Pure Mathematics is the class of all propositions of the form “p implies q,” where p and q are propositions containing one or more variables, the sam… - William Rowan Hamilton

It was mathematics, the non-empirical science par excellence, wherein the mind appears to play only with itself, that turned out to be the science of sciences, delivering the key to those laws of nature and the universe that are concealed by appearances.

Physicists have been drawn to elegant mathematical relationships that bind the subject together with economy and style, melding disparate qualities in subtle and harmonious ways. But this is to import a new factor into the argument—questions of aesthetics and taste. We are then on shaky ground indeed. It may be that M theory looks beautiful to its creators, but ugly to N theorists, who think that their theory is the most elegant. But then the O theorists disagree with both groups...

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. It was, however, a part of this conception, that the progression here spoken of was understood to be continuous and unidimensional: extending indefinitely forward and backward, but not in any lateral direction. And although the successive states of such a progression might (no doubt) be represented by points upon a line, yet I thought that their simple successiveness was better conceived by comparing them with moments of time, divested, however, of all reference to cause and effect; so that the "time" here considered might be said to be abstract, ideal, or pure, like that "space" which is the object of geometry. In this manner I was led, many years ago, to regard Algebra as the Science of Pure Time: and an Essay, containing my views respecting it as such, was published in 1835. ...[I]f the letters A and B were employed as dates, to denote any two moments of time, which might or might not be distinct, the case of the coincidence or identity of these two moments, or of equivalence of these two dates, was denoted by the equation,B = Awhich symbolic assertion was thus interpreted as not involving any original reference to quantity, nor as expressing the result of any comparison between two durations as measured. It corresponded to the conception of simultaneity or synchronism; or, in simpler words, it represented the thought of the present in time. Of all possible answers to the general question, "When," the simplest is the answer, "Now:" and it was the attitude of mind, assumed in the making of this answer, which (in the system here described) might be said to be originally symbolized by the equation above written.