Pure mathematics is, in its way, the poetry of logical ideas. ... [By seeking] logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.
The years of searching in the dark for a truth that one feels but cannot express, the intense desire and the alternations of confidence and misgiving until one breaks through to clarity and understanding, are known only to him who has experienced them himself.
No matter how we may single out a complex from nature...its theoretical treatment will never prove to be ultimately conclusive... I believe that this process of deepening of theory has no limits.
It would be foolish to despise tradition. But with our growing self-consciousness and increasing intelligence we must begin to control tradition and assume a critical attitude toward it, if human relations are ever to change for the better.
It followed from the special theory of relativity that mass and energy are both but different manifestations of the same thing - a somewhat unfamiliar conception for the average mind. Furthermore, the equation E = mc², in which energy is put equal to mass, multiplied by the square of the velocity of light, showed that very small amounts of mass may be converted into a very large amount of energy and vice versa.
All conditions and all circumstances in our lives are a result of a certain level of thinking. If we want to change the conditions and circumstances, we have to change the level of thinking that is responsible for it.
We are in the position of a little child entering a huge library, whose walls are covered to the ceiling with books in many different languages. The child knows that someone must have written those books. It does not know who or how. It does not understand the the languages in which they are written. The child notes a definite plan in the arrangement of the books, a mysterious order, which it does not comprehend but only dimly suspects.
If one asks the whence derives the authority of fundamental ends, since they cannot be stated and justified merely by reason, one can only answer: they exist in a healthy society as powerful traditions, which act upon the conduct and aspirations and judgments of the individuals; they are there, that is, as something living, without its being necessary to find justification for their existence.
The best that Gauss has given us was likewise an exclusive production. If he had not created his geometry of surfaces, which served Riemann as a basis, it is scarcely conceivable that anyone else would have discovered it. I do not hesitate to confess that to a certain extent a similar pleasure may be found by absorbing ourselves in questions of pure geometry.
What is the meaning of human life, or, for that matter, of the life of any creature? To know the answer to this question means to be religious. You ask: Does it make any sense, then, to pose this question? I answer: The man who regards his fellow creatures as meaningless is not merely unhappy but hardly fit for life.