Several years ago I attended a colloquium talk of an expert in Galois theory. He motivated some of his work on its relation with the inverse Galois problem. During the talk, a guy from the audience asked: ``why should I, as a number theorist, should care about the inverse Galois problem?"
I must say that as a young graduate student that works on Galois theory, I was amazed or even perhaps shocked from this question. But later, I realized that I should have asked myself this question long ago.

Can you pose reasons to convince a mathematician (not just number theorist) of the importance of the inverse Galois problem? or maybe why it's unimportant if you want to ruin the party ;)