Accessible Publishing at the AMS

In this article, we define what is meant when discussing “accessibility” in publishing, discuss the challenges, and provide an overview of the work being done in the AMS Publications Division to address these challenges.

The mission of the Publications Division of the AMS is twofold: to disseminate mathematical research and provide services and information of interest to the AMS membership and the worldwide mathematical community.

These are broad goals, aiming to provide access to valuable mathematics content to as wide an audience of the global mathematical community as possible, without limitations due to gender, sexual orientation, race, ethnicity, economic status, geographical location, institutional affiliation, physical disabilities, or learning differences.

Barriers to access, for both readers and authors, can be economic or technical. In order to address economic barriers, the AMS publishes a large amount of content online that is publicly accessible, introduced tiered pricing based on factors such as institution size, created the MathSciNet for Developing Countries (https://www.ams.org/news?news_id=6672) program, and participates in Research4Life (https://www.research4life.org) to bring our journal content to developing countries. AMS Journals are published using a range of open access models (https://www.ams.org/publications/journals/open-access/open-access) including Diamond, Gold, and Green, with all journal content free-to-read after five years.

Technical barriers can limit whether all users are able to effectively use the content, regardless of their physical disability or learning difference.

In the rest of this article, we will describe some of the steps the AMS is taking to provide optimal online content for all our readers and remove barriers to use.

Accessibility and Online Content

AMS Publications has long supported various programs to provide accessible content for readers with disabilities, and recently created the internal Accessibility Working Group including members from the AMS Web Working Group, Information Technology, Information Systems, Publishing Technology, Book and Journal Production, and Marketing, to coordinate these ongoing efforts. An important goal of the working group is to move from a project-based approach to incorporating these ongoing efforts into the continuous work of AMS Publications staff. AMS Publications recognizes that achieving this goal will require a long-term commitment as standards and technologies continue to evolve.

We strive to adhere as closely as possible to the Web Content Accessibility Guidelines (WCAG) of the World Wide Web Consortium (https://www.w3.org/TR/WCAG21/). These guidelines include standards for addressing a wide range of disabilities in order to improve access for the approximately 25% of people globally who have a disability 1. The guidelines are framed around the “POUR” principles: for all users, content should be Perceivable, Operable, Understandable, and Robust.

Perceivable: Content is not invisible to the senses, regardless of any assistive technology used.

Operable: User interface components and navigation must be operable by all users.

Understandable: Users must be able to understand the information as well as the interface navigation.

Robust: Content can be interpreted reliably by users, including those employing assistive technologies 2.

Bearing these guidelines in mind in our work helps us to fulfill our mission of connecting the global mathematics community and maximizing the reach of our content. Important considerations include keyboard navigation for those with mobility limitations, limiting “flashes” and auto-play video for those with seizure disorder, including video captions for those who are hearing impaired, providing clear color contrast for those with limited vision, and not relying solely on color to show meaning for those with color-blindness. Figure 1 utilizes clear color contrast, uses geometric shapes as well as color for data points in a line chart, and provides a useful legend 3.

Figure 1.

Condition numbers in the case of uniform meshes for $s=0$, $\tfrac{1}{4}$ (left) and $s=\tfrac{1}{2}$, $\tfrac{3}{4}$ (right).

Removing accessibility barriers is essential to continuously supporting engagement with mathematics. A well-documented example is the impact of inaccessible content on people with visual impairment. The Perkins School for the Blind reports that six in ten of their students who enter college will not obtain a degree, in any field 1. While there are examples of blind mathematicians throughout history, completing a higher degree in mathematics as a visually impaired student clearly requires extraordinary determination. Twenty years ago in “The World of the Blind Mathematician” published in Notices, Emmanuel Giroux pointed out “I’m often extremely frustrated because other mathematicians don’t explain what they are doing at the board and what they write.” In the same Notices piece, Lawrence Baggett discussed the challenges of conducting long division in Braille, and the lack of Braille mathematics texts, requiring him to rely on willing classmates to read to him 4.

