[T]he visible world supposes an invisible world as its interpreter, and […] in the application of the mathematics themselves there must (if I may venture upon the word) be something meta-mathematical. Though the senses may make known the phenomena, and mathematical methods may arrange them, yet the craving of our nature is not satisfied till we trace in them the projection of ourselves, of that which is divine within us
From a lecture to astronomy students given by William Rowan Hamilton in 1833 (Graves, 1882-9, vol. 2, p. 68).
Hamilton differed from other mathematicians of his time in his focus on abstract mathematical laws, and in finding inspiration in idealist philosophers such as Immanuel Kant and Samuel Taylor Coleridge, as can be seen from the quote. “Hamilton often argued that certain metaphysical views were the primary motivation for his work in mathematics” (Attis, 2004).