If we can't express what we know in the form of numbers, we really don't know much about it.

The vortex theory [of the atom] is only a dream. Itself unproven, it can prove nothing, and any speculations founded upon it are mere dreams about dreams.

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 can never satisfy myself until I can make a mechanical model of a thing. If I can make a mechanical model, I can understand it. As long as I cannot make a mechanical model all the way through I cannot understand.

I have no satisfaction in formulas unless I feel their numerical magnitude.

Can you measure it? Can you express it in figures? Can you make a model of it? If not, your theory is apt to be based more upon imagination than upon knowledge.

[Referring to Fourier's mathematical theory of the conduction of heat] ... Fourier's great mathematical poem.