I regard it as an inelegance, or imperfection, in quaternions, or rather in the state to which it has been hitherto unfolded, whenever it becomes or seems to become necessary to have recourse to

Quoted in a letter from Tait to Cayley.

On earth there is nothing great but man; in man there is nothing great but mind.

*Lectures on Metaphysics.*

Time is said to have only *one dimension*, and space to have *three dimensions*. ... The mathematical *quaternion* partakes of *both* these elements; in technical language it may be said to be "time plus space", or "space plus time": and in this sense it has, or at least involves a reference to, *four dimensions*.

And how the One of Time, of Space the Three,

Might in the Chain of Symbols girdled be.

Quoted in R P Graves, *Life of Sir William Rowan Hamilton*

Who would not rather have the fame of Archimedes than that of his conqueror Marcellus?

Quoted in H Eves *Mathematical Circles Revisited* (Boston 1971).

[This is a paraphrase of something Cicero wrote in 75BC after his description of finding the tomb of Archimedes:

"Who in all the world, who enjoys merely some degree of communion with the Muses, ... is there who would not choose to be the mathematician rather than the tyrant?"

In the context, the tyrant is Marcellus.]

In fact, with all my very high admiration ... for Gauss, I have some private reasons for believing, I might say knowing, that he did not anticipate the quaternions. In fact, if I don't forget the year, I met a particular friend, and (as I was told) pupil of Gauss, Baron von Waltershausen, .... at the Second Cambridge Meeting of the British Association in 1845, just after Herschel had spoken of my quaternions and your triple algebra, in his speech from the throne. The said Baron soon afterward called on me here, ... he informed me that his friend and (in one sense) master, Gauss, had long wished to frame a sort of triple algebra; but that his notion had been, that the third dimension of space was to be symbolically denoted by some new transcendental, as imaginary, with respect to √-1, as that was with respect to 1. Now you see, as I saw then, that this was in fundamental contradiction to my plan of treating all dimensions of space with absolute impartiality, no one more real than another.

Letter to De Morgan (1852): Quoted in R P Graves, *Life of Sir William Rowan Hamilton*

JOC/EFR April 2016

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