Front Page Titles (by Subject) 1735: XVI: ON THE USEFULNESS OF THE MATHEMATICS 1 - The Works of Benjamin Franklin, Vol. II Letters and Misc. Writings 1735-1753
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1735: XVI: ON THE USEFULNESS OF THE MATHEMATICS 1 - Benjamin Franklin, The Works of Benjamin Franklin, Vol. II Letters and Misc. Writings 1735-1753 
The Works of Benjamin Franklin, including the Private as well as the Official and Scientific Correspondence, together with the Unmutilated and Correct Version of the Autobiography, compiled and edited by John Bigelow (New York: G.P. Putnam’s Sons, 1904). The Federal Edition in 12 volumes. Vol. II (Letters and Misc. Writings 1735-1753).
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ON THE USEFULNESS OF THE MATHEMATICS1
MATHEMATICS originally signified any kind of discipline or learning, but now it is taken for that science which teaches or contemplates whatever is capable of being numbered or measured. That part of the mathematics which relates to numbers only is called arithmetic; and that which is concerned about measure in general, whether length, breadth, motion, force, &c., is called geometry.
As to the usefulness of arithmetic, it is well known that no business, commerce, trade, or employment whatsoever, even from the merchant to the shopkeeper, &c., can be managed and carried on without the assistance of numbers; for by these the trader computes the value of all sorts of goods that he dealeth in, does his business with ease and certainty, and informs himself how matters stand at any time with respect to men, money, or merchandise, to profit and loss, whether he goes forward or backward, grows richer or poorer. Neither is this science only useful to the merchant, but is reckoned the primum mobile (or first mover) of all mundane affairs in general, and is useful for all sorts and degrees of men, from the highest to the lowest.
As to the usefulness of geometry, it is as certain that no curious art or mechanic work can either be invented, improved, or performed without its assisting principles.
It is owing to this that astronomers are put into a way of making their observations, coming at the knowledge of the extent of the heavens, the duration of time, the motions, magnitudes, and distances of the heavenly bodies, their situations, positions, risings, settings, aspects, and eclipses; also the measure of seasons, of years, and of ages.
It is by the assistance of this science that geographers present to our view at once the magnitude and form of the whole earth, the vast extent of the seas, the divisions of empires, kingdoms, and provinces.
It is by the help of geometry the ingenious mariner is instructed how to guide a ship through the vast ocean, from one part of the earth to another, the nearest and safest way and in the shortest time.
By help of this science the architects take their just measures for the structure of buildings, as private houses, churches, palaces, ships, fortifications, &c.
By its help engineers conduct all their works, take the situation and plan of towns, forts, and castles, measure their distances from one another, and carry their measures into places that are only accessible of the eye.
From hence also is deduced that admirable art of drawing sun-dials on any plane howsoever situate, and for any part of the world, to point out the exact time of the day, sun’s declination, altitude, amplitude, azimuth, and other astronomical matters.
By geometry the surveyor is directed how to draw a map of any country, to divide his lands, and to lay down and plot any piece of ground, and thereby discover the area in acres, rods, and perches; the gauger is instructed how to find the capacities or solid contents of all kinds of vessels, in barrels, gallons, bushels &c.; and the measurer is furnished with rules for finding the areas and contents of superficies and solids, and casting up all manner of workmanship. All these and many more useful arts too many to be enumerated here, wholly depend upon the aforesaid sciences—viz., arithmetic and geometry.
This science is descended from the infancy of the world, the inventors of which were the first propagators of human kind, as Adam, Noah, Abraham, Moses, and divers others.
There has not been any science so much esteemed and honored as this of the mathematics, nor with so much industry and vigilance become the care of great men, and labored in by the potentates of the world,—viz., emperors, kings, princes, &c.
Mathematical demonstrations are a logic of as much or more use than that commonly learned at schools, serving to a just formation of the mind, enlarging its capacity, and strengthening it so as to render the same capable of exact reasoning, and discerning truth from falsehood in all occurrences, even subjects not mathematical. For which reason, it is said, the Egyptians, Persians, and Lacedæmonians seldom elected any new kings but such as had some knowledge in the mathematics, imagining those who had not, men of imperfect judgments and unfit to rule and govern.
Though Plato’s censure, that those who did not understand the 117th proposition of the 13th book of Euclid’s Elements ought not to be ranked amongst rational creatures, was unreasonable and unjust; yet to give a man the character of universal learning, who is destitute of a competent knowledge in the mathematics, is no less so.
