Heavier-than-air flying machines are impossible.

Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.

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.

Simplification of modes of proof is not merely an indication of advance in our knowledge of a subject, but is also the surest guarantee of readiness for farther progress.

Symmetrical equations are good in their place, but ' vector ' is a useless survival, or offshoot from quaternions, and has never been of the slightest use to any creature.

To measure is to know.

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