My soul is an entangled knot,
Upon a liquid vortex wrought
By Intellect in the Unseen residing,
And thine doth like a convict sit,
With marline-spike untwisting it,
Only to find its knottiness abiding;
Since all the tools for its untying
In four-dimensional space are lying,
Wherein they fancy intersperses
Long avenues of universes,
While Klein and Clifford fill the void
With one finite, unbounded homoloid,
And think the Infinite is now at last destroyed.
The Life of James Clek Maxwell
The numbers may be said to rule the whole world of quantity, and the four rules of arithmetic may be regarded as the complete equipment of the mathematician.
Quoted in E T Bell, Men of Mathematics
The mind of man has perplexed itself with many hard questions. Is space infinite, and in what sense? Is the material world infinite in extent, and are all places within that extent equally full of matter? Do atoms exist or is matter infinitely divisible?
Quoted in E Maor, To infinity and beyond (Princeton 1991)
In order to obtain physical ideas without adopting a physical theory we must make ourselves familiar with the existence of physical analogies. By a physical analogy I mean that partial similarity between the laws of one science and those of another which makes each of them illustrate the other. Thus all the mathematical sciences are founded on relations between physical laws and laws of. numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers.
On Faraday's Lines of Force (1856).
Every existence above a certain rank has its singular points; the higher the rank the more of them. At these points, influences whose physical magnitude is too small to be taken account of by a finite being may produce results of the greatest importance.
Mathematicians my flatter themselves that they possess new ideas which mere human language is as yet unable to express. Let them make the effort to express these ideas in appropriate words without the aid of symbols, and if they succeed they will not only lay us laymen under a lasting obligation, but, we venture to say, they will find themselves very much enlightened during the process, and will even be doubtful whether the ideas as expressed in symbols had ever quite found their way out of the equations into their minds.
I have also a paper afloat, with an electromagnetic theory of light, which, till I am convinced to the contrary, I hold to be great guns.
In a letter to C. H. Cay, 5 January 1865.
What's the go of that? What's the particular go of that?
Comments made as a child expressing his curiousity about mechanical things and physical phenomena.
... that, in a few years, all great physical constants will have been approximately estimated, and that the only occupation which will be left to men of science will be to carry these measurements to another place of decimals.
[Maxwell strongly disagreed with these views and was attacking them.]
Scientific Papers 2, 244, October 1871.
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