Nemeth Code is the code for mathematics and scientific notation in North America. During my years of studying and teaching mathematics, I developed a great respect for Dr. Abraham Nemeth, who had developed this braille code. He has had a very active academic career in mathematics and computer science, and he remains very active in his retirement. I was delighted that he agreed to talk with us about the background of the Nemeth Code and about himself.
Q. How did you get involved with developing the Nemeth Code?
A. I began working on my braille math code in 1946 or 1947. At that time I had a day job at the American Foundation for the Blind (AFB), and I was taking night classes in math at Brooklyn College. Boys were returning home from World War II and going back to school. Many of them had passed Calculus I before the war and were now taking Calculus II. After that long interruption they needed some extra help. There was a room with a large blackboard where volunteers helped them with their math problems. Each student stationed himself at one panel of the blackboard and wrote out the problem he wanted help with. I was one of the volunteers. I asked the student to read me the problem, and then I worked out the solution on the blackboard. I didn't find it difficult to write on the blackboard. Apparently the Chairman of the Math Department happened to observe me and was impressed. One day I received a telegram from him asking if I could replace a member of the math faculty who was ill. The telegram asked if I could start next Monday. I said yes.
When I wanted to take notes, I needed a way to write things down. At the time people used the Taylor Code from England for writing mathematics in braille. I thought that the Taylor Code used too many grouping symbols. I had already come up with rules to tell my readers how to read mathematics aloud to me. I began working on a braille code which simulated my rules for speech. For example, when you say "x to the n power," the phrase "to the" means "begin a superscript," and the word "power" means "return to the baseline." So in my braille code I created symbols that mean "begin superscript" and "return to the baseline." My personal code for braille mathematics began to evolve. I used it for my work in calculus and statistics.
Q. Before you tell us how you came to share your private braille math code with the rest of us, I'd like to know how you started taking evening math classes at Brooklyn College.
A. I was always interested in math. I went to the New York City public schools, and I spent a lot of after-school time at the Jewish Guild for the Blind. I had a good buddy there who was younger, and I showed him a lot of math. When he got to high school, he took a math placement test. The result was no surprise to me. It showed he knew a lot of algebra and could skip the first algebra class. That was the first case of advanced placement I ever heard of.
Anyway, I always liked math. But various counselors told me that I couldn't have a career in math because I was blind. I heard this from so many counselors that I believed it. After all, there's a saying, "If three people tell you that you're drunk, you'd better lay down." So I majored in psychology. I got a B.A. in psychology from Brooklyn College and an M.A. in psychology from Columbia University. But it wasn't so easy to get a job as a psychologist either. I got a job at the AFB but not as a psychologist. My first wife, Florence, who died in 1970, knew how much I loved math. She asked, "Wouldn't you rather be an unemployed mathematician than an unemployed psychologist?" So I started taking math classes at night at Brooklyn College and then got the teaching position there. I worked toward a Ph.D. in mathematics at Columbia University. I got a mathematics teaching job at the University of Detroit and finished my Ph.D. at Wayne State University in Detroit.
Q. How did your braille math code become an official code?
A. Another blind employee at AFB was Dr. Clifford Witcher, a physicist from Columbia University. One day he asked me if I had a table of integrals in braille. I said that I had one, but it was in my own private braille code. So he asked me to teach him my code. When I showed him the code, he really liked it. Dr. Witcher happened to be a member of the Mathematics Subcommittee of the Joint Uniform Type Committee. This committee, an ancestor of BANA, was responsible for braille codes in the U.S. and England (the word "Joint" for U.S. and England).
[Editor's note: A table of integrals is a long list of formulas for performing a calculus operation called integration. A table of integrals is part of the holy liturgy for calculus students, engineers, physicists, and many others.]
Q. This really brings back memories for me. When I was a freshman in college, my new friend, David Holladay, asked me if I had a table of integrals in braille. I told him that my braille calculus textbook had a table of integrals at the end. He said that he had a much better one in print and wanted to braille it for me over Christmas vacation. He asked me how the braille math code worked and spent half an hour taking one page of notes on Nemeth Code. He took my Perkins Braillewriter home over the vacation and did a really good job of brailling his favorite table of integrals.
Anyway, what happened after Dr. Witcher became a fan of your private braille math code?
