Presentations

Schedule of Events

Abstract

The characters of mathematics to be discussed are not persons, though mathematics has more than its share of that type of character, but the building blocks of its notation. What exactly are the signs and symbols, tokens, or building elements of the mathematical writing system, and from where did they come? These questions may easily be thought trivial, until you consider them for a while. They generated some of the heftiest controversy there was in the course of developing the MathML specification.

Notation is very important for mathematics. It has helped both to advance and to impede it over the years. The introduction of zero a long time ago was a watershed for mathematics, and the adoption of "the deism of Liebniz over the dotage of Newton" changed the course of calculus. Good notations are part of the effective abstraction mechanism underlying the progress of mathematics and science in general. What notation MathML enables, and perhaps even the unforeseen uses of it, may determine how fast MathML catches on. MathML already offers notations of new types as well.

For MathML the fateful decision was taken to work with the Universal Character Set (UCS), as developed by the Unicode Consortium and standardized by the International Standards Organization as ISO 10646. This should be part of the basis for MathML's success and widespread adoption. Yet, in the development of MathML, it imposed a considerable burden on the Working Group. It even made the preparation of the published specification noticeably more difficult. The presentation will explain some of the reasoning behind the decision over character sets for MathML. It will emphasize how the choice of character sets is important both generally for science and mathematics on the web and directly for those trying to publish science and mathematics.

Once you have decided what characters you want, you need to get them to be part of the standards environment. This means you have to get them into the UCS, through the Unicode Technical Committee, and you will have to have fonts to display them. What this means for public use of characters will be explained.

Mathematics uses letters differently from text. How are the alphabetical symbols of mathematics different from the letters they resemble? How does this tie in with the clear separation of content and style that is much advocated as good practice in generic markup? These questions lie at the root of some of the controversial aspects mentioned above. The reasons why will be explored.

What happens when you invent new notational symbols, and how do you get them to work with MathML? How can they come to be accepted? How did that used to happen? An example of how to use a new notation will be given.