Nemeth Braille Code

The Nemeth Braille Code for Mathematics and Science Notation — usually just called the Nemeth Code or Nemeth Braille — is a Braille code for writing mathematics and science in standard six-dot braille cells. It lets a reader who is blind work through arithmetic, algebra, geometry, trigonometry, calculus, and modern mathematics up to research level, all rendered linearly in tactile form.^[1] It was invented by the blind mathematician Abraham Nemeth for his own use while he took evening mathematics classes, and it became the official mathematics braille of the United States — and later Canada and New Zealand — carrying the name of its inventor ever since.^[2]

The inventor

Abraham Nemeth was born on October 16, 1918, in New York City, to Jewish immigrant parents, and grew up on the Lower East Side. He was blind from infancy and attended regular New York public schools as a totally blind child — at a time when most blind children were steered into basket-weaving and chair-caning, not academics.^[4]

He earned a B.A. in psychology from Brooklyn College in 1940 and an M.A. in psychology from Columbia University in 1942.^[5] His real love was mathematics, but advisors and the vocational system counseled him into psychology on the assumption that a blind person could not be a mathematician — there was simply no practical way for him to read or write mathematical notation.^[6]

While working at the American Foundation for the Blind and taking night courses in mathematics and physics at Brooklyn College, Nemeth began building a private braille notation for the symbols his textbooks could not show him.^[7] That private notation grew into the code that now bears his name.

He later joined the University of Detroit as a mathematics instructor in 1955, rising to full professor in 1976 and serving thirty years on the faculty; he earned his Ph.D. in mathematics from Wayne State University in 1964.^[8] He taught, among other things, Fortran, assembly language, automata theory, and numerical analysis — and remained an active Federationist, Hebrew scholar, and musician. He died on October 2, 2013, in Southfield, Michigan, aged 94, of congestive heart failure, two weeks short of his ninety-fifth birthday.^[9]

Why it was needed

Braille is a six-dot code that is excellent for writing words but was, for most of its history, poor at mathematics. A mathematics textbook is full of superscripts, fractions, radicals, matrices, and special symbols — spatial, two-dimensional notation that does not survive being flattened into a line of dots. Blind students who wanted to study science had to rely on sighted readers, and had no precise way to write their own work.

Nemeth's insight was that mathematics could be encoded linearly and unambiguously using the same six-dot cells as ordinary braille, by reusing and combining cells in disciplined ways. A fraction, a power, a limit, an integral — each got a definite tactile spelling.^[11]

Development and adoption

Nemeth dated the beginning of his code to 1946 or 1947, while he was taking night classes and working at the American Foundation for the Blind.^[12]

The code became official through the Joint Uniform Braille Committee, the mid-century forerunner of today's Braille Authority of North America (BANA). Cliff Witcher, a member of that committee's Mathematics Subcommittee, asked Nemeth to write up his proposal. According to the American Foundation for the Blind, Nemeth presented his code one morning in 1951, and that afternoon it was adopted unanimously.^[13]

The first official code book — The Nemeth Code, 1952 edition — was published by the American Printing House for the Blind in 1952, assembled from Nemeth's own proposal with only minor editorial changes.^[7]

In 1956 the code book was reorganized; the rules not needed until after tenth grade were moved into a separate section at the back — a decision Nemeth later recalled as a mistake.^[7]

The code was subsequently revised in 1965 and again in 1972. The Nemeth Code for Mathematics and Science Notation, 1972 Revision became the standard edition — the one generations of students learned — and is the version named in BANA's later resolutions.^[14]

The code itself

The Nemeth Code covers essentially all of technical literature in six-dot braille:^[15]

• Arithmetic, including column arithmetic with carrying and borrowing, and long division
• Algebra
• Geometry (notation, though not the drawing of figures)
• Trigonometry
• Calculus
• Modern mathematics up to the research level

Its defining feature is linearity: a two-dimensional expression such as a fraction is read and written as an unambiguous one-dimensional string of cells. Digits get their own dedicated shapes — the literary a–j patterns dropped one row — so a numeral can never be mistaken for a letter. This is what made it possible for a blind student to write mathematics, not merely listen to it.^[16]

The UEB transition

In November 2012, the United States members of BANA voted to adopt Unified English Braille (UEB) to replace the older English Braille American Edition (EBAE) for literary text — while maintaining the Nemeth Code for mathematics and science, along with the Music Braille Code and the IPA Braille Code.^[17]

BANA set January 4, 2016 — Louis Braille's birthday — as the implementation date. As of that date, the official codes for the United States are UEB, Nemeth, Music, and IPA.^[18]

Because the literary text surrounding mathematics moved from EBAE to UEB, BANA issued formal guidance for switching between UEB and Nemeth within a single document, so that mathematics could continue to be transcribed in Nemeth inside UEB text.^[19] In September 2020 BANA clarified the terminology: technical material can be transcribed either in UEB ("UEB Math/Science") or in Nemeth ("UEB with Nemeth"), and the choice is made per reader.^[20]

Modern Nemeth

In 2022 BANA published The Nemeth Braille Code for Mathematics and Science Notation 2022, a modernized edition that clarifies existing rules and newly adopted rules for using Nemeth within UEB, with an errata sheet issued afterward.^[21]

The code remains governed by BANA and in active use across the United States and Canada, and it is used in New Zealand as well.^[22]

Timeline

Sources

1. Abraham Nemeth, interviewed by Caryn Navy, "The History of the Nemeth Code," Future Reflections (National Federation of the Blind), reprinted from Raised Dot Computing Newsletter — nfb.org/history-nemeth-code-interview-dr-abraham-nemeth
2. "Dr. Abraham Nemeth: The Louis Braille of Mathematics Dies at Age 94," AccessWorld, American Foundation for the Blind (November 2013) — afb.org/aw/14/11/15736
3. William Yardley, "Abraham Nemeth, Creator of a Braille Code for Math, Is Dead at 94," The New York Times (October 6, 2013)
4. "Nemeth, Abraham, Dr.," University Honors, University of Detroit Mercy Libraries
5. "Abraham Nemeth," Hall of Fame, American Printing House for the Blind — sites.aph.org/hall/inductees/nemeth/
6. Matt Schudel, "Abraham Nemeth, 94, developer of Braille math code, dies," The Washington Post (October 5, 2013)
7. "Braille World Loses a Legend," press release, Braille Authority of North America (October 3, 2013)
8. "What is MathSpeak?," DO-IT, University of Washington — doit.uw.edu/knowledge-base/what-is-mathspeak/
9. "The Abraham Nemeth Equation," Science / AAAS
10. "Nemeth Code," Braille Authority of North America — brailleauthority.org/nemeth-code
11. "What is Nemeth Code?," DO-IT, University of Washington — doit.uw.edu/knowledge-base/what-is-nemeth-code
12. "Implementation of Unified English Braille (UEB)," Braille Authority of North America (statement approved November 9, 2014)
13. "Braille and Talking-Book Program Embraces New Braille Code," Library of Congress, National Library Service (January 16, 2015)
14. "Nemeth-UEB Guidance," Braille Authority of North America
15. "Terminology: UEB Math/Science and UEB with Nemeth," Braille Authority of North America (adopted September 2020)

See also

• Abraham Nemeth
• Braille
• Louis Braille
• Unified English Braille
• MathSpeak
• Braille Authority of North America