The verb mamy would have me translate as "which century do we have ?", which seems very different from "what century is it?"
It's important to remember that languages are about semantics. One-to-one translations aren't perfect, so you should be translating ideas rather than exact words.
True, you need to be careful with certain expressions. Similarly, Polish people wouldn't tell they "are X years old". They say they "have X years".
If I understand correctly...
"Który mamy wiek?" and "Jaki to wiek" are nearly the same questions for exactly the same answer!?
Why not "Which century is this?"
Cue time traveler song