There is nothing self-evident about 3 + 2 = 5 or 9 x 3 = 27. Certainly, even to non-rationalists, who know nothing because they only assume instead of demonstrate what is true, it might seem very obvious that these and other mathematical relationships are true, to the point where some of them might think of them as self-evident. Logical axioms are self-evident because they cannot be rejected or doubted without relying on them, because they cannot be false without still being true. Since the logical necessity of one thing following or not following from another could not be false unless it followed by logical necessity from the nature of reality that logic is false, it is still true. For another example, it is impossible for something to be anything other than what it is (the logical law of identity), for then whatever else it would be is still what it is.
Because the law of identity's relevance to basic numeric truths is relevant to what some might think of as more obvious, I will focus on this first. What is self-evident is not that 9 = 9, because this is but a particular case of something dictated by the law of identity and not the law of identity itself, which is true prior to and independent of examples. The law of identity's status as a logical axiom is what makes 9 = 9 rather than the other way around. Because a thing can only be what it is, whether a concept, a thought (which can grasp concepts), a physical object, or anything else, 9 cannot be 5 or 673 or any other number, but it is not the fact that 9 is 9 that specifically determines this. Instead, it is true that 9 is 9 because logic requires this, and thus it is knowable, for someone who makes no assumptions, with absolute certainty.
Likewise, nothing can logically follow from anything else in a particular case beyond pure logical axioms unless logical axioms are already true independent of concrete examples. Nothing would or could make anything else true if so. If a prime number is a number that can only be factored by itself and 1, then it follows logically that 24 and 38 are not prime numbers (the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24; the factors of 38 are 1, 2, 19, and 38) and that 27 is prime. This is not true because numbers ground themselves, though the facts about them are indeed necessary truths. It is because logic, which is true in itself, makes all of this so. It cannot be true that nothing follows logically from anything else by necessity, because then it would follow from something (whatever the basis) that logic is necessarily false. This being false requires that it is still true!
Logical axioms like this objective facts are metaphysically self-necessary because they cannot be false or have been any other way, and so they are epistemologically self-evident, since a person cannot cease to rely on their truth even when denying or desperately hoping to flee from them. They are therefore inescapable on every level. Now, mathematical truths as well as broader/more foundational logical necessities do govern all other things, such as scientific phenomena. Just as pure logic is independent of and prior to logical truths about mathematics, mathematics is independent of and prior to scientific matters.
Mathematical concepts are strictly logical truths, but not all logical truths are strictly, specifically about numbers. As described, some logical truths are true in themselves, and this is what makes anything true about numbers and other non-axiomatic things. It is therefore not that there are mathematics and science, as if all aspects of reality pertinent to such things reduce to just these two categories. Pure logic, starting with the self-necessary axioms that cannot be or have been untrue, governs mathematics, which in turn (along with other logical necessities) governs science. Numeric truths are in no way self-evident because they depend on prior logical facts--and scientific ideas are much further removed from self-evidence than this, in part because it is impossible for humans to logically prove them rather than amass fallible sensory evidence for them!
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