mi: ILLTSTH AT Kl) HEW
Blind Man Who is Famous as a Mathematician
"Blue Ribbon" Beer
Novi'inbr 2, 1002.
Copyright 1W2, by Henry Allston.)
TONR HUM) from his birth, tun
notwithstanding this groat hand
icap, a world-rccognizcd nutht-r-Ity
on tho so-cnlli'd hiiih'-r
mathematics, Lewis H. Carll i f
Prooklyn, is shortly to Issuo in book form
tho risult of twenty years of research over
tho most abstruse mathematical problems
ever roneeive-l by tlie mitnl of man.
This book will look like so mueh dn-ek '
or Sanskrit even to the man wivi prides
limself on his knowledge of algebra mni
geometry. When It Is Riven to the math
ematical world it will In- found that, for
the first time, many of the problems that
have defied solution since the days of th
ancient calculator who phouted "Kuroka"
n a certain memorable cecasicii have been
interpreted logically ami corn el ly by a
man whoso pupils include well known o 1
lego mat noma: leal professors and wh has
1m en consulted by tii li m i it'll t nil In Ti
tles as l'rof. Simon Newcimb.
This will be Mr. ('Mill's second book
Mis first was Issued in 11, after ten yeaiv
of study and research. It has ."f.S pages
ami is called the "Cal.ulus of Variations.'
It Is the only book of its kind extant and
has hein out of print pome years, fur llier
are not many mathematically Inclined per
sons who care to wrestle with the varia
tions, to say nothing of differential and In
tegral cab uiiH. before which the average
mind quails. The demand for the sec
ond bo.ik will bo even smaller, by
reason of the fact that it will deal exclu
sively with several Isolated points that
Mr. ("aril was unable to make clear in
his first work. "Hut now," ho said the
other day as ho sat In tho library of hi
Ilrooklyn homo, "now, after twenty
years of hard and continual work on
those most difficult of all problems, I have
solved them at last. And just think, please,
that In return for all these years of patient
and delicate research I shall not receive a
cent. My first book netted me $2 .10. Two
hundred and fifty dollars for ten years'
labor, not a cent for twice ten years' toil!
I!ut the fame ah!"
It was his desire for a reputation, limited
though it might be to a small circle, that
led Mr. Carll to take up a lino of work that
hundreds of eminent mathematicians from
Kuelid down either have seduoiisly avoided
or given up in despair as being unsolvable
by them. m
When Mr. Carll graduated from Columbia
university. In 1 STe), pressing Seth Low, now
mayor of New York, hard for first honors,
he wanted to become a teacher of the
classics. To that end ho had worked with
Infiinite patience in an institution for the
blind and all through his college course.
He first had to have someone read Greek
and Iatin to him, then he had to transcribe
the pavsagrs by means of tho point system
of writing for tho blind, then he had to
learn his lessens like any other student.
M. Carll's lessons were read to him by
a classmate, who was sent through college
by Mr. Carll's father in order that he might
be eyes to his son. Most of the reading
was done on the train while tho two stu
dents traveled between tho college and Mr.
Card's father's farm at WhitcKtone, Long
Island, tho blind student's companion being
the son of a neighboring farmer. Then in
the evening Mr. Carll would study over tho
lessons that he had taken down in the point
system of writing. On Saturdays his com
panion would read to him for six or eight
hours, and in this way Mr. Carll managed
to keep ahead of his class and do the stipu
lated amount of outside work.
After he had done all this and thoroughly
equipped himself as a elassical scholar he
could secure no pupils who were looking
forward to the degree of n. A. Instead, all
who camo to him at his father's home
wanted instruction In mathematics.
