The Milan exchange. (Milan, Gibson County, Tenn.) 1874-1978, 1875-09-16
Zerah COIburn, the Marvellous Mathe.
matician.

/erah COlburn was the son of an
American peasant or small farmer
/ When he was not vet six years of age,
/ he surprised his father by his readiness
in multiplying numbers and solving
other simple arithme;ical problems. lie
was brought to London in 1872, when
only eight years old, and his powers
/ were tested by Francis Baiiy and other
skillful mathematicians. From Carpen-
/ ter's synopsis of the experiments thus
made the following account Is taken,
/ technical expressions being as Tar as
possible eliminated (or not used until
explained):
He would multiply any number less
/ than 10 into itself successfully nine
/ times, giving the results (by actual null
| tiplication, not from memory faster
than the person appointed to record
them could set them down. lie multi
piled into itself fifteen times, or, in
technical terms, raised it to the sixteenth
power; and the result, consisting of fif-
teen digits, was right in every figure.
| He raised some numbers of two figures
as high as the eighth power, but found
a difficulty in proceeding when the re-
suit contained great number OF tig-
ureS.
SO far there is nothing that cannot be
! explained Tor which could not, if other
/ facts did not render the explanation in
valid) by assuming that the child pos
| sessed simply the power Of multiplying
/ mentally, with extreme rapidity and cor
rcctness, but in the ordinary way. But
/ the next test removes at once all pOssi-
/ bilitv of explaining his work as done in
the ordinary manner. He was asked
what number, multiplied by itself, gave
| 1O6,929, and he answered 327,
before the original number could
/ be written down. This was Won
derful. But he next achieved a more
wonderful feat still, Judging his work by
the usual rules. He was asked what
number. multiplied twice into ITSELF
gave 268,336, I25-in other words, to
/ find the cube root of that array of dig
its; with equal facility and promptnesS
| he replied 6I5. Now, any one acquaint-
ed with the process for finding the cube
root-even with the most convenient
| form of the process, as presented by
| ColensO and others-knOwS that the
cube root of number of nine digits
could not promptly be determined, with
pen and paper, in less than three or
/ four minutes, if so soon. If the COM
puter had so perfect power Of calculat-
/ inc mentally that he could proceed rs
/ though writing down every step, and as
/ rapidly with each line rs Colburn HIM
/ self in the simple process before describ-
/ ed. he would yet need half minute at
| least to get the correct result. This,
/ too, would imply such power of men
| tally picturing sets of figures that, even
! if il explained Colburn'S S work, it would
| still be altogether marvellous, if not ut
! tcrlv ineXplicablc We know, however,
| that Colburn was not following Ordina
rv rules, but a method peculiar to him
! self. In point of fact, he was so en-
tirelv ignorant of the usual modes of
procedure, that he could not perform
on paper simple sum in multiplied
ton or division.
/ On being asked how many minutes
| there are in IS years, he answered, be
! fore the question could be written down,
/ %. .22S, 800; which is correct, if the extra
DAYS for leap years are left out of ac-
count. He Immediately after gave the
correct number of seconds.
We come next, however, to results
which appear much more surprising to
the mathematician than any of the
above. because they relate to questions
for which mathcmaticians have not been
able to provide any systematic method
Of procedure whatever. He was asked
TO name two numbers which, multiplied
together, would give the number 24I,-
4S3, and he Immediately named 941 and
| 263, which are the only two numbers
satisfying the condition. The same
problem being set with respect TO the
number III. .3gj, he named the following
pairs of numbers: and 81 ,279; and
24,4S5: 80 land 2.905: IS and 2,OG5; 30
and /. .S97: 295 and jSl; and, lastly, 4l3
aud 415. (We presume, as Mr.. BaIly
giveS the pairs in this order, that they
were so announced by Colburn. The
point is of some importance in consider
inc the explanation of the boys mental
procedure). The next feat was Il Won
derful one. He was asked to name Il
number which viii divide $685. exact
", and he Immediately replied that
there is no such number; in OtherwOrds
he recognized this number as what Is
called prime number, or a number on
" divisible by itself and by unity, just
as readily and quickly as most people
would recognize II, -, or % as such a
number, and Il great deal more quickly
than probably nine persons out OF ten
would recognize 5} or 80 aS such.
Now, if a mathematician were set
such problem, he would have no other
resource than to deal with it by direct
trial. OF course he would not try every
number from / upward to 36, ,OS3. He
would know that, if the number can be
divided at all, it must be diviSible by a
number less than 100: for any greater
divisor would 70, exactly, some smaller
, number of times into 80, ,0S3; and that
I smaller number would itself be a divisor
He would see that the number i
not even, and therefore cannot be divid
| cd bv2, 4, Is. or any even number. Tho
| number is not diviSible by 3; for, ac
+ cordinr to a well-known rule, if it were
the sum of its digits would be so diviSi
BILE: therefore he would at once dismis:
3, 9, 10, and all numbers divisible by
not already dismissed. SO with TO
D. the number does not end with 81; st
+ with Z. by trial; IL, IS, Il, and SO on
: But he would have to try many number
;. of two and three figures by actual divi
. sion before he had completed his proc
: that ,0S3 has no dvisors. Probabl.
I Qor we must confess we have not tried
. he would require about a quarter of al
y hour of calculation before he could b.
i confident that So, ,0S3 is prime number
;, Here however was child, eight year
i old, who, TO all appearance, completes
. the work Immediately the number wa
: proposed!
The next feat was of the same nature
Y but very much more difficult; indeed
e taxed the young calculator's power
: more than any other feat he accom-
+ pished. Fermat. mathematician.w VIII
d gave great attention to the theory o
;. numbers, had been led, by reasOnin!
e which need not here be considered, {
4 the conclusion that, if the number b
/ multiplied into itself 81 times Ohat Is
q raised to the thirtv-second pOwer), an