Nemeth Braille

The Nemeth Braille Code for Mathematics and Science Notation is a Braille code for encoding mathematical and scientific notation linearly using standard six-dot Braille cells for tactile reading by the visually impaired. The code was developed by Abraham Nemeth. The Nemeth Code was first written up in 1952. It was revised in 1956, 1965, and 1972. It is an example of a compact human-readable markup language.
Nemeth Braille is just one code used to write mathematics in braille. There are many systems in use around the world.

Principles of the Nemeth Code

The Nemeth Code Book opens with the following words:
One consequence is that the braille transcriber does not need to know the underlying mathematics. The braille transcriber needs to identify the inkprint symbols and know how to render them in Nemeth Code braille. For example, if the same math symbol might have two different meanings, this would not matter; both instances would be brailled the same. This is in contrast to the International Braille Music Code, where the braille depends on the meaning of the inkprint music. Thus a knowledge of music is required to produce braille music.

Table of Nemeth braille codes

General signs

Symbol	*	,	...
Braille

Number signs

Operators

Symbol	+	-	×	·	÷	.	√	i√
Braille
Symbol	inner √	inner √	end 1st √	end 2nd √	long division	/	!	-
Braille								-

Parentheses and brackets

Symbol
Braille

Fractions

Other modifiers

Symbol	∵	∴	:	∷		″
Braille

Symbol	∞	∝	°	%	✓
Braille

Braille indicators

Symbol

Punctuation

Superscript

Subscript

Baseline

Omission

Cancel

Run Over

Directly Over

Directly Under

Beginning

Termination

Braille

Comparison signs

Symbol	⋝	⋜	⪚	⪙
Braille

Symbol	><	<>	>=<	<=>
Braille

Symbol	=	≠	≯	≮	~	≈	≅	±	∓
Braille

Geometry

Symbol	Parallel	Perpendicular	Angle	Right angle
Braille

Symbol	Arc down	Arc up	Trapezoid	Square	Rectangle	Parallelogram
Braille

Symbol	Rhombus	Isosceles trapezoid	Triangle	Right triangle	Circle	Ellipse
Braille

Arrows

Symbol	⟶	⟵	⟷
Braille

Symbol	→	⇌	⇒
Braille

Trig functions

Function	Sine	Cosine	Tangent
Braille

Function	Secant	Cosecant	Cotangent	Logarithm
Braille

Set theory

Symbol	∈	∋	∪	∩	∅
Braille

Symbol	⊂	⊃	⊆	⊇
Braille

Misc. signs

Symbol	⊕	⊗	⊡
Braille

Symbol	Intersecting lines	@	Ditto	Tally mark	+-	-+
Braille

Symbol		≃	≡	—		. dot
Braille

Polygons

Symbol	Pentagon	Hexagon	Heptagon	Octagon	Nonagon	-agon
Braille						+

Triangles

Symbol	Acute	Right	Isosceles	Obtuse	Scalene
Braille

Other signs

Symbol	Acute angle	Right angle	Obtuse angle	Hexagon star	¶	§
Braille

Symbol	ref. indicator			letter sign	composite function	det matrix	∫	∂
Braille

[Greek letters] and [Latin letters]

Greek and Latin letters are based on the assignments of International Greek Braille.

Symbol	small Latin letters	capital Latin letters	small Greek letters	capital Greek letters
Braille		+	+	+