Part 1 explained how Western mathematics originated in mathesis and religious beliefs about the soul. Hence, mathematics was first banned by the church, and later reinterpreted, in a theologically-correct way, as a “universal” metaphysics. This post-Crusade reinterpretation (based on the myth of “Euclid”) was not historically valid, for the Elements did use empirical proofs. Eventually, Hilbert and Russell eliminated empirical proofs (in the Elements and mathematics) and made mathematics fully metaphysical. Even so, this metaphysics is not universal, but has a variety of biases, as was pointed out. It has nil practical utility. In contrast, most math of practical value originated in the non-West with a different epistemology,1 which permitted empirical proofs (which do not diminish practical value in any way). While the West adopted this math for its practical value, it tried to force-fit it into its religious beliefs about math: first that math must be “perfect” (since it incorporates eternal truths), and, second, that this perfection could only be achieved through metaphysics, since the empirical world was considered imperfect. (Hence, the idea that math must be metaphysical.) Present-day learning difficulties in math reflect the historical difficulties that arose in this way, because the West imposed a religiously biased Western metaphysics on practical non-Western mathematics.
A highlight from the paper
>Formal set theory is so difficult that only a few mathematicians bother to learn it—the head of the math department of an IIT could not even state the formal definition of a set, when publicly challenged to do so by this author.
A highlight from the paper
>Formal set theory is so difficult that only a few mathematicians bother to learn it—the head of the math department of an IIT could not even state the formal definition of a set, when publicly challenged to do so by this author.