I frequently feel that the things I learn are not motivated properly. My understanding is that this is a common enough problem among students that it gets its own acronym: "What can you do with this?" (WCYDWT)
Here is a sample question and answer pair that I would have liked a few months ago:
Me: I have just learned Lagrange's theorem. WCYDWT?
Math.SE: The first proof in the wikipedia article about Euler's theorem is mostly based on Lagrange's theorem.
Would such a question have been on topic? I suspect it will almost always be a community wiki, except for very specific concepts.
I can ask this exact question (or another one) if we would like a trial run.
To clarify a bit:
- I come from a programming background, and have always attributed my success (or lack thereof) to the three virtues. Is it impatient of me to demand results immediately, and arrogant to expect to understand the reasoning? Probably, but I'm not convinced that this is a character flaw.
- I was inspired by Joriki's question, which wondered how to help people who ask questions beyond their expertise. I don't know the answer, but I do know that if the only goals in math are attainable only after years of study, you'll end up with a bunch of people who try to cut corners, or give up on math entirely. So I thought this might be one way of finding "intermediate" goals.
Anyway, it sounds like the community is unanimously against the acronym, but at worst neutral about the idea. So if I run into a time when I would like to ask a question like this, I think I will try it out.