"Naturally," said Mr. Carll the other day,
"I was sorely disappointed, but I wanted
to be independent, so I taught mathematics,
In which I had never prided or distinguished
myself. As time went on more pupils came
to me; I became more Interested In mathe
matics; I studied Its branches as earnestly
and enthusiastically as I had my Latin and
Greek, which now were deserted. Pret0
soon, after I had mastered differential and
Integral calculus, I found that nobody knew
very much about calculus of variations, ex
cept that there was such a branch. Then
I said to myself, 'Why don't you find out
something about It, and perhaps, if you do.
you'll gain some fame.' So. when I could
find time between students, I struggled in
the new field. Now I am known to all
mathematicians by my works, but the gen
eral public hasn't heard much about me,
and I never expected It would. Still, I fool
that I have done what I set out to do anl
I am satisfied."
"How have I worked? How have I done
It?" A pmlle played on the speaker's gen
tle face. "Ah, It Is a long story, but If you
want to know, I'll tell you.
"Well, when I began to look up the sub
ject of calculus of variations I found, to
my amazement, that only one book on the
subject ever had been published In the Eng
lish language. It had appeared In lS.'l, and
was from the pen of Prof. John II. Jellet of
the t'nlverslty of Dublin. Put, try as hard
as I could In this country and Europe, I
could not secure a copy of It. The book
seemed to have disappeared.
"There was nothing left for rne to do ex
cept to gather my necessary working mate
rial from all sorts of sources here and
abroad, so I set to work In earnest. New
York's libraries possessed at that time
, .. ;: "v t- ?;: y TT -?'- ' " 11
w
-j JSil I ULJU1I1JLLJ 1 I IIIIIWI fl""
LEWIS H. CARLL WORKING OI
THE AID OF A SLATE FOR
scarcely any of the books that I needed In
my researches. Therefore I was compelled
to send out postal cards to the libraries at
Yale and Harvard and In Europe, asking If
they hail certain mathematical books and
Journals. When they replied in the affirma
tive I then asked for the loan of the books
and papers, the officials of Columbia uni
versity guaranteeing the libraries that I
would take good care of their precious and
rare documents. In this way I secured my
necessary working data. This took, all
told, about throe years.
"Put after I had the books, how could I
make use of them, you will ask. Well, my
brothers, and one In particular, Addison,
.were very good to mo. I trained them how
to read mathematics and once every two
or three days I'd get one of them to read
for about five minutes to mo. If tho book
win ill a foreign tongue, as often it was, I
had first to translate It. Then I'd tell him
to stop, after which I'd lock myself In my
room and while pacing up and down tho
floor think it over, arrange and rearrange
hundreds of times, and apply to the prob
lems I had in mind tho matter that had
been read to me. Sometimes it would take
me a week to secure a complete under
standing of tho few lines that I had listened
to. After I had grasped It all I would
have Addison read another short passage
and once more I'd lock myself up and think.
In this way I worked out my first book
and my second, except that In tho case of
the latter I did not have to look up ma
terial, for I had all that I needed In my
first work."
Mr. Carll paused and pointed to his sight
less eyes. "Of course, they kept me from
using pen and paper in my tasks," ho
said, "so I have had to carry every Intri
cate problem and there are hundreds of
them In my mind. One problem I turned
over in my head for three years before I
wrote it down In the point system. It
covers pages upon pages In my first book,
but as I solved It step by stop my memory
stored it away to bring it forth In all Its
completeness when at last I had the answer
and was ready to write It all down. And I
believe that, if all tho copies of my book
and the plates and tho manuscript were to
be destroyed. I could produce thi book
again by calling my memory Into service.
Once these problems get Into my head they
seem to stay there In all their minute
details.
"In such manner I produced the copy for
both my books. As the point system of
writing Is based on punctures in paper
made by a stylus and are similar to holes
made by a pin point in paper, you can
readily see how long I was about the task,
especially when you bear In mind that I
had to create in this writing all the many
different characters usi d in the "Var'a
t ions."
"Of course, after I had written down
the problems some one had to transcribe
them in ordinary writing. My brother Ad
dison wrote the first book for me; my wife
has Just finished this task with tho second.
When the proofs of my first book came
Addison read them to me and made the
corrections that I ordered. Only a half
dozen mistakes have been found In tho
book In all these years and these are mis
spelled words.
