Fourier is a mathematical poem.
When you measure what you are speaking about and express it in numbers, you know something about it, but when you cannot express it in numbers your knowledge about is of a meagre and unsatisfactory kind.
Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherialization of common sense.
I am never content until I have constructed a mechanical model of what I am studying. If I succeed in making one, I understand; otherwise I do not.
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.
Presidential address to British Association 1871
Heavier-than-air flying machines are impossible.
(Speaking in 1895)
I have not the smallest molecule of faith in aerial navigation other than ballooning, or of the expectation of good results from any of the trials we hear of.
Letter to Baden-Powell (1896)
Radio has no future.
(Speaking in 1897)
[Of the ether] it is no greater mystery at all events than the shoemakers' wax.
I have not had a moment's peace or happiness in respect to electromagnetic theory since November 28, 1846. All this time I have been liable to fits of ether dipsomania, kept away at intervals only by rigorous abstention from thought on the subject.
Remark to FitzGerald 1896.