Scientific wealth tends to accumulate according to the law of compound interest. Every addition to knowledge of the properties of matter supplies the physical scientist with new instrumental means for discovering and interpreting phenomena of nature, which in their turn afford foundations of fresh generalisations, bringing gains of permanent value into the great storehouse of natural philosophy.

I need scarcely say that the beginning and maintenance of life on earth is absolutely and infinitely beyond the range of all sound speculation in dynamical science. The only contribution of dynamics to theoretical biology is absolute negation of automatic commencement or automatic maintenance of life.

Suppose that you could mark the molecules in a glass of water; then pour the contents of the glass into the ocean and stir the latter throughly so as to distribute the marked molecules uniformly throughout the seven seas; if then you took a glass of water anywhere out of the ocean, you would find in it about a hundred of your marked molecules.

Heavier-than-air flying machines are impossible.

We all confidently believe that there are at present, and have been from time immemorial, many worlds of life besides our own. . . . [This] may seem wild, and visionary; all I maintain is that it is not unscientific.

The fact that mathematics does such a good job of describing the Universe is a mystery that we don't understand. And a debt that we will probably never be able to repay.

Nothing can be more fatal to progress than a too confident reliance on mathematical symbols; for the student is only too apt to take the easier course, and consider the formula not the fact as the physical reality.