Mathematics: One Career for the Blind
Reprinted from the Braille Monitor
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.
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
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.
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.
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.
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.
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.
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."
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
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
the weekend I got the textbooks, boned up to know just
enough to teach the following Monday evening, and launched
my teaching career.
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.
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.
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.
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.
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,
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
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.
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
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.
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
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."
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.
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.
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
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
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.
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
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.
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.