As someone that wasn't a math major, I regularly get excited about Mathematica but then have trouble figuring out why I would actually want to use it. If someone were to give me an assignment that they knew could be accomplished with Mathematica, then that would be easier to start, but I feel like it takes a while to make that translation between having a vague desire to figure something out, and then realize that Mathematica could do it for me quickly. Like, I wouldn't have thought to plot out last year's trip to Europe using it. So for new users, there's something of a "well sure it's easy AFTER you know how to do it" gap.
It kind of reminds me of when search engines first came out - I regularly witnessed a gap between people having fun typing in some example queries, and realizing that they could type in anything search-engine-ish and get back information they actually didn't know ahead of time; information they had conditioned themselves not to ask out of not wanting to schedule an afternoon trip to the library.
I'm not a Mathematica user, but I've always enjoyed browsing the Mathematica Stack Exchange, which might be what you're looking for. For example, here someone asks how to generate random snowflakes, and many interesting solutions are provided.
I use Mathematica for most of the programming I do. It makes ordinary programming (file handling, database handling, etc.) much easier (at least for me) than it would otherwise be. I even run nightly backups with a Mathematica script, taking advantage of Mathematica's logical operations.
It kind of reminds me of when search engines first came out - I regularly witnessed a gap between people having fun typing in some example queries, and realizing that they could type in anything search-engine-ish and get back information they actually didn't know ahead of time; information they had conditioned themselves not to ask out of not wanting to schedule an afternoon trip to the library.