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Silhouette of Dr. Jacob Bolotin, text reads National Federation of the Blind Bolotin Award Winner

MathCAT: Math Capable Assistive Technology

is a library that supports conversion of MathML to:

A goal of MathCAT is to be an easy to use library for screen readers and other assistive technology to use to produce high quality speech and/or braille from MathML. It is a follow-on project from MathPlayer (see below) and uses lessons learned from it to do to produce even higher quality speech, navigation, and braille. MathCAT takes advantage of some new ideas the MathML Working Group is developing to allow authors to express their intent when they use a notation. E.g., $(3, 6)$ could be a point in the plane or an open interval, or even a shorthand notation for the greatest common divisor. When that information is conveyed in the MathML, MathCAT will use it to generate more natural sounding speech.

Todo: incorporation of third party libraries to support a common subset of TeX math commands along with ASCIIMath.

Documentation for different MathCAT Users

There are many different audiences for MathCAT and each audience has different interests/needs. Please see the following documentation for details based on your needs:

Some Technical Details

MathCAT is written in Rust and can be built to interface with many languages. To date there are interfaces for:

MathCAT uses a number of heuristics that try to repair poor MathML and put it in a recommended format. For example, TeX converters and WYSIWYG editors will take “1,234+1” and break the number “1,234” apart at the comma. MathCAT recognizes that and folds the number into a single mn. Other repairs are structural such as creating mrows based on information from MathML’s operator dictionary and adding invisible function application, multiplication, addition (mixed fractions), and separators (e.g, between the $i$ and $j$ in $a_{ij}$) when it seems appropriate. This simplifies speech and Nemeth generation and may be useful to other apps. Currently the cleanup is not exposed in an API, but potentially it could be another service of MathCAT. In general, MathCAT is somewhat conservative in its repair. However, it likely will do the wrong thing in some cases, but the hope is it does the right thing much, much more frequently. Finding common mistakes of translators to MathML and patching up the poor MathML is an ongoing project.

Current Status (updated 8/14/23)

MathCAT is under active development. Initial speech, navigation, and braille (Nemeth, UEB) generation is complete and NVDA add-on now exists. It should be usable as a MathPlayer replacement for those using the English version or one of the supported translations. It is not as complete or polished in some ways as MathPlayer though. However, it supports both Nemeth and UEB technical braille generation. The Nemeth braille is substantially better than that provided by MathPlayer and other MathML → Nemeth translators. It also includes integration with navigation (uses dots 7 and 8 to indicate the navigation node). Because of the high quality braille output, BrailleBlaster uses MathCAT for braille generation from MathML.

A number of other AT are working to incorporate MathCAT into their products. Notable among these groups is Vispero/JAWS. No release date for a version of JAWS with MathCAT has been announced yet. [Other companies: if you have incorporated MathCAT into your product and would like to be mentioned here, please contact me by email or add an issue to update the documentation]

A demo to show off some of MathCAT’s features and also as an aid for debugging was developed. Visit the demo and please report any bugs you find. This demo is not how AT users will typically interact with MathCAT but does show features that AT can potentially expose to end users such as highlighting of the speech, navigation, and braille.

Timeline:

2022

2023

2024

Longer term

These plans are very tentative and will likely change based on feedback from users and AT developers. I also have commitments for working on the MathML spec, so that can also delay some of these dates.

Why MathCAT?

MathCAT is a follow-on to MathPlayer. I developed MathPlayer’s accessibility while at Design Science starting back in 2004 after I joined Design Science. At the time, MathPlayer was chiefly designed to be a C++ plugin to Internet Explorer (IE) that displayed MathML on web pages. For quite some time, it was the most complete MathML implementation available. The original work for display of math was done by Design Science’s founder Paul Topping and their chief technology officer, the late Robert Miner. Eventually, for numerous reasons, IE withdrew the interface that MathPlayer used for display and did not implement a replacement as the world was moving towards using JavaScript in the browser and not allowing security threats posed by external code. This left MathPlayer as an accessibility-only library called by other programs (chiefly NVDA). MathPlayer was proprietary, but was given away for free.

In 2016, I left Design Science. In 2017, WIRIS bought Design Science. I volunteered to add bug fixes for free to MathPlayer and initially they were supportive of that. But when it came time to do a release, a number of the people around at the time of the buyout had left and the remaining team was not interested in supporting MathPlayer. That decision was not finalized until late 2020. In 2021, I started work on a replacement to MathPlayer. As a challenge, I decided to learn Rust and did the implementation in Rust. For those not familiar with Rust, it is a low level language that is type safe and memory safe, but not automatically garbage collected or reference counted. It is often touted as a safer replacement to C/C++.

