Mathematics, in its widest significance, is the development of all types of formal, necessary, deductive reasoning.
No one who achieves success does so without acknowledging the help of others. The wise and confident acknowledge this help with gratitude.
Civilization advances by extending the number of important operations which we can perform without thinking of them.
It is the business of the future to be dangerous; and it is among the merits of science that it equips the future for its duties.
In formal logic, a contradiction is the signal of defeat, but in the evolution of real knowledge it marks the first step in progress toward a victory.
The task of a university is the creation of the future, so far as rational thought and civilized modes of appreciation can affect the issue.
The total absence of humor from the Bible is one of the most singular things in all literature.
Art attracts us only by what it reveals of our most secret self.
We think in generalities, but we live in detail. To make the past live, we must perceive it in detail in addition to thinking of it in generalities.
Governments are best classified by considering who are the “somebodies” they are in fact endeavoring to satisfy.
Heaven knows what seeming nonsense may not tomorrow be demonstrated truth.
The aims of scientific thought are to see the general in the particular and the eternal in the transitory.
As society is now constituted, a literal adherence to the moral precepts scattered throughout the Gospels would mean sudden death.
I consider Christian theology to be one of the greatest disasters of the human race.
In a sense, knowledge shrinks as wisdom grows: for details are swallowed up in principles.
The ideas of Freud were popularized by people who only imperfectly understood them, who were incapable of the great effort required to grasp them in their relationship to larger truths, and who therefore assigned to them a prominence out of all proportion to their true importance.
Error is the price we pay for progress.
Wisdom alone is true ambition’s aim, wisdom is the source of virtue and of fame; obtained with labour, for mankind employed, and then, when most you share it, best enjoyed.
The vitality of thought is in adventure. Ideas won’t keep. Something must be done about them. When the idea is new, its custodians have fervor, live for it, and if need be, die for it.
I have suffered a great deal from writers who have quoted this or that sentence of mine either out of its context or in juxtaposition to some incongruous matter which quite distorted my meaning, or destroyed it altogether.
No religion can be considered in abstraction from its followers, or even from its various types of followers.