UMA: A System for Universal Mathematics Accessibility
A. I. Karshmer, G. Gupta, E. Pontelli, K. Miesenberger, N. Ammalai, D. Gopal, M. Batusic, B. Stöger, B. Palmer, H-F. Guo · 2004 · Proceedings of the 6th International ACM SIGACCESS Conference on Computers and Accessibility (Assets 04) · doi:10.1145/1028630.1028642
Summary
This paper presents the Universal Mathematics Accessibility (UMA) system, a multi-institution collaboration to make mathematical content interoperable between the notation systems used by blind and sighted individuals. The fundamental problem is that blind mathematicians use Braille-based notations (Nemeth in the English-speaking world, Marburg in German-speaking countries) while sighted mathematicians use visual formats (LaTeX, MathML, OpenMath), and these worlds have remained largely isolated from each other, preventing effective communication between blind students/mathematicians and their sighted peers. The UMA system has two major subsystems: a Conversion Platform that translates between all five formats through a Common Interchange Format based on the OpenMath standard, and a Navigation Platform (called MathGenie) that provides interactive aural and visual exploration of mathematical expressions. The Nemeth-to-LaTeX translator is particularly complex because Nemeth Braille code is context-sensitive, space-sensitive, and ambiguous — the same Braille character can have different meanings depending on surrounding context. The system uses Prolog-based logic programming with definite clause grammars to handle this complexity. For Marburg notation, the challenge is different: it uses a "projective" technique to represent two-dimensional mathematical structures (like fractions and superscripts) linearly, requiring a parser built with GNU Flex and Bison. The digital format conversions between LaTeX, MathML, and OpenMath leverage XSLT transformations and the structured tree representations these XML-based formats provide.
Key findings
The system successfully demonstrates bidirectional conversion between Nemeth Braille and LaTeX, with a sample conversion shown of complex mathematical expressions including trigonometric functions, angles, and spatial arrangements from an analytical geometry textbook. The Nemeth-to-LaTeX conversion handles literary Braille text, Nemeth mathematical expressions, and spatial arrangements (matrices, determinants) through separate processing pipelines that are recombined into the final LaTeX document. The Marburg-to-MathML converter is operational as a standalone program, DLL, and C library. The MathGenie navigation component operates on the OpenMath interchange format and provides hierarchical exploration of mathematical expressions — users can drill into subexpressions, move between siblings, and hear aural descriptions at different levels of detail. MathGenie also offers visual presentation with color coding to support users with dyslexia, and multilingual aural output in English and Spanish. A key architectural insight is using OpenMath as the interchange format because its Content Dictionaries provide explicit semantic definitions of every mathematical symbol, enabling richer navigation and description than would be possible with purely presentational formats. The system is under continuous development, with integration of VoiceXML for interactive navigation being explored.
Relevance
This research addresses one of the most persistent barriers in STEM accessibility: the inability of blind students and professionals to seamlessly exchange mathematical content with sighted colleagues. For accessibility practitioners, the UMA system illustrates several important principles. First, accessibility in specialized domains like mathematics requires domain-specific solutions — generic screen readers and text-to-speech systems cannot adequately handle mathematical notation because mathematics is inherently two-dimensional and relies heavily on spatial relationships. Second, the interoperability challenge between Braille math notations and digital math formats mirrors broader accessibility interoperability problems. Third, the aural navigation approach — allowing users to explore complex expressions hierarchically rather than hearing them linearly — is a transferable design pattern for making any complex structured content accessible. The main limitation is that the system was still under active development at the time of publication, with some conversion paths incomplete and no formal user evaluation reported. The choice of OpenMath over MathML as the interchange format was pragmatic but may have limited adoption given MathML's wider support in web browsers.
Tags: mathematical accessibility · braille · visual impairment · STEM accessibility · MathML · Nemeth Braille · aural navigation · format conversion · assistive technology
Standards referenced: MathML · OpenMath