Some of the more interesting hypertext projects that I've been involved in are discussed in my listing of recent web projects. . One of the most exciting to me has been the development of a virtual mathematical art gallery, "Surfaces Beyond the Third
Dimension" . This project is documented in , and has lead recently to a traveling (physical) exhibit in Portugal and Brazil. This process is described in .
Another highly visible project was the creation of the Math Awareness Month poster and web site for April
2000 . Banchoff and I designed and produced the poster sent to thousands of schools across the country, and developed an accompanying web site that was an interactive version of the poster. This gave students access to information about various people and concepts involved in the idea of dimension, which was the theme for the math. The project is the subject of a join paper with Banchoff , available from the publications list .
A more ambitious effort was the unveiling of a new electronic journal, Communications in Visual Mathematics , co-founded with Tom Banchoff in 1996. In marked contrast to the most common type of electronic journal available today, ours hoped to promote the use of new approaches to using hypertext and multimedia documents to disseminate mathematical research. Unfortunately, a number of problems have plagued this effort, and the journal has remained in prototype form, essentially untouched since 1998.
There were several factors that contributed to the lack of success of the CVM, some administrative, and some technical. An important one is that the notation is so difficult to produce in a web browser. The current HTML language does not provide sufficient functionality to generate all the symbols required by mathematicians, nor can their positions be suitably controlled. Although the proposed HTML3.0 specification (back in the mid 1990s) included mathematical formatting commands, the browser manufactures (Netscape and Microsoft) actively lobbied to have them removed, since they were more interested in colored backgrounds and flashing letters than in crucial functionality. When it was pointed out that there are thousands of scientists who need this ability, their response was "Only thousands?" As a result, W3Com, the web standards organization, initiated the MathML project to develop a formal specification for mathematics on the web. This was longer in being developed than we expected, and even though it has now been released, it is based on the XML language, an emerging technology that has yet to become widely available. There are some specialized plug-ins and commercial browsers that support the MathML specification, but it will not be an appropriate basis for a journal until it is available with little difficulty to most mathematicians.
One of the things that became clear while I was writing my first hypertext paper in 1994 was that a database of mathematical glossary information to which other papers could link would be very valuable on the web. Today, one of the main entry points to that original on-line paper is through the glossary page for the Klein bottle (arrived at via the results of a search engine), so it is obvious that people are looking for this kind of basic information. Some mathematical sites of this sort now exist, notably the history of mathematics
site at the University of St. Andrews, Scotland, and their collection of famous mathematical curves More recently, a refereed collection of manipulable geometric objects from current mathematical research has become available.
My own contribution in this area was a project called the "Topological
Zoo" that I initiated while a prostdoc at the Geometry Center. This was intended to be a pictorial dictionary of important surfaces that would include definitions, equations, images, animations, and interactive versions of these objects. Unfortunately, the Geometry Center lost its funding just as this project was beginning, so it was cancelled almost before it was started.
The pages that are part of the zoo were developed by two talented young mathematics students, Susan Dziadosz and Rosabel Hernandez, as part of the Geometry Center's Summer Institute program for talented college students. The movies and images were created by them using a very early version of my
I have involved students at Union in this type of work as well. A thesis student of mine (Risa Tolin) wrote a very attractive hypertext document concerning the optical illusion present in a renaissance Italian cathedral
dome . Three other thesis students (Joe Caruso and Kevin Christie, Jennifer Gabriel) worked on developing materials that explain the mathematics underlying several of the Olivier models owned by the college. An electronic companion for these physical models would be a wonderful addition to the collection, and could serve as a showpiece for the college that would be available internationally.
Finally, I have given dozens of lectures and presentations around the country to researchers, department heads, college students, and high-school teachers that use these electronic resources to introduce them to some interesting mathematics, as well as suggest some of the ways that this technology can be useful in research and education. These have been well received, and I have been asked to participate on an AMS panel on electronic media and on an NSF review panel for electronic libraries (though I was not able to do so).