We may as well cut out group theory. That is a subject that will never be of any use in physics.

All discussion of the ultimate nature of things must necessarily be barren unless we have some extraneous standards against which to compare them.

Put three grains of sand inside a vast cathedral, and the cathedral will be more closely packed with sand than space is with stars.

Kant, discussing the various modes of perception by which the human mind apprehends nature, concluded that it is specially prone to see nature through mathematical spectacles. Just as a man wearing blue spectacles would see only a blue world, so Kant thought that, with our mental bias, we tend to see only a mathematical world.

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 universe can best be pictured as consisting of pure thought, the thought of what for want of a better word we must describe as a mathematical thinker.

The human race, whose intelligence dates back only a single tick of the astronomical clock, could hardly hope to understand so soon what it all means.