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THE BOOK OF ZERAH COLBURN

Part One, Chapter One

SOURCE:
*Journal of Natural Philosophy, Chemistry, and the Arts 34*, 5
[1813].

The words of the anonymous author are in **bold**.

**
**

**
(The present article is copied from a printed paper, which I
**[*presumably
William Nicholson, editor of the journal*]**
obtained from Messrs. Johnson and Co., booksellers, in St. Paul's
Church-yard. This boy has been publicly exhibited in America
and in London, and some time ago subscriptions were solicited
for placing him to be educated under the inspection and care of
several mathematical gentlemen : but I have been informed,
that the plan was relinquished, from some reasons on the part
of his father ; and he is again to be seen by the public. A
subscription is now solicited for publishing a portrait of him
on the following terms) :
**

**
ZERAH COLBURN, a child just eight years of age,
without any previous knowledge of the common rules of
arithmetic, or even of the use and power of the Arabic numerals,
and without having given any particular attention to the subject,
possesses (as if by intuition) the singular faculty of solving a
great variety of arithmetical questions by the mere operation of
the mind, and without the usual assistance of any visible symbol
or contrivance.
**

**
This print will be engraved from a drawing by Mr. Trumbull ;
and the size of it will be about 12 inches by 10.
**

**
The price to subscribers will be One Guinea, to be paid at
the time of subscribing : and the plates will be delivered
according to the order of subscription.
**

**
The following gentlemen (who are well acquainted with the
extraordinary abilities of this child) have kindly undertaken to
attend to the progress and execution of the work, and to see to
the distribution of the plates, viz.
**

**Sir James Mackintosh**[*social scientist and political reformer*]**Dr. W. H. Wollaston, Sec. R. S.**[*discoverer of palladium and rhodium*]**William Vaughan, Esq.**[*scientifically-inclined merchant who re-engineered and modernised the port of London*]**John Bonnycastle, Esq., Math. Prof.**[*at the Royal Military Academy*]**Francis Wakefield, Esq.**[*probably the Nottinghamshire merchant and philanthropist who assisted Coleridge*]**William Allen, Esq., F. R. S., F. L. S**[*Quaker scientist and abolitionist*]**John Guillemard, Esq., F. R. S., F. Amer. S.**[*scientist remembered chiefly as a member of the commission that tried to settle international financial disputes caused by the American Revolution*]- Samuel Parker, Esq.
**Francis Bailey, Esq.**[*probably Francis Baily, the astronomer remembered today for having noticed the dramatic highlighting of mountains on the limb of the Moon during a solar eclipse.*]

**
**[*If I have identified them correctly,
these men all belonged to the same social set,
which also included the Wedgwoods, the
Darwins, and Charles Babbage.
Most if not all
of them were what Gibson and Sterling have
called "Industrial Radicals", pro-science
Romantics who hoped that technological
advances would lead to deep social changes
and the collapse of the old order.*]**
**

**
Subscriptions are received by either of the above gentlemen,
or by Messrs. Johnson and Co., No. 72, St. Paul's churchyard :
and printed receipts will be given for the same, which must be
produced and given up at the time the plates are delivered.
**

**
Zerah Colburn is at present to be seen at the Exhibition
Rooms, Spring Gardens. Many persons of the first eminence
for their knowledge in mathematics, and well known for their
philosophical inquiries, have made a point of visiting him : and
they have all been struck with astonishment at his extraordinary
powers. It is correctly true, as stated of him, that --
**

**
" He will
not only determine, with the greatest facility and dispatch, the
exact number of minutes or seconds in any given period of time;
but will also solve any other question of a similar kind.
**

**
" He will tell the exact product arising from the multiplication of
any number, consisting of two, three, or four figures, by any
other number consisting of the like number of figures.
**

**
" Or, any number, consisting of six or seven places of figures,
being proposed, he will determine, with equal expedition and
ease, all the factors of which it is composed.
**

**
" This singular
faculty consequently extends not only to the raising of powers,
but also to the extraction of the square and
cube roots of the
number proposed ; and likewise to the means of determining
whether it be a prime number (or a number incapable of
division by any other number) ; for which case there does not
exist, at present, any general rule amongst mathematicians."
**

**
All these, and a variety of other questions connected therewith,
are answered by this child with such promptness
and accuracy
(and in the midst of his juvenile pursuits) as to astonish every
person who has visited him.
**

**
At a meeting of his friends, which was held for the purpose
of concerting the best method of promoting the views of the
father respecting his education, this child undertook, and
completely succeeded in, raising the number 8 progressively
up to the sixteenth power : and in naming the last result, viz.
281,474,976,710,656, he was right in every figure.
**

**
He was then tried as to other numbers, consisting of one figure ; all of which
he raised (by actual multiplication and not by memory) as high
as the tenth power : with so much facility and dispatch, that the
person appointed to take down the results was obliged to
enjoin him not to be so rapid.
**

**
With respect to numbers consisting of two figures, he would raise
some of them to the sixth,
seventh, and eighth power ; but not always with equal facility :
for the larger the products became, the more difficult he found
it to proceed.
**

**
He was asked the square root of 106,929, and
before the number could be written down, he immediately
answered 327. He was then required to name the cube root of
268,336,125, and with equal facility and promptness he replied
645. Various other questions of a similar nature, respecting
the roots and powers of very high numbers, were proposed by
several of the gentlemen present, to all of which he answered in
a similar manner.
**

