Ask HN: Should I buy "The Art of Computer Programming"?

Yes.

Not because it's a research resource, although it is, but because knowing that stuff is likely to be relevant to your success in said research.

Only if you are in the market for comprehensive reference. Reading through TAOCP is a good project for the eager-to-learn beginner, but you probably already know the essentials of the material from your coursework. It's a compendium of the "proven useful" stuff, which tends to be older material. Research papers will have more/newer information. TAOCP will have more examples.

If you're still a student, check it out from the library and see if it suits you.

I just checked and all three volumes are checked out for at least a month.

No, it's more like a decoration piece then anything. Read research papers online of the areas you're interested in.