Learn English – Do we say and write 21 / 31 / 41 item or itemS

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".

Singular and plural are both correct.

The singular form is also used because "two and two" is an arithmetic formula. The verb agreement in that case is with the formula as a single entity.

• Two and two makes four.

• Two plus two is four.

• Four times four divided by two is
  eight.

In your example in particular, Google indicates that the plural form occurs more often:

"two plus two make four" = 353K results
"two plus two makes four" = 77K results

And while Google hit counts are notoriously, the result is supported by Google Ngrams.