Comment by selimthegrim

If you read the older editions of physics (and my comment applies to physics, not math) textbooks like Lanczos and Kittel (let’s leave Landau out of this) where the examples and problems are interspersed in the text often with solutions, the clear implicit invitation is to the students to come up with their own problems (ideally paradoxes!). This is related to point 4 in throwawaymath’s comment: https://news.ycombinator.com/item?id=19265709

If you don’t expect them to be potential future faculty, then by all means let other people hand you the problems and paradoxes unless you’re in contact with experiment.