Henrik Spoon currently serves as the Physics, Astronomy, and Mathematics Librarian at Cornell University. In 1993, he assisted a mathematician at the Space Research Organization Netherlands (SRON) by reading mathematics journal articles out loud. Spoon comments “For the assistant it is vitally important to be really focused when reading equations in the mathematical journal article. Any mistakes in spelling out the equation and starting over will make it hard for the visually impaired person to conceptualize the equation in his/her brain.”

Clearly, mathematicians dealing with disability have historically gone to great lengths, and sought out significant resources, to be able to access content and participate fully in the discipline. As content has migrated from print to digital, the challenge has shifted. This move from print to online delivery requires publishing staff and authors to think about content differently. Rather than focus on how the content will display on the printed page, consideration needs to be given for how the content is structured in order to effectively “feed” a variety of formats and assistive technologies. As Peter Krautzberger, consultant to the AMS and Invited Expert at the W3C ARIA Working Group (https://www.w3.org/groups/wg/aria), reminds us, content must be processed by a browser, then an operating system, then assistive technology. “That’s quite a complicated set of layers to actually work through,” Krautzberger points out.

Achieving accessible content in mathematics is particularly challenging due to the rendering of equations. For example, many users with visual impairment rely on screen reading technology. This can include those with mild to severe visual impairment, as well as those with learning differences such as dyslexia. While the AMS has not surveyed our audience at large, a recent survey by the American Chemical Society found that 5% of their readers use a screen reader 5. Jason Khurdan, Manager of Central Services and Ketty Ombadykow, Alternate Format Text and Assistive Technology Administrator, both of Rutgers Access and Disability Resources at Rutgers University, remind us that these challenges effect students not only studying math, but across the STEM disciplines and those taking quantitative courses in social science and other areas. They discussed the compounding challenges of providing accessible course materials for a screen reader user even for relatively simple math, with proper coding needed in the content, but also proper interaction between that coding and a range of different operating systems, browsers, and screen reading tools.

A key challenge for a screen reader user in addressing equations, according to Krautzberger, “is not that you can’t describe it, but the complexity of the description is so high that you need to be able to explore it on different levels, especially if you are doing it non-visually.”

Volker Sorge, Professor at the School of Computer Science and Chair in Document Analysis and Accessibility, University of Birmingham, and member of the MathJax (https://www.mathjax.org/) team adds “Why is it important to have specialist rendering of mathematics? Because it is quite unlike rendering usual text. Normally browsers differentiate between text and graphics. And unfortunately, math is somewhere in between. And the real problem is that the layout of a mathematical expression, or at least most mathematical expressions, is two-dimensional.”

An important step in making online content accessible is to move beyond PDF, which is—at its core—an inaccessible format. In most PDFs, the equations will render as randomly placed characters, or worse, as images, which will not be picked up effectively by a screen reader or interact with other assistive technologies.

It will not surprise the reader that the overwhelming majority of content published by the AMS is submitted as LaTeX (https://www.latex-project.org/), the most popular application of Donald E. Knuth’s TeX type-setting program. TeX continues to set the standard for high-quality output, primarily of the printed page.

However, the most accessible medium today is the collection of technologies known as the “web platform” (https://en.wikipedia.org/wiki/Web_platform), including the computer languages and application progamming interfaces (APIs) originally created to support the publication of web pages. To leverage this platform, mathematics must be converted from LaTeX to web content [or web-adjacent formats such as EPUB (https://en.wikipedia.org/wiki/EPUB)].

The AMS has supported the development of several key tools to create accessible mathematics content:

•

MathJax, which combines high-quality display of equations on the web with powerful built-in accessibility features;

•

AMS texml, which converts well-structured LaTeX documents into well-structured XML (Extensible Markup Language) (https://www.w3.org/standards/xml/core), which makes the relationship between elements explicit and consistent; and

•

The AMS HTML toolkit which builds on texml and MathJax to create high-quality, accessible web and eBook experiences.

MathJax

The core of the MathJax project is the development of its state-of-the-art, open source, JavaScript platform for the display of mathematics on the web. It provides high-quality visual and nonvisual rendering with a broad set of configuration and customization options. For well over a decade, it has proved the ideal solution for realizing formula layout in web content. Without it, we would not see high-quality rendering of mathematics online.

