Just as the imagery of the the world in which I am imbedded is a product of the outside and the inside, of itself and of my nervous system, so is science, the social understanding of that world, a product of the outside world, of the society and, so far as I am concerned, of the ultimate inside, of myself. What seems remarkable to me about mathematics, is that in contemplating mathematics, I discern merely the skimpiest evidence of anything beyond self and society.  Only the natural numbers are a hint, however faint, of anything outside of me, of an absence of continuity, of the "cuts" (Schnitte) that divide the world into "things", into objects. Thus the claim of mathematics to be royalty, to serve as "queen of the sciences", arises in my consciousness almost wholly independent of the realm which mathematics purports to rule.

The natural numbers, whatever correspondence to leaves or stars or other entities of nature they may have, are at least partially confirmed by the iterations of the individual mind, of the steps that I take, of my breaths and of the pulsing of my heart. For the rest, so far as I can understand, up to, - or no, rather down to - mathematical logic, mathematics is an excrescence (Wucherung) of the human mind as it flourishes in (the compost of) society.  This it seems to me is especially true with respect to mathematical proofs.

The (existential) nature of mathematical proofs becomes apparent in the context of verbal statements, which are by their nature assertions of "truth" or "validity". One should note also, that in any event, in order to be communicated, mathematical proof requires assertions of "truth", ideals of integrity to which symbols may serve as pointers, but for which they can never substitute. Whatever evidence mathematical proof may shed on the validity of mathematical assertions, the evidence which mathematical proof sheds on the frivolous and feckless nature of mathematics is "inescapable". I ask myself whether my denigration of mathematical certainties is my expression of resentment for my mathematical incompetence.