Math for blind people...

Question

What happens if some blind person want to study math? Is there some "braille alphabet" for mathematical symbols? Are there math books, at least for undergraduate students, written for blind people?

Answer 1

There exists a certain variation-or rather "enrichment"-of the Braille Alphabet, named Nemeth Braille, after its' creator, Abraham Nemeth, which is also using the standard six-dot Braille cells to create mathematical symbols.

I am not sure on whether it is exhaustive-that is, if all mathmematical expressions can be written by making use of its symbols-but I am pretty certain that is sufficient for a full undergraduate course.

This pdf file contains a full version-I believe it is the latest version-of the Nemeth Code.

As an example, of typical mathematical statements written in Nemeth Braille check this (taken from the afformentioned file):

In general, learning by audio lectures can also help, while the presence of many on-line material, such as in various youtube sources, even though they are not specifically made for the blind or visually impaired people, can be a great educational asset.

The Soviet mathematician Lev Pontryagin, mentioned in the comments, is a fine example of someone who studied and contributed greatly to mathematics while being blind since he was 14. Also, one can mention, with the danger of sounding..sacrilegeous, the example of Euler, whose productivity was not in the least affected after losing his eyesight-actually one could argue that it was increased.

Answer 2

Reading and writing mathematics is fundamentally different than reading and writing text. While Braille is adequate for the representation of text, it is not up to the task of representing mathematics. The two basic reasons for this are:

Linearity

Text is linear in nature while mathematical equations are two dimensional. What you have been reading in this text is a good example of this problem. In contrast, examine the following relatively simple equation

$$a = \sqrt{\frac{x^2 - y}{z}} $$

One will immediately notice that the equation contains a superscript and a fraction - both being two dimensional in nature. The equation could have been written in a linear form, for example:

a = sqrt(((x super 2) - y) / z)

For this relatively simple equation, a linear representation is adequate for reading to a blind user. But, with any increase in complexity it becomes apparent that linear representations are no longer useful. 

Note: Making mathematics accessible to the blind is a challenging and difficult process. The computer and its range of output devices has become the foundation of numerous projects that have brought this goal closer to a reality. With I/O devices such as high-quality speech, musical tones, refreshable Braille, haptic feedback and high reliability speech input, new and effective tools will soon be on the market. Other research into direct neural connectivity, will in the future, make the picture even brighter.