It is a matter for considerable regret that Fermat, who cultivated the theory of numbers with so much success, did not leave us with the proofs of the theorems he discovered. In truth, Messrs Euler and Lagrange, who have not disdained this kind of research, have proved most of these theorems, and have even substituted extensive theories for the isolated propositions of Fermat. But there are several proofs which have resisted their efforts.
We must believe that "emotion recollected in tranquillity" is an inexact formula. For it is neither emotion, nor recollection, nor without distortion of meaning, tranquillity. It is a concentration, and a new thing resulting from the concentration of a very great number of experiences which to the practical and active person would not seem to be experiences at all; it is a concentration which does not happen consciously or of deliberation. These experiences are not "recollected" and they finally unite in an atmosphere which is "tranquil" only in that it is a passive attending upon the event.
Among civilized and thriving nations, on the contrary, though a great number of people do no labor at all, many of whom consume the produce of ten times, frequently of a hundred times more labour than the greater part of those who work; yet the produce of the whole labour of the society is so great, that all are often abundantly supplied, and a workman, even of the lowest and poorest order, if he is frugal and industrious, may enjoy a greater share of the necessaries and conveniencies of life than it is possible for any savage to acquire.
With regard to philosophical metaphysics, I always see increasing numbers who have attained to the negative goal, but as yet few who climb a few rungs backwards; one ought to look out, perhaps, over the last steps of the ladder, but not try to stand upon them.
This night I hold an old accustomed feast, Whereto I have invited many a guest, Such as I love; and you among the store, One more, most welcome, makes my number more.
The higher a man stands on the social ladder, the greater the number of people he is connected with, the more power he has over other people, the more obvious is the predestination and inevitability of his every action.
Some Socialists seem to believe that people should be numbers in a State computer. We believe they should be individuals. We are all unequal. No one, thank heavens, is like anyone else, however much the Socialists may pretend otherwise. We believe that everyone has the right to be unequal but to us every human being is equally important.
This great increase of the quantity of work which, in consequence of the division of labour, the same number of people are capable of performing, is owing to three different circumstances; first, to the increase of dexterity in every particular workman; secondly, to the saving of the time which is commonly lost in passing from one species of work to another; and lastly, to the invention of a great number of machines which facilitate and abridge labour, and enable one man to do the work of many.
If torture is going to be administered as a last resort in the ticking-bomb case, to save enormous numbers of lives, it ought to be done openly, with accountability, with approval by the president of the United States or by a Supreme Court justice.
To leave the number of births unrestricted, as is done in most states, inevitably causes poverty among the citizens, and poverty produces crime and faction.
The United States is doing our part by increasing the number of refugees we resettle and I want again to commend Angela [Merkel], and more importantly, the German people for the extraordinary leadership and compassion that you have shown in the face of what I know is a very difficult challenge.