Can the form of a verb be determined by the meaning of the subject instead of its grammatical number?

In school we were taught that a subject in singular form required a corresponding verb, for example:

The multitude of insects is astonishing.

multitude is singular, therefore is must be used.

But now I have been told by an experienced (but not native) speaker that a subject with a plural meaning can be used with a verb "in plural form", for example:

The multitude of insects are astonishing.

multitude means plural, therefore are can be used.

Is this just an exception which is not taught to English language learners, or is it informal use, or is this wrong altogether?

Answer

This involves the question of whether a collective noun should be parsed as singular or plural; but it is more complicated than that, because multitude is actually used in three different senses: as a collective noun, as a singular noun, and, with of, as a quantifier.

The multitude was/were blessed by the Archbishop. ... Here multitude is a collective noun signifying a large group of people who were collectively, not individually, blessed. It may take either a singular or a plural verb.

The multitude of false positives is very discouraging. ... Here multitude is a singular noun signifying ‘(large) quantity’—literally, ‘manyness’. It is not the false positives which are discouraging but the fact that there was a large number of them. It takes a singular verb.

A multitude of celebrities are scheduled to appear. ... Here a multitude of is equivalent to ‘many’, like a lot of or a whole bunch of. It takes a plural verb.

In your example, “The multitude of insects is astonishing”, it seems to me that the second sense is intended, and you should use the singular verb.

None of these uses is ‘incorrect’ in any register. The second use, however, is more likely to be found in formal registers, and may give ordinary readers pause. If you are writing for a non-academic audience I would suggest something more like

The occurrence of so many false positives is very discouraging.

The third use, on the other hand, is characteristic of informal registers; it is unlikely to be used in a formal context by practised writers, who will avoid both its hyperbole and its implicit ambiguity:

Many celebrities are scheduled to appear.