Science", University of Rome, 1985;

"Fractals in nature and mathematics",Istituto Enciclopedia Italiana e Università Roma II (1988);

"Video & films",Organizzazione della sezione,Cong.Mondiale di Educ.Mat., Budapest (1988);

"L'art et les Mathématiques", Cerisy & Ecole Normale, Paris (1991) "M.C.Escher",Istituto Olandese di Roma (1985) ; " I frattali : la geometrie dell'irregolare", Istituto Enciclopedia Italiana ,Roma (1988);

"L'occhio di Horus; itinerari nell'immaginario mate-matico",Istituto Enciclopedia Italiana, Bologna, Parma, Milano, Roma (1989) "L'enigma del fascino di M.C. Escher", Futuro-Remoto, Napoli, 1989, "Biennale di Venezia : sezione spazio ed informatica"(1986) "Heureka", Zurigo (1991);

Città della scienza, Museo Scienza Viva, Napoli (1996)

3) A selection of books and publications:

H.S.M.Coxeter, M.Emmer, R.Penrose, M.Teuber(Editors) "M.C.Escher : Art and Science", Proceedings ,Amsterdam, North-Holland (1986). M. Emmer, ed., "Visual Mathematics", special issue"Leonardo", Pergamon Press, Oxford, vol. 25 n. 3/4 (1992).

M.Emmer "La perfezione visibile: matematica e arte", Edizioni Theoria, Roma, 1991.

M.Emmer "Le bolle di sapone: viaggio tra arte, scienza e fantasia", La Nuova Italia Editore, Firenze, 1991.

M.Emmer "La Venezia perfetta", Centro Intern. della Grafica, Venezia, 1993. M.Emmer, ed.,"The Visual Mind: Art and Mathematics", The MIT Press, Cambridge,1993; Japanese ed., to appear 1996. M.Emmer, C.Van Vlandereen(editors) "M.C.Escher",catalogo della mostra, Istituto Olandese, Roma (1985).

M.Calvesi,M.Emmer (editors) "I frattali: la geometria dell'irregolare", catalogo della mostra, Ist. della Enciclopedia Italiana, Roma (1988). M. Emmer(a cura di) "L'occhio di Horus: itinerari nell'immaginario matematico", Istituto della Enciclopedia Italiana, Roma, 1989. M. Emmer "L'enigmatico fascino di M.C.Escher", Catalogo della mostra, Futuro-Remoto; Napoli,CUEN (1989).

 

 

MATHEMATICIANS: THE NEW ARTISTS?
No doubt that in the last years a revival of interest for creativity in mathematics has taken place; mainly for the possible connections with the artistic creativity. The principal motivation for this new interest is the large diffusion of computers with high graphics facilities. This very large diffusion has strongly raised intuition and creativity in that part of mathematical research connected to the possibility of visua-lizing not only known phenomena but to make visible the insivible (1).

Mathematical ideas are not subjects to fashions, they do not vary in centuries; a theorem proved by Euclid is valid today and it will be valid for centuries; it will never be over. How many other human activities have this caracteristic of universility, of immortality? Mathematics as the true art? «Of course the creative process must produce a work that has design, harmony and beauty. These qualities too are present in mathematical creations» wrote Morris Kline in his essay Mathematics in Western Culture (2).

There is no doubt that there are some peculiarities in considering the question of creativity in mathematics and in trying to compare it with the artistic one. Mathematicians state on the one hand that the real universal art is mathematics, on the other hand that they are the only ones able to understand this truth; so only the participants to the scientific community can take part in this « banquet of gods» (3). It seems that the only conclusion is that trying to analyze relationships between mathematical and artistic creativity is a loss of time.

In any case it is possible to discuss the new possibilities opened for the relationships betweent art and mathematics by the new technologies. It is possible to focus on the main directions along which to obtain results of interest for each fields. On the one hand the mathematicians have obtained in the visual investigation of scientific problems images that have arose the interest not only of the scientific community but of a large audience, artists in particular; on the other hand artists, feeling themselves excluded from the possibility of using in full the new visual tools, have asked for cooperation mathematicians and experts in computer graphics.

The great possibility opened with the use of computer graphics of seing mathematical objects of which it was not even possible to imagine the enormous graphic complexity, has opened wide spaces to artistic creativity. Mathematicians very soon became aware of this not secondary aspect of their researches. To give an idea of the growing importance of the visual aspects, to point out the possible connections between some of the most recent mathematical research and the work of artists using visual techniques influenced by mathematical ideas see the volume The Visual Mind: Art and Mathematics (4) .

Impossible to imagine, untill a few years ago, a book like Symmetry in Chaos: a Search for Pattern in Mathematics, Art and Nature. The authors, the mathematicians Michael Field e Martin Golubitsky, wrote in the introduction (5):

«In our mathematics research, we study how symmetry and dynamics coexist. This study has led to the pictures of symmetric chaos that we present throughout this book. Indeed, we have two purposes in writing this book: to present these pictures and to present the ideas of symmetry and chaos - as they are used by mathematicians - that are needed to understand how these pictures are formed.... One of our goals for this book is to present the pictures of symmetric chaos because we find them beautiful, but we also want to present the ideas that are needed to produce these computer generated pictures.» The authors recall the volume of Peitgen and Richter The Beauty of Fractals (6) and add: «It is worth noting that the images we present have a different character from those found in fractal art. While fractal pictures have the sense of avant garde abstract modernism or surrealism, our typically have the feel of classical design.»

Who could have imagined a few years ago that such declarations could have been found in the introduction of a volume written by two mathematicians?

We are probably facing a possible revolution in the . relationships between mathematics and art, in which the creativity of artists and mathematicians will have the possibility of a very profound cooperation; perhaps a new Renaissance? (7)

(1) These words are said by David Brisson in: M. Emmer, Dimensions, video, series "Art and Mathematics", (Roma: FILM 7 INT., 1984). The film is dedicated to him.
(2) M. Kline, Mathematics in Western Culture (Harlondsworth, UK: Penguin, 1953).
(3) F. Le Lionnais, Les grands courants del la pensès mathèmatique, (Paris: A. Blanchard,1962)
(4) M. Emmer, ed., Visual Mathematics, special issue, Leonardo, 25 No. 3/4 (1992). __________, The Visual Mind: Art and Mathematics, (Boston: The MIT Press, 1993).
(5) M. Field & M. Golubitsky,Symmetry in Chaos: a Search for Pattern in Mathematics, Art and Nature. (Oxford: Oxford University Press, 1992).
(6) O. Peitgen & H. Richter The Beauty of Fractals , (Berlin: Springer 1986).
(7) M. Emmer , Le mathèmaticien artiste, preprint presented to the Colloqium at Les Treilles.

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