That's a very specific problem that your professor had a proof for. Someone had to determine that at some point and then did so because they asked questions. At this point we're at a philosophical difference. I believe that asking all questions is worthwhile. Like "Can the beauty of art be explained?" Yes. You assumed no, and didn't want to ask the question to begin with.
Yes it is a philosophical difference.
Some questions I believe can be meaningful questions without ever really having an answer. I guess it's the "If a tree falls in the woods" question thing. The search might be good, but that doesn't mean I believe the search will ever yield an answer. Some things I believe are just set up that way.