The Future of Mathematical Text: A Proposal for a New Internet Hypertext for Mathematics
The Internet has transformed the practice of mathematical writing, and mathematical texts of all kinds are moving online. But the fundamental change to come in mathematical publication is not just moving print forms to electronic documents, but recreating mathematics in a new architecture: a hypertext that reflects the deep unity and universality of mathematics, that can grow and diversify as mathematics changes. It is argued that hypertext is a natural representation of mathematical thought, with its deep interconnection of ideas, the need for constant revision, and the multiplicity of viewpoints. The design of a hypertext must take into account how mathematics is structured and how it is understood: its internal consistency, the need for preparation and review, and the importance of strong tool support for reading and writing text. A high-level design is proposed, combining structured and network hypertext, with a simple link and editorial structure, and design issues concerning language representation, medium- and high-level structure, editorial policy, administration, and technology are examined. A hypertext of sufficient quality and usability will powerfully influence how mathematics is taught, communicated and used, in the classroom, in the workplace and in research. This change in how the Internet is used is not primarily technical: it is the extension of current technology towards a new goal. Gaps and weaknesses of the design are discussed, as well as possible solutions, and a plan to implement the hypertext on the Web is developed.