The original Greek “-ikos” was both the feminine singular when refering to “the art” (the whole field), and the neuter plural when refering to “things pertaining to the art”. Latin took just the feminine singular, and most Latin-based languages today still use a singular, including English terms older than 1500 or so, like chemistry rather than chemics, taxonomy v. taxonomics, or arithmetic as opposed to arithmetics‽

Later in the Renaissance, people remembered Greek existed, and decided to try and bring back the neuter plural by taking a perfectly good -ic and slapping an s on it. Thus we get the somewhat newer sciences of physics, mathematics, ballistics, demographics, statistics, and so on.

The shortening of mathematics to “math” and “maths” was done much later, around 1900, give or take a few decades. Both versions can be found as purely written contractions beforehand, but their use in speech and whether the s was thruncated appears random.

Thus, if you must use a plural, the original useage has singular for the field (“Biomechanics is a difficult subject.”), and plural for things relating to the field (“The mathematics used are difficult to parse.”); don’t try to justify using several thousand year old grammar (from a region remote enough that we forgot about it for several centuries) with syntax rules not present in the original. English is plenty fucked up as it is, let it build it’s own syntax and heal a bit, eh?