―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

finite series,

*calculation of im-*

possible quantities,the

possible quantities,

*arithmetic*

of infinities,and the like, he is sure

of infinities,

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,

―286―

sections.

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.