It is impossible not to envy the man who can dismiss reason, although we know how it must turn out at last.

All the followers of science are fully persuaded that the processes of investigation, if only pushed far enough, will give one certain solution to each question to which they can be applied.... This great law is embodied in the conception of truth and reality. The opinion which is fated to be ultimately agreed to by all who investigate is what we mean by the truth, and the object represented in this opinion is the real.

The one [the logician] studies the science of drawing conclusions, the other [the mathematician] the science which draws necessary conclusions.

Another characteristic of mathematical thought is that it can have no success where it cannot generalize.

We cannot begin with complete doubt.

Fate then is that necessity by which a certain result will surely be brought to pass according to the natural course of events however we may vary the particular circumstances which precede the event.

There is not a single truth of science upon which we ought to bet more than about a million of millions to one.