The Genre of Mathematics Documents and its Implications for Digital Documents.

Abstract

The genre of mathematics writing has several distinctive features that point to some of the weaknesses of current digital documents. Some of these weaknesses are surprising. While it might be expected that the importance of formatting and special symbols in mathematics writing would pose challenges for digital documents, the linked, chunked style of mathematics writing, with its Theorems, Lemmas, Corollaries and Remarks explicitly referring to each other, resembles standard hypertext so closely that one would expect that mathematics writing would take well to online hypertext form. It does not. This failure points to deficiencies in our understanding of the true strengths and weaknesses of digital documents. This paper describes mathematics writing, with particular emphasis on features of interest with respect to digital documents. The difficulties in producing effective digital mathematics documents are then examined and used as a basis for talking about general challenges for digital documents. The paper then discusses strengths of digital documents and some of the problems that need to be overcome before digital documents can live up to claims made for them. It also examines some of the misguided claims, such as superior support for non-linearity, that are commonly made for digital documents, explains why these claims are unwarranted, and speculates on why the claims have been made anyway. Suggestions are then given as to what the true benefits of digitization are, including performing computations on text, flexible control of time, and better support for hiding information. The paper concludes with a list of questions whose answers are critical to understanding the capabilities, and therefore the future, of digital documents.