>>11854662>>11854681These two posts simultaneously get a lot wrong and a lot right. So, let's parse the content of the two and correct each. The former post will be labeled A, and the latter B, for convenience.
A correctly states that math is discovered, and not invented. This is to A's credit.
Unfortunately, A then incorrectly states that Newton "merely" re-discovered knowledge which he attributes to the ancients, which they did not in fact posess. Euclidian and Archemedian approximation by method of exhaustion, although a step in the right direction, was never carried through to its limit-point, to give precise answers for the area question. And no, don't bother bringing up volume formulae for pyramids and cones, notwithstanding that Euclid XII.10 is one of the more pertinent and impressive results on this head, actually giving a precise and correct relationship. Thus we proceed to B.
B begins with a generally agreeable statement. A science with any claims to exactness must provide exact answers on what it claims to treat. If it can't do so, then it fails at its purpose and is therefore void. Still, B makes a wrongheaded rhetorical choice by placing Newton/Leibniz around the same territory as our we wuz Nubians et al. No, B, Newton and Leibniz provided correct results despite lack of rigor. And no, this defense does not contradict the above similar point about the ancients, because Newton and Leibniz provided demonstrations which were later renovated by 19th century gang and put on more solid ground. To underline, THEY MANAGED TO PROVIDE EXACT AND CORRECT ANSWERS DESPITE GAPS IN RIGOR. Because they had the requisite insight. This is the reason why they are properly and jointly credited.
I am happy to have put right these confusions.