The usefulness of some particular parts of the mathematics in the common affairs of human life has rendered some knowledge of them very necessary to a great part of mankind, and very convenient to all the rest that are any way conversant beyond the limits of their own particular callings.
Those whom necessity has obliged to get their bread by manual industry, where some degree of art is required to go along with it, and who have had some insight into these studies, have very often found advantages from them sufficient to reward the pains they were at in acquiring them. And whatever may have been imputed to some other studies, under the notion of insignificancy and loss of time, yet these, I believe, never caused repentance in any, except it was for their remissness in the prosecution of them.
Philosophers do generally affirm that human knowledge to be most excellent which is conversant amongst the most excellent things. What science then can there be more noble, more excellent, more useful for men, more admirably high and demonstrative, than this of the mathematics?
I shall conclude with what Plato says in the seventh book of his Republic with regard to the excellence and usefulness of geometry, being to this purpose;
“Dear friend; you see then that mathematics are necessary, because by the exactness of the method we get a habit of using our minds to the best advantage. And it is remarkable that all men being capable by nature to reason and understand the sciences, the less acute, by studying this, though useless to them in every other respect, will gain this advantage—that their minds will be improved in reasoning aright; for no study employs it more, nor makes it susceptible of attention so much; and those who we find have a mind worth cultivating ought to apply themselves to this study.”
ON TRUE HAPPINESS1
The desire of happiness in general is so natural to us that all the world are in pursuit of it; all have this one end in view, though they take such different methods to attain it, and are so much divided in their notions of it.
Evil, as evil, can never be chosen; and though evil is often the effect of our own choice, yet we never desire it but under the appearance of an imaginary good.
Many things we indulge ourselves in may be considered by us as evils, and yet be desirable; but then they are only considered as evils in their effects and consequences, not as evils at present and attended with immediate misery.
Reason represents things to us not only as they are at present, but as they are in their whole nature and tendency; passion only regards them in their former light. When this governs us we are regardless of the future, and are only affected with the present. It is impossible ever to enjoy ourselves rightly if our conduct be not such as to preserve the harmony and order of our faculties and the original frame and constitution of our minds; all true happiness, as all that is truly beautiful, can only result from order.
Whilst there is a conflict betwixt the two principles of passion and reason, we must be miserable in proportion to the struggle, and when the victory is gained and reason so far subdued as seldom to trouble us with its remonstrances, the happiness we have then is not the happiness of our rational nature, but the happiness only of the inferior and sensual part of us, and consequently a very low and imperfect happiness to what the other would have afforded us.
If we reflect upon any one passion and disposition of mind abstract from virtue, we shall soon see the disconnexion between that and true, solid happiness. It is of the very essence, for instance, of envy to be uneasy and disquieted. Pride meets with provocations and disturbances upon almost every occasion. Covetousness is ever attended with solicitude and anxiety. Ambition has its disappointments to sour us, but never the good fortune to satisfy us; its appetite grows the keener by indulgence, and all we can gratify it with at present serves but the more to inflame its insatiable desires.
The passions, by being too much conversant with earthly objects, can never fix in us a proper composure and acquiescence of mind. Nothing but an indifference to the things of this world, an entire submission to the will of Providence here, and a well-grounded expectation of happiness hereafter, can give us a true satisfactory enjoyment of ourselves. Virtue is the best guard against the many unavoidable evils incident to us; nothing better alleviates the weight of the afflictions or gives a truer relish of the blessings of human life.
What is without us has not the least connexion with happiness only so far as the preservation of our lives and health depends upon it. Health of body, though so far necessary that we cannot be perfectly happy without it, is not sufficient to make us happy of itself. Happiness springs immediately from the mind; health is but to be considered as a condition or circumstance, without which this happiness cannot be tasted pure and unabated.
Virtue is the best preservative of health, as it prescribes temperance and such a regulation of our passions as is most conducive to the well-being of the animal economy, so that it is at the same time the only true happiness of the mind and the best means of preserving the health of the body.
If our desires are to the things of this world, they are never to be satisfied. If our great view is upon those of the next, the expectation of them is an infinitely higher satisfaction than the enjoyment of those of the present.
There is no happiness then but in a virtuous and self-approving conduct. Unless our actions will bear the test of our sober judgments and reflections upon them, they are not the actions and consequently not the happiness of a rational being.
[1 ]From the Pennsylvania Gazette, October 30, 1735.
[1 ]From the Pennsylvania Gazette, November 20, 1735.