Communicating Mathematics Across the Web

In emails to each other, mathematicians tend to write TEX source code to make their mathematics understood. Apparently, this level of precision can be achieved without too much trouble in letter writing on a keyboard and often suffices for interpretation by the receiver. But electronic networking can provide us with a much higher degree of precision and, in fact, can facilitate the creation of less ambiguous messages, to the extent that sophisticated computer software can be used to interpret them. This precision is required to profit optimally from the emergence of computer algebra, proof checkers and databases, which are bound to lead mathematics to new ways of operation. In this essay, I will elaborate on this theme; I will describe a precise way of expressing mathematics within a given context, namely the OpenMath language. But first, by means of a few scenarios, I will sketch the kind of mathematical interaction that I expect to become feasible soon (and certainly would like to have) over the World Wide Web. After introduction of the OpenMath framework, I will argue that it is sufficiently powerful to handle the mathematical content in the Web activities discussed in the three scenarios.