The Library of the Institute Henri Poincaré in Paris is presenting an exhibition and lecture series “MATHEMATICS AND ARTS”,  January 22 – June 30.

This exhibition is part of a larger project conceived in September 1989 who conducted to the creation of the association ARPAM by an international college of mathematicians including Laurent Schwartz, honorary member, Jean Cerf former President of the French Mathematic Society and Valentine Poenaru, who are today its vice-presidents.

The idea was to establish in an outdoor setting nearby Paris, France, ten small buildings whose architecture, form and decoration, would illustrate particularly significant concepts and mathematical facts. Permanent and temporary exhibits would also find in this site a natural welcoming home.

Museums have been created to preserve the memory of significant works and creative individual achievements. Wouldn't it be time to dedicate a space to present a unique body of mathematically inspired works upon which their undeniable artistic value is partially based?

One will discover in the Institute Poincare exhibit several works selected for their unusual aesthetic character in relation to the world of mathematics. Their contents are enlightening as spectators may seek to deepen their experience at various levels, and under many disciplinary angles.

The visitor may notice a work: which reasons (physiological, sensory, psychological, cultural) guided its choice? Is he/she interested in the technical aspects of the realization of the work (natural, manufacture of the support, techniques, physical and data processing of impression), in its conceptual aspects (psychology, training and philosophy of the author on one hand, concepts and tools mathematical on the other hand), or in the value of this work according to many possible criteria? Are the questions put forth by this visitor relevant to the field being explored? What already known mathematical data have appealed to him/her, and which new data will he/she have been able to acquire? Will he/she have been brought to explore and solve an old problem, even a new problem?

The field of mathematics being covered in this exhibit is vast: polyhedrons (Hart), tessellation (in Euclidean geometry and hyperbolic) (Austin-Casselman, Field, Rousseau, Wright), numerical analysis (polynomial equations resolution) (Kalantari), fractal universe (Colonna, Constant, Friedman), differential topology (knots, spheres, tori and bottles) (Apéry, Banchoff-Cervone, Colonna, Constant, Jeener, Robinson, Sullivan, Termes), minimal surfaces (Colonna, Jeener, Sullivan), solitons (Constant), dynamic systems (Field).

One finds in the body of work presented in this exhibit the inspiration and support for multiple expressions on all levels of mathematical and data processing explorations.

In addition, this exhibit raises the general problem of the representation of the mathematical objects and the procedures of acquisition of knowledge in this field. Accordingly, the visualization of mathematical statements plays an essential part in this project.

This project is also an attempt to encourage further collaboration between science and art in particular in the field of dynamic visualizations, where one sees objects moving, take shape, project themselves, put themselves in correspondence, change shape as done in short films or videos where one can control the tape, speed it to adapt it to one’s physiology. These visualizations are most penetrating, because they instantly follow the rhythm of the thinking process according to the participant’s own pace.

Mathematics and arts take part of the same activity of representation. Devoted not only to mathematics, the universe of the symbol par excellence, but also to the arts which also take part of our symbolic system activity, the exhibition underlines the bond linking the intellectual art as practiced by the mathematicians with arts of more sensory expression.

Couldn't the community of the artists draw a better party from the abundant wealth and any news acquired by the mathematicians? A renewal of artistic teaching could contribute to give a new vitality to creation by this community. As it has been successfully carried out in the United States, the mathematicians, or the artists - even helped by mathematicians, could with tact, introduce mathematical concepts adapted into the schools of art, those of differential topology in particular, without causing in any way traumatisms or rejections. Shouldering one and the other, art and mathematics advance in concert to offer the spirit of the finest pleasure.

C.P. BRUTER

Paris XII University, Paris. France.