...nature seems very conversant with the rules of pure mathematics, as our own mathematicians have formulated them in their studies, out of their own inner consciousness and without drawing to any appreciable extent on their experience of the outer world.

Science should leave off making pronouncements: the river of knowledge has too often turned back on itself.

To travel hopefully is better than to arrive.

The plain fact is that there are no conclusions. If we must state a conclusion, it would be that many of the former conclusions of the nineteenth-century science on philosophical questions are once again in the melting-pot.

The essential fact is that all the pictures which science now draws of nature, and which alone seem capable of according with observational facts, are mathematical pictures.

In real science a hypothesis can never be proved true...A science which confines itself to correlating phenomena can never learn anything about the reality underlying the phenomena, while a science which goes further than this and introduces hypotheses about reality, can never acquire certain knowledge of a positive kind about reality; in whatever way we proceed, this is forever denied us.

The stream of knowledge is heading towards a non-mechanical reality; the universe begins to look more like a great thought than like a machine. Mind no longer appears to be an accidental intruder into the realm of matter...we ought rather hail it as the creator and governor of the realm of matter.