Is mathematics discovered or invented It seems to me that, from the perspective of the absolute, logic was discovered, not invented, and mathematics was invented, not discovered, but from the perspective of the transient part that is man, both logic and mathematics were discovered, not invented.
It is often presumed that one is eternally equal to itself and that therefore the mathematical identity, one plus one equals two, is most assuredly, eternally true, and that therefore, the entire system of mathematics, which follows by necessity from the truthiness of this supposedly absolute identity, is eternally true as well; but does not the equality one equals one beg the question, “one what?” What does the number one refer or point to? Must the number one point to the essence of some particular thing, whether it be conceptual and purely abstract, or concrete and spatially extended in its nature, that actually exists, or can it point to nothing at all and therefore exist eternally in itself apart from anything else as an abstract number which refers to nothing that floats by its lonesome self in a sea of nothingness. I suppose this raises the question then, can an abstract value which retains its identity over time exist apart from time? If it cannot exist apart from time, it cannot exist apart from essence; and if it can hold true apart from time, or memory, how does the number one as a purely abstract value which points to nothing retain its identity? Does the number one necessarily have ontological value in the absolute sense of the word, or does it not? And if one can be a reference to nothing, that is, something which does not possess an essence, yet still remains equal to itself, as such, is not mathematics in the absence of ontology then akin to calculating the number of angels that can dance on the head of a pin and therefore meaningless? Relatively speaking, a number cannot exist apart from the thing or concept in which it represents, so wherefore originated the idea that numbers can exist in themselves apart from at least one other existent thing that is ontologically one in itself? Do not wish to argue that mathematics does not have practical value in the relative sense of the word, but that mathematics has practical value only when the value of one refers to something ontological, that is, something which has actual being, whether it be a physical object or an abstract concept, and that therefore, mathematics should root its foundations, not in the clouds of nothingness, as is currently so, but in being itself in the non-relative sense. Essentially, if there is not a field of mathematics which concerns mathematics as it relates to ontology, there should be, because without ontology, mathematics is meaningless.
Further, if mathematics has its root in the law of identity 1 = 1, how is it that more complex algebraic identities were abstracted from it, or do they follow by necessity from it and are thus true so long as the law of identity has been true? According to my philosophy, between the law of identity and law of non-contradiction and mathematics and physics, there lies, necessarily, subjectivity, that is, consciousness, for one cannot go from the law of identity and the law of non-contradiction to more complex mathematical identities without the comparison of at least two abstract concepts and an abstraction of a third from them, that is, an intellect.