Learn English – Is “public” plural or singular

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".

First, you're confusing the issue a bit with a misuse of "a record" in the adjectival sense. "There was a record of 28,000 runners participating" technically¹ means that documentation existed for this number of runners – perhaps there were more runners, but the remainder were not documented. Here, the subject is "record", so the verb is singular. If you're trying to unambiguously remark on the fact that 28,000 is a large number, you need to leave out the "of": "There were a record 28,000 runners participating." Here, the subject is "runners", so the verb is plural.

^{1 In practice, it's an ambiguous statement, because lots of people use "a record of" incorrectly.}

In the general case of "a [x] of [y]", the verb should agree with [x], unless it's one of the special cases (e.g. a lot of) where [x] itself is sorta-kinda plural in meaning, and so can take a plural verb. To figure it out, you can remove the extra words and see if the result sounds correct.

• There was a record of these statements. (There was a record.)
• The use of apples instead of pears was unexpected. (The use was unexpected.)
• It was a time of mass uprisings and protests. (It was a time.)
• There were a lot of people present. (There were a lot.)
• A variety of options were available. (A variety were available.)