Which is correct: "...infinite ways..." or "...an infinite number of ways..."?

"There are infinite ways to..."
"There are an infinite number of ways to..."

One of my colleagues wrote the first sentence, but it didn't sound quite right to me. The second version seems more grammatical to me. Are both of these grammatically correct or is one version preferable to the other?

The OED’s second definition of infinite is, when it is used with a plural noun:

unlimited or indefinitely great in number; innumerable, very many, “no end of”

There this supporting citation with ways from 1775:

Thus there are . . . infinite ways of being vicious, though but one of being virtuous.

However, the entry describes this use as being now archaic or rare. It is probably best avoided for that reason and because, as the other answers show, its use is controversial.

In the example, an infinite number of ways is preceded by There are rather than There is because an infinite number of premodifies the plural ways. This contrasts with the infinite number of ways, where singular number is the head of the noun phrase and so would require singular agreement.

I agree with you, but your colleague is not alone: many people do use "infinite" to mean "infinitely many". For example, "infinite ways" occurs in thousands of books (according to Google Book Search), "infinite possibilities" in tens of thousands, "infinite reasons" in hundreds, and so on.