Mathematics: One Career for the Blind
Editor's Note: Mathematics is a field which has often been considered beyond the capacity of the blind to master. This attitude continues to exist despite the evidence presented by the careers of world-class blind mathematicians such as Dr. Abraham Nemeth. In 1985 Dr. Nemeth retired, having spent forty years teaching college-level mathematics. His successful career has provided inspiration and hope to later generations of blind students interested in pursuing jobs involving mathematics.
In fact he invented the basic system for reading and writing mathematical and scientific materials in Braille which has been used by thousands of blind students. Here Dr. Nemeth tells the story of his struggle first to obtain an education in mathematics and then to obtain a position teaching it.
I was born congenitally blind, on the Lower East Side of Manhattan in New York City. And I want you to know that my parents raised me in a very close and loving family. I had a brother and a sister and two sets of grandparents and lots of aunts and uncles and cousins. We led a very happy life. And although my parents were both immigrants and lacking in any kind of formal education, they instinctively knew not to overprotect me on account of my blindness. So I became streetwise in a tough neighborhood on the Lower East Side of Manhattan at a very early age. Without knowing it, my father taught me what today would be called mobility and orientation. Whenever we walked to a familiar destination, he would take me there by a different route. As we talked, he would tell me such things as "We are now walking west, and in a moment we will be making a left turn, and then we will be walking south. We are passing a luncheonette, and after that we will be passing a bakery. Now the traffic on this street is one way going west. On the next street the traffic is one way going east, and there is a fire hydrant at the corner. Across the street there is a mailbox." So he instilled in me a very good sense of direction.
He also taught me the formation of printed letters by letting me touch the raised letters on mailboxes and on police and fire call boxes. He bought me wooden blocks with raised printed letters to play with, and he got me large rubber stamps on which I could feel the printed letters.
My elementary education began at Public School 110. Now you know that New York is such a big city that we run out of eminent people's names, so we just put numbers to the schools. The one I went to was Public School 110, which happened to be within walking distance of my home. One of my aunts walked with me every day to and from school.
In my daily activity, I attended regular classrooms with all the sighted students for general curriculum subjects like arithmetic, spelling, and reading. But when the sighted students were engaged in activities like art, penmanship, and things of that kind, I returned to the resource room for training in specific blindness skills like Braille, typing, and even geography. There was a very large globe of the world with raised land masses and even more highly raised mountain ranges. Because of family circumstances, I went to live and continue my education at the New York Jewish Guild for the Blind in Yonkers, New York. At the Yonkers Home children were encouraged (although not required) to engage in activities like music, handcrafts, light sports and athletics, and religious education after school. While I was there, my father came to visit me almost every Sunday, no matter how severe the weather was. My mother would come whenever her busy household chores would allow, about every other week, I would say. They would bring me my favorite foods, and they were refrigerated and dispensed to me during the week by kindly kitchen staff.
In the spring and summer months many of my uncles and aunts would also come to visit me. We would all go to a picnic area in a nearby park and enjoy the food they brought as well as such activity as the park provided. My father's favorite was rowing.
One of my grandfathers was particularly attentive to me, and he gave me the religious training that I now possess. He would try to find messages that would be encouraging to me and that would serve as a guide for me as a blind person. One of those messages, which has stayed with me and which has had particular impact on me during all the years that I was growing up and by which I am still guided, is: "It is better to light a candle than to curse the dark."
Now you may not believe this, but at school I experienced particular difficulty with arithmetic. I graduated from the eighth grade of PS 16 deficient in mathematics, but with my father's earnest and sincere promise to the school that he would see to it that the situation was remedied. So I enrolled in the fall at Evanderchild's High School in the Bronx, to which I was also bussed back and forth from the Yonkers Home. In one year's time, I not only caught up with all the arithmetic skills I should have had in elementary school, but I also received top grades in a first-year algebra course in which I was enrolled.
I continued to do well in all my high school courses, and during this period I became keenly aware of an ambition to be a teacher particularly, believe it or not, to teach mathematics. One of the boys at the Yonkers Home was a good friend, but he was one grade behind me in school. As I learned algebra, I shared with him my knowledge and my enthusiasm on that subject. When he entered high school a year later, he was able to pass an algebra exam with honors and was thus exempted from first-year algebra.
In due course I graduated from high school and returned to live at home with my parents and my brother and my sister, who by now had moved to Brownsville, Brooklyn.
Then it was time for me to go to college. By that time I had already acquired independent travel skills. I knew the routes of all the New York City subways and most of the Brooklyn bus lines. Equipped with this skill and with a high proficiency in Braille, I entered Brooklyn College. I knew that I wanted to major in mathematics, but my guidance counselors were not at all supportive of this goal. They insisted that mathematics was too technical a subject for a blind person, that notation was specialized, that there was no material available in Braille, that volunteer or even paid readers would be difficult to recruit, and that no employer would be likely to consider a blind person for a position related to mathematics.
