William R Hamilton - Collected Quotes

“There seems to me to be something analogous to polarized intensity in the pure imaginary part; and to unpolarized energy (indifferent to direction) in the real part of a quaternion: and thus we have some slight glimpse of a future Calculus of Polarities. This is certainly very vague […]” (Sir William R Hamilton, “On Quaternions; or on a new System of Imaginaries in Algebra”, 1844)

“The difficulties which so many have felt in the doctrine of Negative and Imaginary Quantities in Algebra forced themselves long ago on my attention […] And while agreeing with those who had contended that negatives and imaginaries were not properly quantities at all, I still felt dissatisfied with any view which should not give to them, from the outset, a clear interpretation and meaning [...] It early appeared to me that these ends might be attained by our consenting to regard Algebra as being no mere Art, nor Language, nor primarily a Science of Quantity; but rather as the Science of Order in Progression.” (William R Hamilton, “Lectures on Quaternions: Containing a Systematic Statement of a New Mathematical Method… “, 1853)

“Each mathematician for himself, and not anyone for any other, not even all for one, must tread that more than royal road which leads to the palace and sanctuary of mathematical truth.” (Sir William R Hamilton, “Report of the Fifth Meeting of the British Association for the Advancement of Science”, [Address] 1835)

“Instead of seeking to attain consistency and uniformity of system, as some modern writers have attempted, by banishing this thought of time from the higher Algebra, I seek to attain the same object, by systematically introducing it into the lower or earlier parts of the science.” (Sir William R Hamilton) 

”Mathematical language, precise and adequate, nay, absolutely convertible with mathematical thought, can afford us no example of those fallacies which so easily arise from the ambiguities of ordinary language; its study cannot, therefore, it is evident, supply us with any means of obviating those illusions from which it is itself exempt. The contrast of mathematics and philosophy, in this respect, is an interesting object of speculation; tut, as imitation is impossible, one of no practical result.” (Sir William R Hamilton)

"Metaphysics, in whatever latitude the term be taken, is a science or complement of sciences exclusively occupied with mind." (Sir William R Hamilton)

"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." (Sir William R Hamilton)

“We are naturally disposed to refer everything we do not know to principles with which we are familiar.” (Sir William R Hamilton)