Together with the Society for Industrial and Applied Mathematics, the AMS was a founding sponsor of the MathJax Consortium. Although the management of the project has been reorganized under the auspices of the NumFOCUS Foundation (https://numfocus.org/), development continues today under the direction of Davide Cervone and Volker Sorge, and the AMS remains a Partner, with several AMS senior staff members serving on the steering committee.

As a continuing Partner-level sponsor, the AMS is able to benefit from MathJax improvements, but more importantly, continuous communication allows AMS developers to provide feedback to the MathJax team, as well, to support improved content.

AMS texml

AMS texml combines a powerful implementation of TeX’s programming facilities with a flexible and robust way of generating XML based on the popular Journal Article Tag Suite (JATS) (https://jats.nlm.nih.gov/). Experience has shown that AMS texml can handle the vast majority of LaTeX files submitted for publication with only minor modifications. Without this tool, it would be much more difficult to get clean output. Of course, the quality of the output depends on the quality of the input—AMS texml can only preserve existing structure, not create new structure. The AMS publishing technology staff invests considerable effort in cleaning up and enhancing submitted LaTeX files, which also benefits the creation of PDF files for both print and digital use.

The AMS has made AMS texml freely available under an open license on GitHub (https://github.com/AmerMathSoc/texml).

AMS HTML Toolkit

The AMS HTML Toolkit is an umbrella term for the in-house tools and processes that transform texml output into various forms of web content. These tools include a unique way of leveraging MathJax and its sister project, Speech-Rule-Engine (https://speechruleengine.org), which converts formulas to speech, to enrich equations.

The Toolkit is essential to the creation of full text HTML articles optimized for Notices of the AMS and to build two distinct products, AMS MathViewer and eBooks in the EPUB format.

AMS MathViewer

AMS MathViewer (https://www.ams.org/AMSMathViewer) provides an option for viewing journal articles directly in a browser, offering an interactive and accessible alternative to PDF and print reading. MathViewer articles are HTML with robust semantic markup. Equations are accessible and feature accurate, explorable descriptions. MathViewer is built with the WAI-ARIA Module (https://www.w3.org/TR/dpub-aria-1.1/#introduction), a technology for digital publishing which provides semantic metadata to help users of assistive technologies navigate through articles more easily. MathViewer is currently available on six AMS research journals with plans to roll it out on both Proceedings of the AMS and Transactions of the AMS in early 2023.

eBooks

The AMS has long worked with university disability coordinators and librarians to provide accessible electronic files and other alternative formats of our books for students and researchers who need them, having fulfilled over 120 such requests over the past 10 years, according to Erin Buck, Rights, Permissions, and Licensing Specialist at the AMS.

Recognizing the limitations of the PDF and the challenges of working with LaTeX source files, the AMS is also increasingly leveraging the Toolkit to offer eBooks in the adaptable EPUB format. An EPUB file is reflowable, meaning that it allows users to change the font and size of the text and the content will adjust. It also allows users to change the background color and supports accessible equations. From 2020 onward, titles in our best-selling Graduate Studies in Mathematics series are available in EPUB format; we have also created an EPUB version of our top-selling textbook, Partial Differential Equations, by Lawrence C. Evans. We are prioritizing our textbooks for EPUB conversion moving forward.

Contributing to the Mathematics Community

It is often pointed out that improvements made for disability purposes generally help everyone, which is certainly true for much of what has been discussed in this article. Careful use of color and contrast makes content clearer for everyone to understand. Improvements in presenting mathematics content in a range of formats increase the ability for all users to benefit from this content in the format they prefer.

In addition, this work is important to fulfilling the AMS Publications mission of providing content not only for today’s mathematics community, but we hope our efforts will support the potential mathematics community. By providing accessible content from undergraduate textbooks through research journals and the MathSciNet database, our goal is to remove barriers so that students who are inspired by studying mathematics find tools that enable them to pursue a degree and a career as future mathematicians.

As Khurdan and Ombadykow of Rutgers Assistive and Disability Resources point out, the challenge is only growing with the increased enrollments in STEM among undergraduates and in the explosion of online tools instructors employ in their courses. Students need access to not only book material, but also online visualization modules, study tools, homework, and assessments.

Through the development of the AMS HTML Toolkit, and the availability of open source tools such as AMS texml, AMS Publications has the opportunity to set a high standard for accessibility in online mathematics content.