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Scholarpedia

Wikipedia is useful for finding quick information, answering trivia questions, and for getting up to speed on things you think you should know.  But whether Wikipedia ought to be used for an academic citation is another story. 
One scholar, Eugene M. Izhikevich (author of Dynamical Systems in Neuroscience), has decided to harness the concept of Wikipedia into a format that is more likely to please academics:  he has founded Scholarpedia, a peer-reviewed version of Wikipedia.  Each article in Scholarpedia has a "curator", usually a leading researcher or scholar in that field.  The initial version of an article is submitted for a peer review process, and each successive version is permanently saved for purposes of citation.  While (in the spirit of a Wiki) anyone can propose changes to an article, the curator is responsible for approving these changes. 
Scholarpedia's current content focuses on Computational Neuroscience, Dynamical Systems and Computational Intelligence, but it plans to move in other directions if all goes well. 
An exciting aspect of Scholarpedia is that some articles are written and curated by the very people who discovered the concept - as in the case of Lotfi Zadeh, who has written about Fuzzy Logic, or Mandlebrot, who is slated to write the article on Mandelbrot sets.   And who can argue with that kind of citation?

The Visual Mind Project

By Michele Emmer

Mathematics and Culture

I started my annual conference on Mathematics and Culture in Venezia at the university of Ca’ Foscari in 1997. In this meeting the relationships between art and mathematics are of great importance. Many artists and mathematicians have participated and have written texts for the proceedings published first in Italian then in English.   At the most recent meeting I made an overview of all the projects I have been involved in recent years connecting mathematics and culture, mathematics and art in particular. So I gave a presentation of the Visual Mind project.

In 1977 Frank J. Malina, a founding member of Leonardo, the journal on the relationships between art, science and technology wrote the following in the preface of the volume Visual Art, Mathematics & Computers:

In one way or another, mathematics underlies the ideas and the artworks discussed – only elementary echoes are evident in some, but there are sophisticated applications of the ‘queen of sciences’ in others. To understand the non-figurative or abstracts artworks presented requires, in general, a comprehension of messages of a kind different from those that artists have traditionally used – works generally needs an understanding of messages that are of a different nature from those traditionally used by artists.

Will these new developments take to a synthesis between art and mathematics? Digital computers offer many possibilities for two- and three-dimensional art, both figurative and non-figurative. Some artists have engaged computers as an aid to creativity. The volume is to understand whether artists will have a more serious interest in cybernetic aesthetics than that they had in past theories on aesthetics, thus arriving at a synthesis between mathematics and art. These words, written in 1977, inspired the project The Visual Mind, on the relationship between mathematics and art.

Visual Mathematics

Since then, many years have gone by and computers have profoundly modified the way of life of at least a part of humanity. Among other possibilities, computers are instruments that allow developing mathematical experiments that open entirely new perspectives. The scanty graphic capacities computers were equipped with at the end of the sixties have become ever more sophisticated, leading to the development of another important chapter in the relationship between mathematics and art.

It became possible to construct a surface on a video terminal and to move it and transform it in order to study its properties. In addition to being aids to intuition, computers became essential instruments for the construction of models. The great potential of computer graphics as a research tool was recognised by mathematicians as soon as the new technologies were available. As tools and software became more sophisticated, the depth and the relevance of the applications of computer graphics to mathematical problems increased.  After the first steps in the seventies, the significant increase of computer graphics in mathematics has lead to the development of a specific area of mathematics that can be called Visual Mathematic.  It is not only – as could be imagined – rendering visual or visualising well-known phenomena through graphic tools, but rather, using visual instruments to make oneself an idea of mathematical problems that are still open. Thus, it refers to the use of the computer as a tool to experiment and formulate conjectures in and of itself.