A. Dr. Witcher asked me for a document proposing my braille math code to the Joint Uniform Type Committee. Various members of the Mathematics Subcommittee were supposed to write different parts of the official code. But they ended up using my proposal, with minor editorial changes, as the official code book. That was the Nemeth Code, 1952 edition. It was published by the American Printing House for the Blind (APH). In 1956 they reorganized the code book. They made a separate section at the back of the book with all the rules not needed until after tenth grade. They soon realized what a mistake that was. The whole math curriculum changed when the U.S. wanted to catch up with the Russians after the Sputnik launch in 1957. Set theory was moved into the elementary school curriculum, but the set theory symbols were at the back of the Nemeth Code rule book.
Q. If Nemeth Code was proposed to the Joint Uniform Type Committee for the U.S. and England, why don't they use Nemeth Code in England?
A. I don't know. At some point the Braille Authority, with only three members, became responsible for braille codes in just the U.S. Later they added Canada, and it became BANA (the Braille Authority of North America). I think they should add New Zealand and Australia to make it BANANA.
Q. What were the other revisions to the Nemeth Code?
A. APH published two newer editions of the official code book in 1965 and 1972.
Q. Were there any major changes in these revisions of the code book?
A. In 1965 we got rid of a rule about using two spaces to switch between text and mathematics. We also made parentheses more consistent. In 1972 the changes were noticed by transcribers but probably not by anybody else. Since 1972 there have been two addendums, for key caps (symbols for keys on a keyboard) and for ancient numeration systems.
Q. When will the Nemeth Code be finished?
A. When will mathematical notation be finished? The purpose of changes is improvement, not changes. Mathematicians are intrinsically lazy creatures. They spend years trying to find an easier way to do things.
Q. How do braille teachers, blind students, and transcribers learn Nemeth Code?
A. The official rule book is a reference book, not an instructional manual. There have been books written to teach the Nemeth Code. One was Introduction to Braille Mathematics by Bernard Krebs and Helen Roberts. The Library of Congress, National Library Service for the Blind and Physically Handicapped (NLS) adopted it as their instructional manual without sending me a copy. They had to add many correction pages. I was not happy that the name "Nemeth Code" is nowhere to be found in that book. There is another instructional book about Nemeth Code for braille teachers written by Ruth Craig. When I learned that APH was going to publish it without the name "Nemeth Code" in the title, I called my lawyer.
Anyway, Nemeth Code is part of the college curriculum for braille teachers. Blind students learn it from their braille teachers and by reading and using it. NLS certifies Nemeth Code transcribers and offers a correspondence course for those preparing for certification. Braille transcribers also have an active network through the National Braille Association (NBA) and the California Transcribers and Educators of the Visually Handicapped (CTEVH). Both of these groups conduct Nemeth Code workshops, distribute the workshop materials, and publish articles about Nemeth Code. You do not need to understand the mathematics that you are transcribing in Nemeth Code. My personal transcriber, Pearl Hartman, had not gone to college. When she talked about transcribing a topology book for me, her friend asked what topology is. She said, "I don't know. It must be very advanced because the book doesn't have any numbers in it."
Q. What have you been doing more recently?
A. I have developed a new uniform braille code. You can use one code to transcribe literary material, mathematics, and computer notation. With a uniform code, you don't have to use different braille signs in different codes for the same inkprint symbol; the braille sign for a dollar sign is always the same. You don't have to learn more than you need. If you read only literary material, you don't need to learn how mathematics is done. The main difference between literary material in my uniform code and in the current literary braille code is that numbers are done with dropped digits. I serve on the Research and Development Committee of the National Federation of the Blind (NFB), and I wrote a 20-page document in this uniform code to share with the committee. They didn't even realize until page five that they were reading a different braille code. I would like to see a uniform braille code adopted by BANA.
I have written a scientific calculator program for MS-DOS computers which is sold by the NFB. One of my current projects is writing a program in the C language for a new formatter for the Braille 'n Speak. It makes better use of space at the end of the line. If they like it at Blazie Engineering, they may use it in the Braille 'n Speak.
Q. How long have you been involved with computers?
A. For a very long time. Back in 1959 and 1960 I wrote a grade two braille translator in machine language on the IBM 650. The IBM 650 required a special room that was always cool. It took so long to warm up the machine in the morning that we said it had morning sickness. In 1976 my wife, Edna, and I went to the Soviet Union for a computer conference at the invitation of the All Russia Society for the Blind. The topic of the conference was methods of getting braille computer output.
Q. So you have witnessed many changes in the sensory aids field?
A. Yes. The Braille 'n Speak is a much more powerful computer than the IBM 650, it does not require a special room, and you don't have to wait for it to warm up.
[Editor's note: Dr. Nemeth heard this poem on a show called Chip Talk on the CBS Radio Network. We don't know who wrote it. He liked it so much that he called his local radio station, and they gave him a copy on tape. Here it is, with thanks to the unknown author:]