CNN/Money has an article on how not finding proper candidates for jobs means that even with rising unemployment many jobs are staying vacant. What this means to me is that the recruiters, and the hiring managers who are working with them, aren't necessarily qualified to be hiring for these positions. Anyone who has done a lot of hiring, which I have, knows that when an employer states "must have two years of industry experience" or "must have five years of professional C++ programming experience" or anything else what they really mean is "it'd sure be nice if we found the perfect candidate who is not only clever, hard working and personable, but also already knows everything they'll ever need to know to do this job". But if you're not filling jobs by sticking precisely to the criteria, it's time to actually (God forbid) think about the candidates as individuals and be flexible about the letter of the requisition.
When I was doing a lot of hiring, we often had more success with candidates who did not fit the letter of our requisition, but who had the spirit the company needed: whip smart, hard working, mentally flexible, and willing to dedicate themselves to learning whatever they needed to excel whether or not they came in the door with it. Those kinds of people (who, by the way, most often came through employee referrals) generally did much better than the recruiter-submitted "perfect" candidates whose resumes dotted every "I" and crossed every "T", but when the rubber hit the road the person just wasn't able to deliver as fully as their "lesser qualified" counterparts.
Talk to the people with the mathematics degrees who haven't had a "real" job yet (or someone with any other "irrelevant" degree or prior job experience). Figure out which ones are those incredibly smart, dedicated, flexible and personable types who are also so hungry to get into your industry that they'll outperform the "better" candidate if given the opportunity. Then hire them. Within two years, they'll also have two years experience, and a positive attitude towards the company that gave them their "in" that can also translate into lower employee turnover rates.
Part of the job of recruiting is understanding people, thinking critically and flexibly about requisitions and candidates, and actually working to put the two together (rather than letting a sorting system do it for you). If your recruiters and hiring managers can't solve the problem of open requisitions during a down economy, maybe it's time for their bosses to think more flexibly and find new recruiters and hiring mangers who can.