―284―

For the Literary Magazine.

on mathematical studies.

MATHEMATICIANS, in gene-
ral, regard every other tract of hu-
man pursuit as absolutely, or, at
least, comparatively, futile and nu-
gatory. If it were possible to light
upon an impartial person, with un-
questionable skill in the objects of
his animadversion, I would submit
the justice of this conclusion to him.
I should even appeal to him whether
the zeal of mathematicians arises
from any other cause than the plea-
sure which the understanding finds
in the exercise of its own powers.
Should he point out the various ap-
plications of which mathematical
truths are capable, to the ordinary
comforts of society, to facilitating
the measurement of land, the pas-
sage of the ocean, the building of
houses, and the like, I should not
think my question satisfactorily an-
swered: for, admitting the useful-
ness of mathematics to this purpose,
I am far from thinking that mathe-
matical students owe their zeal to
the contemplation of this purpose.
On the contrary, I suspect that the
ideas of abstract utility form no part
of their motives, and that their dia-
grams and symbols would be speedi-
ly abandoned, if they had no other
recommendation than their useful-
ness.

―285―

The mind is so formed as to cre-
ate, if I may so speak, its own rid-
dles, and to find the greatest ima-
ginable entertainment in solving
them. In meditating upon two
lines, some question occurs as to
their relative proportions. The
means of settling these proportions
are not obvious: at first sight it
seems impossible to find them out.
At length, after much thought, the
true expedient occurs, and the labo-
rious enquirer feels the utmost de-
light at the discovery.

If this discovery has been made
by some other, his labours are di-
rected to the finding out a different
method of attaining the same point;
and if his endeavours succeed, he is
rendered happy. If he should dis-
cover a shorter or more simple me-
thod than that of his predecessor,
his exultation is proportionably
greater, and yet the importance
which his mind annexes to the pur-
suit seems entirely the offspring of
his own fancy.

I have often been surprised at the
folly and inconsistency of studious
people. With regard to those ob-
jects to which their taste is indif-
ferent, they are irresistibly prone to
question or deny their utility. If
their own pursuit be called into
question, they think it necessary to
show some common domestic or
economic purpose to which it may
be made subservient. They, mean-
while, entirely forget that this pur-
pose formed no part of their motive
in chusing this pursuit, and that
their adversary labours at his tools
by virtue of exactly the same stimu-
lus, and in pursuit of exactly the
same end as themselves. More ac-
cident has fixed their curiosity on
different objects, and the grand se-
cret of our pleasure is in finding
what we are seeking, without any
reasoning as to further consequen-
ces.

This is true of all pursuits, but
seems particularly evident with
respect to mathematics. The plea-
sure which this science affords
seems more purely rational, more
intellectual, more divested of all in-

fluence on the fancy, the senses, or
the appetites, than any other. Plea-
sures of the latter kind are more
intelligible to the bulk of mankind,
because all have fancy, senses, and
appetites to be pleased. But those
of the mathematical student are
resolvable into those which are con-
nected with the mere exercise of
the intellectual powers of reasoning
and deduction.

This view of things has often oc-
curred to me in conversing with
mathematical enquirers. In conse-
quence of dealing in things which
exist only in abstraction, the lan-
guage of this science is more unin-
telligible than that of any other to
the unlearned apprehension. The
terms, indeed, of a geometric de-
monstration are less likely to be
understood by one who is no adept,
than a sentence of Greek and Latin
is to one not instructed in these lan-
guages. In the latter case there
are sounds somewhat allied to those
of his own tongue, and the sentence,
if a moral or historical one, relates
to objects with which he is previ-
ously acquainted; but when our
friend talks about the logarithms of
negative quantities, the sums of in-
finite series, the calculation of im-
possible quantities, the arithmetic
of infinities, and the like, he is sure
of being utterly impenetrable to all
but those versed in the same science.

I often burst upon the retirements
of a friend who is a votary of D'A-
lembert and Euler. I find him ge-
nerally wrapt in deepest meditation
over a paper, with circle and epicy-
cle scribbled o'er, of which I can
equally make nothing, whether I
examine the paper for myself, or
listen to the explanations which he
always gives me with alacrity. I
found him, the other day, wiping
his brows, and drinking a glass of
water, as after some fatiguing pil-
grimage. Enquiring from what
journey he had just returned, he
told me how many days he had been
employed, with no intervals but
those of a few minutes at meals,
and a few hours in bed, in demon-
strating a certain theorem in spheric

―286―

sections. Enquiring what it was,
he informed me, that Viviani, and
many other mathematicians, had
shown what portion of the spherical
surface was taken away when the
sphere was pierced perpendicularly
to the plane of one of its great circles,
by two cylinders, whose diameters
are equal to the radii of the sphere.
They have likewise shown, that the
portion of the spherical surface re-
maining is quadrable, and equal to
four times the square of the radius.
But, continued he, they have not
pointed out a remarkable property
in that portion of the solid of the
sphere, which remains after cutting
out a pair of such cylinders. Now,
after infinite labour, I have succeed-
ed in demonstrating, by the method
of triple integrals, that the remain-
ing portion is cubable, and is equal
to two-ninths of the cube of the
sphere's diameter.

This discovery, my friend, said I,
gives you, doubtless, as much plea-
sure as Mr. Heyne would have de-
rived from lighting on a manuscript
of Virgil, in which the half lines
which occur in the %#xc6;neid had been
drawn out to their due length by
the poet himself; or such as Daines
Barrington would have found on
recovering the original plan of Car-
diff castle; or Barthelemi from a
true series of the coins of Hiero the
Syracusan. Nay, I doubt whether
sir Joseph Banks would have been
equally delighted with a new spe-
cies of blatta, from the bay of Car-
pentaria, or count Rumford with
making a pint of good soup by
means half a farthing less expen-
sive than the mode hitherto in use
in his own cook-shops.

My friend smiled at these compa-
risons, and, as usual, pointed out,
with great solemnity and emphasis,
the superior wisdom of mathemati-
cal researches, by means of which,
among innumerable benefits, men
are enabled to build ships that shall
go through the water with the
greatest possible speed, and to erect
bridges which shall bear the great-
est possible weight without flinching:
whereas none but dreamers and

idiots would waste their time in
looking for the plan of an old castle,
from which no instruction can be
drawn in planning fortresses at pre-
sent; in searching for coins which
are of less value in the market than
the same weight of gold or copper
in the shape of a cent or an eagle;
in restoring the mutilated lines in a
ridiculous story of gods, who were
only devils in disguise, and of heroes
that deserved to be hanged. What
man of common sense, continued my
friend, would find any satisfaction in
discovering a new kind of cock-
roatch, when our domestic comfort
requires that the whole race should
be extirpated; or in compounding a
cheaper soup than turtle, since it
can only serve to multiply the num-
bers, and aggravate the idleness, of
the poor?

Bravo! my friend, cried I, I ear-
nestly advise you to sit down this
moment and write an essay to de-
monstrate that all are heretics who
do not worship Newton, and that all
language, except the language of
algebra, is no better than the chat-
ter of monkeys.

w.