Counselor after counselor told this to me. You know, my wife told me that her mother said if three people tell you that you are drunk, you better lie down. So after several counselors told me this, I obediently declared psychology to be my major, a subject more amenable to the abilities of blind people, my counselors told me.
I took as many psychology courses as I could fit into my schedule. Nevertheless, whenever there was an opening for an elective course, I always chose one from the math department. In taking these courses, there were two things that I did which were, I would say, decisive in my later career. When I found that there was no way of putting mathematical notation down in Braille, just as my counselors warned me, I began to improvise Braille symbols and methods which were both effective for my needs and consistent from one course to the next. So this was the beginning of the Nemeth Code.
The other important skill I developed was the ability to write both on paper and on the blackboard. Sometimes it was the only method I had of communicating with my math professors. And although I was certainly no calligrapher, my handwriting was perfectly adequate for these purposes, and it was surely far superior to the alternative of shouting and arm waving.
In this way I graduated from Brooklyn College in 1940 with a B.A. degree and a major in psychology. Nevertheless, I succeeded in having completed courses in analytic geometry, differential and integral calculus, some modern geometry courses, and even a course in statistics.
I knew that a BA degree in psychology was not a sufficient credential for anyone intending to enter that field professionally. So accordingly, I applied for graduate admission to Columbia University. My grades were adequate to ensure my acceptance at that prestigious institution, so in 1942 I graduated from Columbia University with an M.A. degree in psychology.
Meanwhile, it was time to begin looking for a job. The only work I could find was of an unskilled nature. At one time I worked at a sewing machine, where I did seaming and hemming on pillowcases at piecework rates. I worked for seven years at an agency for the blind, and there I counted needles for Talking Book phonograph records. I collated Talking Book records. I loaded and unloaded trucks in the shipping department. I typed letters in Braille to deaf-blind clients of the agency, transcribing incoming Braille letters from these and other clients on the typewriter. I also designed and organized itineraries in Braille so that they could be read by Helen Keller.
After graduating from Columbia University with a master's degree in hand, I began to look earnestly for work more suited to my training. The employment environment for the blind is never too hospitable, as you well know. But in those days, it was more inhospitable than it is today. In 1944 I was already married; and as time went on, my wife perceived my growing frustration. After working all day at the agency, I would find relaxation in taking an evening course in mathematics. By 1946 I had already taken all the undergraduate math courses offered by Brooklyn College, and my wife perceived that I was much happier in mathematics than in psychology. So one day she asked me if I wouldn't rather be an unemployed mathematician than an unemployed psychologist.
Well, I began to wonder how we would support ourselves if I quit my job and went to school full-time, working toward a graduate degree in mathematics. My wife suggested that I give up my job and do just that. She would go to work while I went to school. If I couldn't find work as a mathematician even after completing my training, I could always get an unskilled job like the one I was currently holding at that same skill level, she pointed out. By 1946 the war was over. Men were returning to civilian life. At Brooklyn College there was a large contingent of men who had taken a first-semester course in calculus, and now (a war later) they were returning to enroll for a second semester course in calculus. I leave it to your imagination how much of the first semester they remembered.
So I offered to be one of the volunteers in a corps that was organized to assist those men. I offered to be one of their volunteers after classes were over in the evening. Each student was stationed at one panel of a blackboard which ran clear around the room. Each wrote on the board as much of the problem as he could do, and the volunteers circulated helping the students to complete their work.
I would ask the student to read me the problem from his textbook and then read as much of the solution as he was able to put on the blackboard. Many times the blackboard panel was blank. I would do my best to show the student how to proceed. Unknown to me, I was being observed by the chairman of the math department. One Friday night I received a telegram from him. He informed me that one of his regular faculty members had taken ill and would be disabled for the remainder of the semester. He asked me to report on the following Monday evening to assume that professor's teaching load.
Over the weekend I got the textbooks, boned up to know just enough to teach the following Monday evening, and launched my teaching career.
My ability to write on the blackboard, I believe, was the difference between continuing as a mathematics teacher and finding some other work to do. I continued this way, doing part-time teaching at Brooklyn College.
In 1951 I again applied to Columbia University and was admitted as a doctoral student toward the Ph.D. degree in Mathematics. My wife went to work.
In the summer of 1953 I registered with an employment agency for teachers. I received a call from that agency to report to Manhattan College the following Monday, there to conduct a course in the mathematics of finance, a course I had neither taken nor known anything about. But anyway, I made sure I knew what to do. Manhattan College is a school run by the Christian Brothers. Brother Alfred was a little dubious when a blind man showed up, but he really had no choice. Classes began in an hour. However, when the summer course was over, Brother Alfred naturally assumed that I would return to teach in the fall, and he handed me my teaching schedule for the semester, beginning in September.
When January came, I received another call, this time from Manhattanville College to fill in for a professor who was on sabbatical. Now Manhattanville College is a very elite girls' school run by the Order of the Sacred Heart. As a matter of fact, Jacqueline Kennedy attended that school, although not in the time that I was there.
