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1 " The third preliminary problem for every theory of reality is that of the experience of transcendence. We saw in the case of Berkeley that his erroneous principle *percipi est esse*, and his assertion that any being which we think, just for the reason that it is thought, cannot at the same time be regarded as subsisting independently of thinking, incorporate a failure to recognize the consciousness of transcendence peculiar to all intentional acts. This is an instance of the failure to recognize that not only all thinking in the narrower sense, in the sense of grasping an object on the basis of “meanings” and grasping a state of affairs through judgments, but *every* intention in general, whether perception, representation, remembering, the feeling of value, or the posing of ends and goals, points beyond the act and the contents of the act and intends something other than the act [*ein Aktfremdes*], even when what is thought is in turn itself a thought. Indeed, *intentio* signifies a goal-directed movement toward something which one does not have oneself or has only partially and incompletely. Berkeley (following Locke, who was the first to make the basic philosophical error which introduced “psychologism” into epistemology) arrived at the principle *esse est percipi* by making the idea [*Vorstellung*] (and even the sensation) into a thing, an immaterial substance, and by failing to distinguish between the act, the content of an act, and the object. Furthermore, Berkeley confused the being of objects with the fact of being-an-object, even though the latter has only a loose and variable connection with the former. On the other hand, the transcendence of the intentional object with respect to both the *intentio* and its present content is common to every instance of being-an-object. It is, for instance, proper to objects of pure mathematics which are certainly not real but ideal (for example, the number 3). These are produced from the *a priori* material of intuition in accordance with an operational law governing the steps of our thought or intuition. Transcendence is further proper to all fictitious objects and even to contradictory objects, for instance, a square circle. All these sorts of objects, e.g., the golden mountain or Little Red Riding Hood, satisfy the basic principle of the transcendence of objects over and above that aspect of them which is, at any moment, given in consciousness, just as much as do real objects existing independently of all consciousness and knowledge." ―from_Idealism and Realism_ "
2 " Sexuality is the only drive that is in itself hindered, perverted: simultaneously insufficient and excessive, with the excess as the form of appearance of the lack. On the one hand, sexuality is characterized by the universal capacity to provide the metaphorical meaning or innuendo of any activity or object–any element, including the most abstract reflection can be experienced as ‘alluding to that‘ (suffice it to recall the proverbial example of the adolescent who, in order to forget his sexual obsessions, takes refuge in pure mathematics and physics–whatever he does here again reminds him of ‘that’: how much volume is needed to fill out an empty cylinder? How much energy is discharged when two bodies collide?…). The universal surplus–this capacity of sexuality to overflow the entire field of human experience…is not the sign of preponderance. Rather, it is the sign of a certain structural faultiness: sexuality strives outwards and overflows the adjoining domains precisely because it cannot find satisfaction in itself, because it never attains its goal. "
― Slavoj Žižek
3 " ...in pure mathematics the mind deal only with its own creations and imaginations. The concepts of number and form have not been derived from any source other than the world of reality. The ten fingers on which men learned to count, that is, to carry out the first arithmetical operation, may be anything else, but they are certainly not only objects that can be counted, but also the ability to exclude all properties of the objects considered other than their number-and this ability is the product of a long historical evolution based on experience. Like the idea of number, so the idea of form is derived exclusively from the external world, and does not arise in the mind as a product of pure thought. "
― Friedrich Engels , Anti-Dühring: Herr Eugen Dühring's Revolution in Science
4 " It was as though applied mathematics was my spouse, and pure mathematics was my secret lover. "
― Edward Frenkel , Love and Math: The Heart of Hidden Reality
5 " In the field of Egyptian mathematics Professor Karpinski of the University of Michigan has long insisted that surviving mathematical papyri clearly demonstrate the Egyptians' scientific interest in pure mathematics for its own sake. I have now no doubt that Professor Karpinski is right, for the evidence of interest in pure science, as such, is perfectly conclusive in the Edwin Smith Surgical Papyrus. "
― James Henry Breasted , The Edwin Smith Surgical Papyrus, Vol 1: Hieroglyphic Transliteration, Translation and Commentary
6 " The object of pure physics is the unfolding of the laws of the intelligible world the object of pure mathematics that of unfolding the laws of human intelligence. "