One reason why mathematics enjoys special esteem,above all other sciences,is
that its laws are absolutely certain and indisputable,while those of all
other sciences are to some extent debatable and in constant danger of being
overthrown by newly discovered facts.
It is not so very important for a person to learn facts. For that he does not really need a college. He can learn them from books. The value of an education in a liberal arts college is not learning of many facts but the training of the mind to think something that cannot be learned from textbooks.
When a man points a finger at someone else, he should remember that three of his fingers are pointing at himself. Do not worry about your difficulties in mathematics; I can assure you that mine are still greater.
Where the world ceases to be the scene of our personal hopes and wishes, where we face it as free beings admiring, asking and observing, there we enter the realm of Art and Science.
It was, of course, a lie what you read about my religious convictions, a lie which is being systematically repeated. I do not believe in a personal God and I have never denied this but have expressed it clearly. If something is in me which can be called religious then it is the unbounded admiration for the structure of the world so far as our science can reveal it.
Yes, we now have to divide up our time like that, between politics and our equations. But to me our equations are far more important, for politics are only a matter of present concern. A mathematical equation stands forever.
The really valuable thing in the pageant of human life seems to me not the political state, but the creative, sentient individual, the personality; it alone creates the noble and the sublime, while the herd as such remains dull in thought and dull in feeling.
There are few enough people with sufficient independence to see the weaknesses and follies of their contemporaries and remain themselves untouched by them.
For every one billion particles of antimatter there were one billion and one particles of matter. And when the mutual annihilation was complete, one billionth remained - and that's our present universe.
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.
That a man can take pleasure in marching in formation to the strains of a band is enough to make me despise him. He has only been given his big brain by mistake; a backbone was all he needed.
Then there are the fanatical atheists whose intolerance is of the same kind as the intolerance of the religious fanatics and comes from the same source.
The ideals which have lighted my way, and time after time have given me new courage to face life cheerfully, have been Kindness, Beauty, and Truth. Without the sense of kinship with men of like mind, without the occupation with the objective world, the eternally unattainable in the field of art and scientific endeavors, life would have seemed to the empty. The trite objects of human efforts — possessions, outward success, luxury—have always seemed to me contemptible.