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.
Not all, nor even a majority, are saved. . . They are indeed many, if regarded by themselves, but they are few in comparison with the far larger number of those who shall be punished with the devil.
There's not a single shred of evidence for the multiverse. If, in order to explain this universe, you need a theory that invents an infinite number of parallel universes - that's not a very good theory.
There cannot be a nation of millionaires, and there never has been a nation of Utopian comrades; but there have been any number of nations of tolerably contented peasants.
Once you've learned to think you can't stop. And an enormous number of people devote their lives to keeping their minds busy and feel extremely uncomfortable with silence.
Far be it from us to doubt that all number is known to Him 'Whose understanding is infinite' (Ps. 147:5). The infinity of number, though there be no numbering of infinite numbers, is yet not incomprehensible by Him Whose understanding is infinite. And thus, if everything which is comprehended is defined or made finite by the comprehension of him who knows it, then all infinity is in some ineffable way made finite to God, for it is comprehensible by His knowledge.
The Hindu religion is the only of the World's great faiths dedicated to the idea that the Cosmos itself undergoes an immense, indeed an infinite, number of deaths and rebirths.
To be quite honest, numbers don't tell you everything because audience reactions differ. Some of the biggest films at the box office are not necessarily films that everyone has loved, they just opened to a good response.
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.
Once you've learned to think you can't stop. And an enormous number of people devote their lives to keeping their minds busy and feel extremely uncomfortable with silence.
The more elevated a culture, the richer its language. The number of words and their combinations depends directly on a sum of conceptions and ideas; without the latter there can be no understandings, no definitions, and, as a result, no reason to enrich a language.
You propound a complicated arithmetical problem: say cubing a number containing four digits. Give me a slate and half an hour's time, and I can produce a wrong answer.
We can learn from IBM's successful history that you don't have to have the best product to become number one. You don't even have to have a good product.