Reading and Writing Mathematics: The MAVIS Project
A. I. Karshmer, G. Gupta, S. Geiiger, C. Weaver · 1998 · Proceedings of the Third International ACM Conference on Assistive Technologies (Assets '98) · doi:10.1145/274497.274524
Summary
This paper from New Mexico State University presents the MAVIS (Mathematics Accessible to Visually Impaired Students) project, an NSF-funded effort to develop comprehensive tools for bidirectional communication of mathematics between blind students and sighted instructors. The authors frame the central problem clearly: blind students read and write mathematics in Nemeth Code (a braille notation for mathematics), while sighted instructors use LaTeX as a markup language. Requiring either group to learn the other's notation is unfair and impractical. MAVIS addresses this through four interconnected tools: a LaTeX-to-Nemeth Code translation filter, a Nemeth Code-to-LaTeX back-translation filter, a screen reader/browser for communicating the structural "first glance" of mathematical expressions, and interactive screen-based tools for reading and creating equations. The technical core of the paper presents a formal approach to language translation using logic programming (Prolog) and denotational semantics, where the meaning of one mathematical language is specified in terms of the other. Using Definite Clause Grammars, the grammar specification automatically acts as a parser, and semantic mappings from parse trees to the target language produce executable translators. The paper demonstrates this with polynomial expressions, showing working Prolog code for both LaTeX-to-Nemeth and Nemeth-to-LaTeX translation.
Key findings
The paper makes several important technical contributions. First, it identifies that Nemeth Code is context-sensitive rather than context-free — the encoding of superscripts and subscripts depends on nesting depth (e.g., x^2 in Nemeth becomes x^^2 when occurring as an exponent of another variable). This means traditional parser generators like YACC cannot handle Nemeth Code directly, but Prolog's Definite Clause Grammars can, because they support context-sensitive parsing through additional computational mechanisms. Second, the paper introduces an "equation browser" that decomposes mathematical expressions into hierarchical chunks presented through parallel sound cues and synthesised voice. Users receive a tonal "glance" at the overall equation structure using timbre, note, and octave, then can interactively drill down into sub-expressions through mouse clicks — single click to decompose further, double click for verbalisation. This chunked approach addresses the fundamental problem that linear Nemeth or LaTeX encodings obscure the semantic structure that sighted readers perceive visually. Third, a working LaTeX-to-Nemeth translation filter had already been built using traditional compiler technology as an add-on to Scientific Notebook software. The paper's logic programming approach aims to make building such filters considerably simpler.
Relevance
The MAVIS project tackled what remains one of the hardest problems in accessibility: making mathematics truly bidirectional between blind and sighted users. The two-way communication model — where both students and instructors can work in their preferred notation with automatic translation between them — is a design principle that applies broadly across accessibility. The equation browser's hierarchical chunking approach, allowing users to get an overview before drilling into details, anticipated similar features in later systems like MathPlayer and the audio rendering capabilities of MathML. For STEM educators today, the paper's core insight remains critical: access to mathematics must go beyond just reading — blind students need to write, edit, and verify their mathematical work independently. The formal framework using logic programming and denotational semantics, while technically dense, demonstrated that principled approaches to notation translation are achievable and extensible to other markup languages beyond LaTeX. Modern tools like MathJax accessibility extensions and screen reader math support have built on these foundations, though fully seamless bidirectional math communication remains an ongoing challenge.
Tags: mathematical accessibility · STEM accessibility · Nemeth code · LaTeX · blindness · braille · sonification · language translation · assistive technology · education