There is or There are ...?

Which of the above is correct or either one is fine?

Are. "Number" is plural.

Um, well, "number" is singular, but "are" is correct.

At first I also thought it was singular but figured you wordsmiths know better.

If you turn the sentence around it is:
A number of problems are/is there.
If "number" is singular it would take a singular verb--"is"-- since problems is the object of a prepositional phrase.

Knocking out the prepositional phrase and the sentence reads: "A number is there" or "There is a number" which sounds perfectly ok.

But using the singular sounds awkward: "There is a number of problems".
Help!!

From the Chicago Manual of Style:

Number as a collective noun takes a singular or plural verb depending on the article (definite the or indefinite a) that precedes it:

The number of pizzas ordered this year has doubled.

but

A number of studies have shown that stuffing a pizza with spinach triples the edibility of that sinewy vegetable.