Dean Mother Brady received a glowing letter of reference from Brother Alfred, and so I had no difficulty securing the position at Manhattanville College. Commuting to Manhattanville College was an entirely different matter, however.
To do that commuting, I had to walk six blocks from home to the local BMT subway station, take the train to 14th Street in Manhattan, and change at 14th Street from the BMT to the IRT line through an intricate maze of stairs and tunnels which, however, I was already familiar with.
Then I had to take the IRT to Grand Central Station. I had to negotiate a complicated route through the New York Central Railroad, and that took me to White Plains, New York, where finally I was picked up by the school bus for the final fifteen-minute ride to the school in Purchase, New York. And of course I had to do this in reverse at the end of the day.
The Sunday before reporting to work, I went alone to Grand Central Station; and there, all day long, I practiced negotiating the route between the IRT subway station at 42nd street and the Grand Central Railroad Station. The most important landmark on that route was the New York Central Railroad Station Information Booth. Every morning I would stop at that booth and inquire on what track the 8:02 for White Plains would be leaving. It was a two-hour commute each day, and I was surely glad when the semester ended. It was time to begin to search for permanent employment. By 1954 I was becoming tired of part-time work. The search for employment is stressful for anyone, particularly for a blind person. So I embarked on a campaign of letter-writing with a view to securing permanent employment.
I consulted hundreds of college and university catalogs in the local library to determine which ones offered a math curriculum in which my teaching skills would be valuable. I arranged my choices in the order of geographical preference by section of the country. I composed a master letter, tailoring it from time to time as circumstances dictated, and I sent out about 250 letters and resumes. I felt it necessary to inform a potential employer in advance about my blindness.
Most replies were negative. They went something like: "At present we have no opening for a person with your training and experience." Many of them were noncommittal: "Thank you for inquiring about a position at our institution. We will keep your letter on file and will contact you if any opening should materialize in the future." Sound familiar?
Some were downright hostile: "We do not feel that a person with a visual impairment can effectively discharge the duties required of professors at our institution."
Nevertheless, I did receive two letters inviting me to appear for an interview: one from the University of Detroit and one from the university in Boulder, Colorado. Since, however, the University of Detroit offered a position leading to eventual permanence and tenure, I responded positively to the invitation from that institution first.
My wife and I both appeared at the university's request. I was interviewed for a full day, and at the end of the interview we were told to return home and that we would be informed of the outcome within a week. So I mentioned in passing that we were going on to Boulder, Colorado, for another interview.
The University of Detroit is a Jesuit university. The following day, early in the morning, I received a call from Father Dwier. He told me that the position was mine if I wanted it. He was calling early so that I could cancel the trip to Colorado if I so desired. I accepted on the spot.
I went to work at the University of Detroit as an instructor in 1955. And in due course I progressed through the ranks to become an assistant professor, an associate professor, and finally a full professor. Along the way I was awarded tenure, and I also completed the requirements for the Ph.D. degree in mathematics and got it from Wayne State University. I received that degree in 1964. For fifteen years I taught all kinds of courses in mathematics at the University of Detroit. But it was becoming increasingly evident to me that my training and skills would soon become obsolete unless I acquired knowledge and skill in computer science. Accordingly, I applied for, and was fortunate to receive, a grant from the National Science Foundation to spend two summers at Pennsylvania State University in State College to train in computer science.
Each session was nine weeks long, and all the students in this program were also college teachers. The pace of instruction was, to say the least, quite lively. My wife and I gave up the comfort of a nice home in Detroit to live in a dorm room for nine weeks of a hot summer during two consecutive years. These were 1968 and 1969. When I returned to the University of Detroit in the fall of 1969, I designed and implemented a graduate curriculum in computer science, and I taught most of the courses. They included elementary courses like FORTRAN and ALGOL and more advanced courses like data structures, artificial intelligence, non-arithmetic programming, automation theory, systems programming, and so on.
During my early years of studying and teaching mathematics I realized that no adequate system existed to represent complex mathematical concepts in Braille. So I set about inventing my own system. Eventually it became a very efficient tool. It worked well for me, and others who learned about it asked me to teach it to them. In 1952 my system was published as the Nemeth Code for Braille Mathematics.
The Nemeth Code features very close simulation of the printed text, and it is that feature which has made it possible for me to communicate with my students just as if I were holding the printed text in my hand. Very complicated formulas I put on cards which I arranged in a small card file in my left jacket pocket in the order in which I planned to present them. At the right moment, I casually walked up to the board and put my left hand into my pocket, read the formula from the top card, and copied it with my right hand onto the blackboard. It gave the students the impression of what a big genius I was, and I tried not to disillusion them. I have been retired ever since September of 1985. I tell my friends that looking back on my working days, I reflect that work wasn't that hard. But it took a whole day.
I believe that the experience that I have had in my lifetime demonstrates how important are the early acquisitions of Braille skills, facility in mobility, a knowledge of print practice, and good attitudes. Equipped with these skills, a blind person can progress as far as his motivation, his ingenuity, and his talent will permit. Without them, a blind person is restricted to semi-literacy and lack of independence.
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