Rust is quite efficient. On a Core I7-770K machine (higher end processor circa 2017), the moderate-size expression

e 1 2 ( x μ σ ) 2

takes about 4ms to generate the ClearSpeak string “e raised to the exponent, negative 1 half times; open paren; the fraction with numerator; x minus mu; and denominator sigma; close paren squared, end exponent” along with the Nemeth braille string “⠑⠘⠤⠹⠂⠌⠆⠼⠈⠡⠷⠹⠭⠤⠨⠍⠌⠨⠎⠼⠾⠘⠘⠆”. This time is split approximately: 2ms to cleanup the MathML + 1ms for speech generation + 1ms for braille generation. This includes time to make sure all the rule files are up to date, which turns out is quite expensive. A preference can be set to turn the checks off (the file checks are mainly useful for debugging). With the check turned off, the time drops to 2.3ms.

Click to see the MathML for this expression
<math>
  <mrow>
    <msup>
      <mi>e</mi>
      <mrow>
        <mo>−</mo>
        <mfrac>
          <mn>1</mn>
          <mn>2</mn>
        </mfrac>
        <msup>
          <mrow>
            <mrow>
              <mo>(</mo>
              <mrow>
                <mfrac>
                  <mrow>
                    <mi>x</mi>
                    <mo>−</mo>
                    <mi>μ</mi>
                  </mrow>
                  <mi>σ</mi>
                </mfrac>
              </mrow>
              <mo>)</mo>
            </mrow>
          </mrow>
          <mn>2</mn>
        </msup>
      </mrow>
    </msup>
  </mrow>
</math>

MathCAT uses external rules to generate speech and braille. These take about 40ms to load; this load only happens the first time the rules are used, or if the speech style, language, or other external preference is changed. An additional 50ms are required to load the full Unicode files for speech and braille, but studies have shown that a vast majority of English K-14 math material uses a surprisingly few number of characters. Using open source math books, the initial load should cover at least 99.99% of the characters used in expressions encountered in English K-14 math textbooks.

The library is about ~3mb in size.

If you are working on an in-browser solution (i.e, you are using JavaScript or some other browser-based language), MathCAT is probably not the best tool for you (although I will probably factor the MathCATDemo into a Javascript interface which the demo is built on top of). Instead, take a look at Speech rule engine (SRE) by Volker Sorge. It is written in TypeScript and will likely meet your needs for an in-browser solution unless UEB braille is important.

Acknowledgements

Several people helped out in various ways with the project. I am very grateful for all their help!

Translators:

The initial translation of many braille characters for braille codes developed in 2024 and beyond was greatly helped by a spreadsheet given to me by Georgious Kouroupetroglou and is the work of a larger team. For more details, see:

Thanks to everyone who volunteered!

About me

I’ve been working on math accessibility since 2002. At the time, I worked on Mathematica’s WYSIWYG math editor and other UI features. Prof. John Gardner, who had lost his sight 15 years earlier, asked whether I could make the Mathematica frontend accessible. I maybe got 80% of the way there, but the company wasn’t interested in pursuing this and ultimately I left the company and the company removed the code. That was the start of my accessibility journey: one step forward, one step back, and then forward again because allowing everyone to have a chance to find the joy of math and science has given purpose to my life.

I then joined Design Science, Inc (DSI) which had an interest in making math accessible. At the time, DSI had recently developed MathPlayer, a plugin for IE6 that displayed MathML. I worked on adding features to that and with the company’s support, applied for and received an NSF grant to make MathPlayer accessible. That work was quite successful and in subsequent years I continued to add features to it. However, for security reasons, Internet Explorer removed the interface that MathPlayer depended upon. It’s tempting to say that is what doomed IE… After that, MathPlayer became an accessibility-only NVDA add-on. Further work through an IES grant with ETS refined MathPlayer’s capabilities; valuable insight was gained via user-studies funded by the grant.

For more information about what happened to MathPlayer and how MathCAT came to be, see the Why MathCAT? section.

All along, I’ve been pushing to make math work on the web and make it accessible. While at Wolfram Research, I helped get the W3C MathML effort started and have been involved with the working group ever since. I currently chair the W3C Math Working Group. I’ve been a member on several other committees over the years pushing strongly to make sure they incorporated math accessibility into their standards. Some of the these groups include NIMAS, EPUB, and PDF/UA.

I’m very honored that in 2023, the National Federation of the Blind gave me the $25,000 Jacob Bolotin award. In part, that was due to my work on MathCAT. I plan to give most of that money back to blind programmers who help out with MathCAT. MathCAT should not just be for the blind community, it should also be by the blind community. Stay tuned for details.