The Chinese were solving 14th degree polynomials in 1303. Why?
One of the things I find interesting about ancient Chinese math is how computational it was (in modern terminology we would say they were only interested in computable numbers); AFAIUI the ancient Chinese were vaguely aware of numbers that could not be computed exactly (i.e. irrationals) but mostly cared about being able to compute approximations up to whatever precision was required for a given task.  So while Western mathematicians were struggling in vain to find a way to double a cube using a compass and straightedge or to derive a quintic formula, the Chinese mathematicians were satisfied with an algorithm that found useful approximations.  There is a profound difference in philosophy, as evidenced by the title of this entire thread:  the Chinese were "solving" 14th degree polynomials, but only in the sense of having an algorithm for doing so (as opposed to having a formula like the quadratic formula; in fact there is no such formula for degree 14 polynomials, or for any polynomials beyond the quartic).