# Is there a definitive guide to speaking mathematics?

Is there a definitive guide to speaking mathematics to avoid ambiguity? I'm writing a program to generate text for a variety of mathematical expressions and would like to code it so that it adheres to some standard. I've found Handbook for Spoken Mathematics, but nothing better. Before settling on this one source, I thought I'd ask this mathematics community.

• I've always had a hard time describing mathematical stuff over the telephone... Apr 27, 2011 at 19:35
• +1 Don't have an answer for you, but thanks for this intriguing question. The source you quoted at least is a start. I found another one you might find helpful. cs.berkeley.edu/~fateman/papers/speakmath.pdf Apr 27, 2011 at 20:27
• I think you need to be more specific. I for one, don't understand what the text would look like or what sort of standard you are thinking of. Apr 28, 2011 at 1:42
• Imagine teaching mathematics to blind students. You'll need to be concise and clear. So, a + b = c is read as "a plus b equals c". a + b / c = d becomes "a plus b divided by c equals d" You'll need to be considerate of differences in how you would write and read to avoid ambiguity. For example, you wouldn't normally write the following in long form (a + b)/c = d, but it may be the best way to communicate the statement to a blind person. "open parenthesis a plus b close parenthesis divided by c equals d" or maybe say "a plus b all of that over c equals d" May 2, 2011 at 14:55
• Very nice question @Michael and very nice idea for a program! If you can come up with something, this will greatly help a lot of people! Greets May 2, 2011 at 15:38

First of all, thanks, Michael, for a great question! And framing it in terms of "imagine teaching mathematics to blind students..." helps us to recognize issues of math accessibility, in this case, accessibility to the visually impaired. You've helped me to educate myself, a bit: for example, whereas written mathematics depends extensively on "2-D" representation: subscripts, exponents, radicals, (the list goes on and on: vector representation...just think of matrices!) -- traditional braille is "linear", not amenable to such usage.

I came across a fabulous survey article, with an abundant bibliography, that may be of interest:

I found it fascinating, and eye-opening: recognizing some of the key obstacles that the visually impaired (and those engaged in teaching such students) confront with respect to accessing mathematics. The first part of the article addresses efforts to transform/modify braille (and to translate from, e.g., LaTeX or ML, to modified braille). The second part of the paper addresses "Dynamic" efforts to make math more accessible, e.g., ways to enable teachers to engage directly with visually impaired students, rather than only indirectly, by translating text to braille. Here is where "spoken math" comes in. There is research comparing the efficacy of alternative modes of speaking math (extra terms: explicit reference to parentheses, symbols, etc.) with variations in parsing (use of pauses, intonation, amplification, etc). And (interestingly), the insertion of additional technical terms ("open parentheses, a plus b, close parentheses") multiplied by 4", was found by at least one researcher to be less effective, in terms of comprehension, that parsing speech appropriately, pausing, e.g., before and after "a + b", using emphasis, ...

I haven't read all of the research, but it may very well examine the use of some combination of these approaches, as well. (See, e.g.)

1. Fitzpatrick, D. (2002). Speaking technical documents: using prosody to convey textual and mathematical material. International Conference on Computers Helping People (ICCHP), Springer Verlag, pp. 494-501.

2. Fitzpatrick, D. (2006). Mathematics: how and what to speak. International Conference on Computers Helping People (ICCHP), Springer Verlag, pp. 1199-1206.

The ultimate question will be whether the mathematics community, at large, will be receptive to accepting, or at least endorsing, the many valiant efforts of those dedicated to making mathematics accessible to ALL by adopting a standard for speaking mathematics. Indeed, information like this could be important to ALL students of mathematics.

Perhaps you are already familiar with much of this work. If I find anything more, I'll be sure to let you know.

I did find a few more interesting resources, including some references and links:

In the above article, mention is made of the research and work by T.V. Raman, who himself is blind but has worked extensively to develop text to speech programming.

Also see Raman's "publications" page:

http://www.cs.cornell.edu/info/people/raman/publications/

Finally, this is one particular work of Raman, autobiographical, that is quite inspiring!:

http://emacspeak.sourceforge.net/raman/publications/thinking-of-math/thinking-of-math.pdf

I don't have a reference for a definitive guide, but like the other answerers, I would encourage you to pursue the blind mathematics student program, and take this as your guide as to the best pronunciation of mathematical text.

When I was a graduate student at UC Berkeley, there were several graduate students in the mathematics program who were blind, whom I found to be very impressive in terms of mathematical sophistication; they made enormous contributions to the class discussion in terms of mathematical ideas and insight, and I was always amazed at their mathematical ability, despite what I personally would find to be a debilitating handicap.

I was employed for a time by the disabled students office to read various mathematics notes into a recording device, which several of these blind students used to study from. I was charged with the task of reading my lecture notes into a recording device, which the various blind students would listen to. They had special tape recorders that could replay the sounds at higher than normal speed---listening to an hour lecture in ten minutes---and this is how they used the recordings, a high-pitched squeal of my reading the mathematical notes. I came to realize that they would listen to these notes at basically the same speed that most people would read text, which is of course a much higher speed than a normal speaking speed. But it was comical to listen to the students studying, since they would listen to me say

"Theorem.Everycountabledenselinearorderwithoutendpointsisisomorphic totherationalline.Proof.Letopenanglebracketblackboardbold$\mathbb{P}$commalessthancloseanglebracket beacountabledenselinearorderwithoutendpoints..."

and so on, at ridiculously high speed, while understanding everything. They would sometimes ask me questions, and play back the tape at high speed, but I would find it difficult to understand except at normal speed.

Through this work, I came to realize how one must speak mathematics for blind students, and I believe that this is the actual answer to your question. The key to reading for blind students was to describe the fonts and logical structure of the expressions in the text as precisely as possible. Thus, $F(f(n))+I(N_i)$ would be pronounced, "upper F of the quantity lower f of n the quantity, plus upper I of the quantity upper N sub lower i" and $\mathbb{Q}(\sqrt{n^3})_k$ would be, "blackboard bold Q open paren square root the quantity lower $n$ cubed the quantity close paren sub lower k". When I failed to describe a question precisely, by failing to say "upper A" instead of "a", for example, I would get questions back from the blind students about what was actually meant, when they found it ambiguous.

So I would encourage you to contact various blind mathematicians and inquire with them what policies and guidelines they recommend.

• This is a wonderful answer, Dr. Hamkins. I can only imagine what a fascinating experience it would be to work with colleagues like that. I bet they approach mathematics in some very interesting ways.
– 000
Dec 31, 2012 at 23:24

Mathematica has functionality to convert mathematical expressions to text. Take a look at the documentation of the SpokenString function. If you need actual speech generation, look at the Speak function.