In the sense of “math book” it is something similar to but not quite an adjective. I think the correct term is an “attributive”.
A “red book”: red is the adjective.
A “math book” is a different thing from, say, a “history book” and the difference is far greater than between a “red book” and a “blue book”. There is an argument that “math book” is therefore a compound noun: a noun made up of two words.
You would refer to a human being as a “Homo sapiens” without thinking in terms of “Homo” (man) being the noun, and “sapiens” (the wise) being an adjective. You would think of “Homo sapiens” as a single thing - almost like one word with a gap in the middle.
English is a funny language and doesn’t follow quite such rigid rules as, say, Latin, and there are often two or more valid ways of describing a word or phrase. However, contrary to earlier posts in this thread, I think it is great that people are still interested enough to have the debate.
Graham, I never knew you had such an intense interest in grammar! I hope and expect that your new interest is reflected in your future posts!
Edit: wait, I thought that “no one cares about whether or not you are gramatically correct” as the thread title suggests (is it safe to point out that there are two 'm’s in ‘grammatically’?)…
I do indeed hate to keep this thread alive, but Mikefule nailed it. Quite impressively, I might add, and apparently off the top of his head.
‘Math’, in the noun phrase ‘math book’ is an attributive noun or a noun adjunct (I had to look it up). It is a noun that acts like an adjective in that it modifies another noun. The Wikipedia article also states that –
… which means that Jeremy was not technically incorrect; he was just a bit old skool in his terminology.