"In addition to my memory I have had
recourse to the slate for the blind.
"This slate Is a square board cut Lp
T PROPLEMS IN CALCULI'S WITH
THE BLIND.
into little sunken squares and into which
are placed type-like affairs that represent
certain figures. For instance, tho numerals
are made nlmi si wholly by the use of tho
letters T and V. In its proper position, T
repreesnts the numeral 1. Turned on Its
side and with the crossllne to the left If is
2. With the crrssline down It is 3, and with
the crossllne to tho right it Is 4. V in
Its natural position Is .1. with tho opening
to the left it Is fi. With the opening down,
7, and with the opening to the right, S.
L represents 3 and a blank type 0. There
are also characters for simple algebra, but
none higher. Therefore, I have had to do-
velop a system of my own, using the regu-
lar and few types employed by the blind,
for I could get no one to cast mo tho
various queer characters that I needed.
This system Is often complex, owing to the
fact that I have had to employ all ho
myriad characters known to algebra,
geometry, trigonometry and calculus, which
last branch Includes Greek alphabetical
characters. Here again In my work
memory plays a largo part, for It would
never do to forget the scores of names I
have given the ordinary types and tho uses
to which I have put them.
"This Is an example of how I use my
slate: I take a common algebraic char
acter and by turning It, as T and V are
turned to secure the numerals, I obtain
f 1
v TTr
i " y ;
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the eight trlgonomerlcal functions, sine,
co-sine, versed-sine, co-verse. tangent,
co-tangent, secant and co-secniit.
"It Is only on rare occasions however,
that I use the slate. 1 much prefer to
solve problems while paring my room, and
1 have to sit down when 1 work with the
late."
Here Mr. Carll raised a warning hand
"Put don't eny me my memer;, he said,
laughingly. "I fear that, for iiMn ordi
nary uses it Isn't much ned. Why, On
you know that It's a fact that I cannot
do simple problems in addition. Mibl tac
tion, multiplication and division in my
bead? When 1 want to figure up my liv
ing expeiisi s, fur Instance, 1 am compelled
to seek aid of my Mate. Strange, Isn't It?
"Neither am I a lightning calculator, as
you might be led to think from my tnathe
tnacal reputation. 1 work with pains
taking slowness from sheer inability to
grasp things mathematical quickly. 1 do
believe that my brain, when it is wrestling
with figures, moves as slowly as that of n
boy Just beginning to learn the significance
of the multiplication tables."
Mr. Carll Is going to call bis new bonk
"Afterthoughts on Calculus of Variations."
These "Afterthoughts" ileal with the tum-t
formidable problems ku.iwn In mathematics,
which also have a formidable sounding
name - isopeiiinet l ie al problems. Robin ii
of technical language, they are probloin.-
tbat have to do with equal perimeters, but
what they have to do with equal perimeters
deponent knoweth not, though bo listened
attentively to a detailed and simplified
explanation by Mr. Carll.
Although Mr. Carll gained Immediate
fame after his first book appeared, be Is
known personally to very few of the mathe
maticians. The absence of sight has kepi
him from attending the gatherings of Un
learned men of figures, but it has not pre
vented him from Instructing eminent schol
ars by mail. l'rof. Simon Newcomb, the
famous scientist and astronomer. Is repre
sentative of the men who have sal at Mr.
Carll's feel.
Mr. Carll Is a fellow at Columbia uni
versify. His friend. Mayor Low, with
whom, during college days, he was wont
to sojourn at Fritz's, a one-time famous
resort for Columbia students, secured Mr.
Carll tho fellowship In recognition of hie
work. Every year be delivers a course- of
lectures at tho university to tho mathe
matical professors, among whom are such
leaders In the educational world as Dr.
Thomas Flsk and Prof. J. H. Van Amrlnge,
head of the mathematical department. The
late Prof. William C. Peck of Columbia,
who made a big name in the college world
by compiling that stupendous mathematical
work, "Davies' Legendre," often consulted
Mr
I
j
'
'
'
Carll.
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