1. Why visual mathematics?
There are many statements that compare mathematics with art. Indeed, mathematics cannot be considered as a field of "natural science" in a narrow sense since it deals with idealized objects. Mathematics provides some interesting concepts, from symmetry to polyhedra, from the golden section to fractals, that are also useful for artists and art historians. On the other hand, mathematics is also the "language of science" and thus it is a natural link between art and science. However, the more recent picture is not blooming, but rather blurring from this point of view. Many fields of abstract mathematics lost the connections with the broader public, including not only artists, but also scholars who work on different fields. Even mathematicians have difficulties to understand some results of different sub-fields. Parallel, mathematics became an increasingly unpopular subject for children. We are facing with an alarming situation: the need for more mathematical knowledge in everyday life versus the increasing mathematical illiteracy. Of course we cannot suggest a general solution for this problem, but we believe that more "visualization" in mathematics and the demonstration of "beauty" in mathematics would be essential for changing the described bleak situation.
When we refer to "mathematical beauty" we think about both:
- "artistic beauty" (in quotation marks) in mathematics,
- artistic beauty (without quotation marks) that illustrate mathematical ideas.
Luckily, there are some modern "champions" of this type of approaches, including
(1) at the side of mathematics
- George Pólya, who authored a large number of books on mathematical thinking and inspired, among others, M. C. Escher by his paper of 1924 with a "visual approach" of symmetry groups in ornamental art,
- H.S.M. Coxeter, who not only "revisited" geometry (referring to one of his books), but also demonstrated its links to art and nature in various papers and the book Introduction to Geometry; he also helped Escher's journey to non-Euclidean symmetries,
- Branko Grünbaum and G. Shephard, who gave a comprehensive survey on the mathematics of tilings and patterns with many new results and artistic illustrations.
(2) at the side of art
- M.C.Escher, the graphic artist whose works are frequently used to illustrate mathematical ideas,
- Helaman Ferguson, the American sculptor (and mathematician) who makes "mathematics in stone and bronze",
- John Robinson, the Australian sculptor, whose works were commissioned by various research institutes and inspired scientific papers.
Although we may continue this list, we cannot speak about a large number of similar personalities. It is true that there is a new helping hand more recently: the world of computers combined with non-linear mathematics. There are many mathematical books on the beauty of fractals and many artistic works generated by computer graphics and related new medias.
Still, we should not forget that computers, which are very useful to help human creativity, are just tools and we should not overemphasize their importance in science and art. For example, we see even more students who can rotate a 4-dimensional cube on the screen, but cannot answer the simple question about the number of vertices of a simple 3-dimensional cube. The fact that the computer "knows" it and this information is not relevant any more is not acceptable. Who will write new softwares for manipulating n-dimensional objects if the basic data of the most simple figures are not widely known? Thus, we should turn back to the "philosophy" of Visual Mathematics: we need both visualization (modern computer graphics) and mathematics (classical problems of this field). The asymmetry would be dangerous. Indeed, the new electronic journal would like to serve as a forum for both sides.
Let us consider mathematics and the visual arts in a historic context. We should pay a special attention to the links between them also to the those aesthetical theories that help the "communication" between the two sided. We obviously need a "new aesthetics" that reflects the most recent developments and past experiences may help to treat the current challenges.