Learn English – Origin of pluralisation of verbs and nouns in English

Etymonline has this to say:

-ics
in the names of sciences or disciplines (acoustics, aerobics, economics, etc.) it represents a 16c. revival of the classical custom of using the neuter plural of adjectives with -ikos (see -ic) to mean "matters relevant to" and also as the titles of treatises about them. Subject matters that acquired their names in English before c.1500, however, tend to remain in singular (e.g. arithmetic, logic).

So yes, at some point in history, there were such things as physic (meaning "natural science"), mathematic (meaning "mathematical science"), etc. that were later turned into plural forms but kept being treated as singular.

Edit: having looked in a few more places, it appears that in contemporary English, it still makes some sense to have both the suffix -ic and its plural form -ics. According to the Collins English Dictionary, the former has kind of specialized in forming adjectives, while the latter is happily forming nouns:

-ic
suffix forming adjectives

1. of, relating to, or resembling: allergic, Germanic, periodic. See also -ical.
   [...]

[from Latin -icus or Greek -ikos; -ic also occurs in nouns that represent a substantive use of adjectives (magic) and in nouns borrowed directly from Latin or Greek (critic, music)]

[...]

-ics
suffix forming nouns (functioning as singular)

1. indicating a science, art, or matters relating to a particular subject: aeronautics, politics
2. indicating certain activities or practices: acrobatics

[plural of -ic, representing Latin -ica, from Greek -ika, as in mathēmatika mathematics]

The key here is that they are not just two unrelated suffixes. Much rather, one is etymologically a plural form of the other. As the American Heritage Dictionary succinctly puts it, -ics is "-ic + -s".

This is all down to the fact that English is a language of acutely mongrel lineage. It has substantive roots in Celtic, Romance and Germanic languages (to name a few) and a grammar that lends itself well to the adoption of "loan words" (non-native words adopted into the native tongue.)

The "standard" means of pluralising a noun is to append -s, with some conventional variations (eg -f becomes -ves, -y becomes -ies) for convenience in spelling and pronunciation.

However latin-based words tend to pluralise in the latin fashion, so for example bacterium becomes bacteria, and cactus becomes cacti. Similarly greek-based words will adopt the equivalent pluralisation appropriate for the original root.

Still other words of Saxon or earlier origin have lovely, earthy plurals that defy the "conventions" due to their traditional forms being maintained. Geese, Mice and Children owe their unusual conjugations to their ancient roots, and to the fact that they are common words whose everyday repetition keeps them from slipping into bland conformity.

In my experience, words which do not pluralise are those which relate to herding, hunting and the counting of animals. These words tend to be saxon (germanic) or celtic in origin owing to the presence of farming and hunting in Britain long before the Norman invasion. This can be inferred by the fact that sheep, cattle and game do not pluralise, while whales, sparrows and elephants (seldom hunted or farmed in Britain!) definitely do.

I suspect these tend to be a contraction of the traditional counting forms for such cases ("head" of cattle, "brace" of partridge, "shoal" of fish) but this doesn't really answer the question of why such plurals take the same form as the singular. It could be that when counted in such a way, the animals being counted were considered an uncountable, continuous quantity (similar to water or money) that could only be "counted" when quantified with their associated counter, so cattle would be rendered an uncountable noun by its quantifying counter head. It's interesting however to note that bird pluralises to birds, while aircraft does not pluralise.

Sadly for the non-native speaker, this makes learning the "rules" of English an arbitrary and frustrating affair. However, spare a thought for the Japanese, who do not have plurals for any but a few unique nouns, and must instead learn a separate counting-suffix and corresponding character (kanji) for almost every class of noun imagineable. There are in fact entire volumes of the things, and it would be nigh-on impossible for any person to learn them all. Wikipedia lists a choice selection.