The use of individual braille cells for mathematics according to the Nemeth Code

Indicators in the Nemeth Code

Dot-4 Accent (@ or `)

Either the ASCII braille or Eurobraille assignment is reasonable. This "accent" indicator is used as a prefix to indicate accented or otherwise decorated letters and symbols, such as the cent sign and dollar sign, that look like modified letters. It is also used to indicate various symbols with a modified appearance, such as indicating a square bracket as a modified parenthesis. There are several other uses including script-type indicator and superposition indicator.

Dot-5 Multipurpose Indicator (")

The assignment of this cell to the neutral double quote is arbitrary. (Note that most Braille transcribing codes don't use this neutral quote but use "smart quotes".) The Nemeth code uses the dot-5 cell as a multipurpose indicator and as a visible space to show the return to the baseline after a subscript or superscript. This is a very appropriate dot pattern for these purposes.

Dots-45 Superscript Indicator (^ or ~)

Dots-45 is Nemeth superscript indicator. This cell is represented by the caret in ASCII Braille since the caret is often used in print-based linear systems to show a superscript. The change to the use of the tilde print character for dots-45 and the subsequent use of the caret for dots-457 in Eurobraille has led to the use of dots-457 for the superscript indicator in computer braille mathematics. This use represents poor tactile mnemonics. (Cf. the dots-56 subscript indicator.)

Dot-6 Capital Indicator and Mathematical Comma (,)

The use of this indicator is context dependent. When used immediately before a letter it means the letter is a capital letter. It is also used as a generic "big" prefix for big symbols, e.g. infinity or enlarged grouping symbols. It is used after mathematical items as a comma separator. The computer braille use of the same symbol for the literary comma and the mathematical comma probably doesn't cause any problems.

Dots-46 Italics Indicator and Decimal Point (.)

The use of this indicator is context dependent. When used immediately before an alphabetic indicator, it means the letter is in italic type. When used immediately before a small or capital letter, it means the letter is in the Greek alphabet. When used after an expression following a radical sign, it is the inner radical indicator. It is also used as a generic "fancy" prefix for fancy symbols, e.g. the union is a two-symbol fancy plus sign.
Dots-46 is also used for the decimal point. The computer braille use of the same symbol for the literary period and the decimal point probably doesn't cause any problems since these are not distinguished in print.

Dots-56 Subscript Indicator; English Letter Indicator(;)

This assignment was made originally because dots-56 visually resembles a print semi-colon. This cell is the Nemeth subscript indicator and its dot pattern intentionally complements the Nemeth superscript indicator to produce good tactile mnemonics.
It is also used as the English Letter Indicator for letters preceded special typefrom indicators.
The use of dots-56 for a semi-colon punctuation mark wastes this important dot pattern and may lead to confusion with the use of dots-23 for the digit two. (The Nemeth code requires that the dots-456 Punctuation Indicator precede punctuation marks in mathematical contexts to avoid ambiguity. ) In any case, this dot pattern is a poor choice for a punctuation mark following a word since punctuation marks after words are more readable if they have one more dots in the left-hand column.

Dots-456 Boldface Indicator; Punctuation Indicator (_)

The computer braille assignment is arbitrary except for the visual mnemonic. Note that Eurobraille apparently replaces this with dots-4567 which is less easy to read tactilely. The Nemeth code uses dots-456 as a prefix indicator for bold-face type, as a German alphabetic indicator, as a Punctuation Indicator when necessary to avoid ambiguity and for several other purposes. This is an important indicator cell because its dot pattern is very recognizable.