Analytical geometry has never existed. There are only people who do linear geometry badly, by taking coordinates, and they call this analytical geometry. Out with them!
Too cheerful a morality is a loose morality; it is appropriate only to decadent peoples and is found only among them.
Our model of the cosmos must be as inexhaustible as the cosmos. A complexity that includes not only duration but creation, not only being but becoming, not only geometry but ethics. It is not the answer we are after, but only how to ask the question.
The Holocaust changed our perception of morality not only because we discovered that morality is the only thing that can stand up to the ultimate evil, but also because it shifted the focus from society to the individual.
Rational egoism is the only morality that is for human life; thus, it is the only morality that is actually moral. Those who choose to be rationally self-interested thereby make the most of their life - and they are morally good because of it.
"Taste is not only a part and index of morality, it is the only morality. The first, and last, and closest trial question to any living creature is "What do you like?" Tell me what you like, I'll tell you what you are."
Must someone, some unseen thing, declare what is right for it to be right? I believe that my own morality - which answers only to my heart - is more sure and true than the morality of those who do right only because they fear retribution.
Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry.
There are those who believe that a new modernity demands a new morality. What they fail to consider is the harsh reality that there is no such thing as a new morality. There is only one morality . All else is immorality.
One geometry cannot be more true than another; it can only be more convenient. Geometry is not true, it is advantageous.
The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry [as did Clifford], for geometry is only a part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought.
The concept of congruence in Euclidean geometry is not exactly the same as that in non-Euclidean geometry. ..."Congruent" means in Euclidean geometry the same as "determining parallelism," a meaning which it does not have in non-Euclidean geometry.
All violence flows from the same source ... the need for power. Power is the only true morality ... the only deathless god, and the appetite for violence is its only commandment.
Morality pertains only to the sphere of man's free will - only to those actions which are open to his choice.
The only absurdity in which I find equally immense compassion and morality is Christianity - though the compassion is outlandish and the morality is blemished.
Everywhere the tendency has been to separate religion from morality, to set them in opposition even. But a religion without morality is a superstition and a curse; and anything like an adequate and complete morality without religion is impossible. The only salvation for man is in the union of the two as Christianity unites them.