**
One of the party requested him to name the
factors which produced the number 247,483, which he
immediately did by mentioning the two numbers 941 and 263 ; which
indeed are the only two numbers that will produce it.
Another of them proposed 171,395, and he named the following
factors as the only ones that would produce it ; viz. 5 × 34,279 ;
7 × 24,485 ; 59 × 2,905 ; 83 × 2,065 ;
35 × 4,897 ;
295 × 581 ; and
413 × 415.
**

**
He was then asked to give the factors of 36,083 ;
but he immediately replied that it had none ; which in fact was
the case, as 36,083 is a prime number.
Other numbers were
indiscriminately proposed to him, and he always succeeded in
giving the correct factors, except in the case of prime numbers,
which he discovered almost as soon as proposed.
**

**
It had been asserted and maintained by the French mathematicians,
that 4,294,967,297 ( = 1 + 2 ^{32}) was a
prime number: but the celebrated Euler detected that
errour by discovering, that it was equal to
6,700,417 × 641. The same number was proposed to this child, who
found out the factors by the mere operation of his mind.
**

**
One of the
gentlemen asked him how many
minutes there were in forty-eight years ;
and before the question could be written down, he
replied 25,228,800 ; and instantly added, that the number of
seconds in the same period was 1,513,728,000. Various
questions of the like kind were put to him ; and to all of them he
answered with nearly equal facility and promptitude ; so as to
astonish every one present, and to excite a desire that so
extraordinary a faculty should (if possible) be rendered more
extensive and useful.
**

**
It was the wish of the gentlemen present to obtain a
knowledge of the method by which the child was enabled to answer,
with so much facility and correctness, the questions thus put to
him : but to all their inquiries upon this subject (and he was
closely examined upon this point) he was unable to give
them any information. He positively declared (and every
observation that was made seemed to justify the assertion) that
he did not know how the answers came into his mind.
**

**
In the
act of multiplying two numbers together, and in the raising of
powers, it was evident (not only from the motion of his lips,
but also from some singular facts which afterward occurred,)
that some operation was going forward in his mind ; yet that
could not (from the readiness with which the answers were
furnished) be at all allied to the usual mode of proceeding with
such subjects : and moreover, he is entirely ignorant of the
common rules of arithmetic, and cannot perform, upon paper,
a simple sum in multiplication or division.
**

**
But, in the extraction
of roots and in mentioning the factors of high numbers it
does not appear that any operation can take place ; since he will
give the answer immediately, or in a very few
seconds, where it
would require, according to the ordinary method of solution, a
very difficult and laborious calculation : and moreover, the knowledge
of a prime number cannot be obtained by any
known rule.
**

**
It may naturally be expected, that these wonderful talents,
which are so conspicuous at this early age, will by a suitable
education be considerably improved
and extended ; and that some
new light will eventually be thrown upon those subjects, for the
elucidation of which his mind appears to be peculiarly formed
by nature, since he enters into the world with all those powers
and faculties, which are not even attainable by the most eminent
at a more advanced period of life.
**

**
Every mathematician must
be aware of the important advantages, which have sometimes
been derived from the most simple and trifling circumstances ;
the full effect of which has not always been evident at first
sight. To mention one singular instance of this kind : The
very simple improvement of expressing the powers and roots
of quantities by means of indices introduced a new and general
arithmetic of exponents ; and this algorithm of powers led the
way to the invention of logarithms, by means of which all
arithmetical computations are so much facilitated and abridged.
**

**
Perhaps this child possesses a knowledge of some more important
properties connected with this subject ; and although he is
incapable at present of giving any satisfactory account of the
state of his mind, or of communicating to others the
knowledge which it is so evident he does possess, yet there is every
reason to believe, that, when his mind is more cultivated and his
ideas more expanded, he will be able not only to divulge the
mode by which he at present operates, but also point out some
new sources of information on this interesting subject.
**

**
The profits of the present print will be given to the father of
this child, in order to enable him to provide a more suitable
education for his son : and it is hoped that the friends of science,
and the public in general, will promote a plan, which promises
to be attended with such advantages.
**

[*The portrait of Colburn promoted by the above circular, if it
was ever created, does not survive.
*

*
Readers may be puzzled by the statement *"It had been asserted
and maintained by the French mathematicians,
that 4,294,967,297 was a prime ..."*Why was this
particular number of interest?
*

*
"Generalised Fermat numbers" are numbers of the form
*

where

*
Despite this disappointment, the Fermat numbers have remained of enormous interest
to number theorists for four centuries both because of their many strange and unexpected
properties -- for example, Gauss showed that a regular polygon can only be
inscribed in a circle by ruler-and-compass construction if the number of its sides
is a power of two times a product of Fermat primes! -- and because some
unusually simple tests exist to determine whether they are prime without actually
factoring them. The latter feature has been exploited in the modern quest for
large prime numbers, a subject which is suddenly of great practical importance in
the Information Age. Interested readers should consult Chris Caldwell's
excellent website
The Prime Glossary.*]

- Next Chapter:
*Upon certain ready Processes for Computation, supposed to have been invented by the American Boy exhibited in London* - Table of Contents