Hi, I wanna give a brief introduction to a new feature in MathML 4 that improves accessibility by allowing authors to communicate their intent to their assistive technology.

Gonna start by talking about the past and the future.

The present is very fleeting, so I'm gonna skip that.

MathML started way back in 1998.

It was the second application of XML, approved by the w3C.

It's had variable success in terms of rendering in the browsers but the accessibility success is great.

It's supported by all the major screen readers JAWS, NVDA, VoiceOver, Orca and they support it by providing speech by providing navigation of the math expression and importantly braille on the refreshable braille display.

It's important to note that braille for math is different than the words that are spoken.

One problem though is that there's ambiguous notation in math.

So I have three expressions here.

The first one might be spoken as x raised to the nth power.

The second one might be spoken as x raised to the capital T-th power but that would be incorrect in some situations because that notation is often used for transpose.

And you wanna say the transpose of X in that notation and the last one, you probably almost never wanna say: x raised to the prime power.

Instead, you either wanna say X prime or maybe the first derivative of X.

So let's go on and let's get to the future.

Here's a page from a publisher that is a glimpse of a dystopian future.

It has no MathML and it isn't accessible.

The blurry equations are an image without all text.

So a screen reader won't say anything when it comes to it and notice that when it does read the math with the perens and the brackets towards the end, they're spoken as if they weren't there, but they are important to the meaning of the equation.

So let's take a listen to how NVDA reads this.

Testing, all intervals to the left and right of these values for F double prime X equals minus sin X minus cos X.

You find that hence F is concave downward on zero comma three PI slash four and seven PI slash four comma two PI and concave upward on three PI slash four comma seven PI slash four.

And it has points of inflection at three PI slash four comma zero and seven PI slash four comma zero.

Changing to our current timeline: Here's the same page with the last part, converted to MathML.

I'll let NVDA read the first part, and then I'll skip to the end because I want to focus on some things there.

Testing all intervals to the left and right of these values for F double prime of X equals minus sign of X minus cosine of X.

You find that F double prime of X is less than zero on open bracket zero comma the fraction with numerator three PI and denominator four close bracket.

Let's enlarge the last three lines.

So we focus on them.

Let's hear what NVDA plus math cat says for the last part.

Hence F is concave downward on open bracket zero comma three PI divided by four PI close bracket and open bracket seven PI divided by four comma two PI close bracket and concave upward on open peren three PI divided by four comma seven PI divided by four close peren and has points of inflection at open peren three PI divided by four comma zero close peren and open peren seven PI divided by four comma zero close peren dot.

Okay, now we hear that the screen reader properly reads the perens and brackets.

So the reader is getting a reasonable reading experience.

In an utopian future, we can do better.

First, a little grade school math refresher because understanding math leads to this utopian future.

The first two bits of math with brackets are closed intervals.

All the points between the values including the endpoints are part of that interval.

The next bit of math with perens is an open interval.

The endpoints are not part of that interval.

And the final two bits of math with perens are not intervals at all.

They are points in the plane and share the same notation as an open interval.

On this page, I have modified the equations with a new feature in MathML 4 that allows authors to tell assistive technology how to pronounce those bits of math.

Let's listen to NDVA with Math Cat.

Hence F is concave downward on the closed interval from zero to three PI divided by four PI and the closed interval from seven PI divided by four to two PI and concave upward on the open interval from three PI divided by four to seven PI divided by four.

And has points of inflection at the 0.3 PI divided by four comma zero and the 0.7 PI divided by four comma zero dot.

Well, what's the magic that makes that happen.

The future always involves a little magic and the magic in MathML are two attributes intent and arg So in the case of an open interval, I have an example here and I have intent equals open dash interval.

And then I provide in a little functional notation the two arguments to that.

I'm not gonna get into the details.

If you want the details, please take a look at the MathML spec, it's in a editor's edition.

I think the first public working draft should be out by the time you see this.

It's at w3c.github.io/mathml/spec.html#mixing_intent.

Also, I invite everyone to come to the MathML working group meeting on Wednesday at 9:00 AM.

We'd really like to hear questions and comments on this new proposal.

And there's another part that I up to to the MathML working group that I haven't talked about, which is the efforts on MathML core which is getting MathML in better shape for browsers.

If you want to know more about that please listen to Brian Kardell's video.

Thanks for listening.