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Kaj_Sotala comments on Open Thread, June 2-15, 2013 - Less Wrong Discussion
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If improving your skills is your main goal, you should just write, regardless of whether better explanations already exist elsewhere. Actually, such explanations already existing could even be an advantage, as it provides you with feedback: after writing your own, you can look up existing ones and compare what you did better and what you did worse.
I see what you are saying, but I would be more motivated if it felt like I was doing useful work, and I don't really know what to write about. So I kind of am looking for inspiration/motivation and ideas.
Are you sure? I wish this was what motivated me, but I've learned from writing about math for awhile that what I'm most motivated to write about is precisely what I'm most curious about at the moment. The usefulness of the writing has very little effect on my ability to actually finish it. (For example, I think it would be really useful to write an introduction to some of the material in Jaynes. But this hasn't motivated me to actually do so yet.) You should try writing a few things first, of varying usefulness and curiousness, and see which thing you actually feel motivated to finish.
What do you really wish someone had explained to you 2 years ago?
The two things that come to mind are things that I am still learning. General category theory (rather than category theory for the purpose of x), and a higher level structural and general viewpoint on Bayes (rather than basic articles on how to compute Bayes theorem and what it means). Also something on what actually happens when you extend mathematical logic using Bayesian probability. I could probably start on the second one right now...
Writing about things you are still learning would probably be a great idea, actually. It would likely help you learn them better (research shows that in peer-to-peer tutoring, the tutors benefit more than tutees). And you can always leave in placeholders that give you more to write about: "I don't know why this is yet, but I'm going to look it up and write about it later."
You might also have an unfair advantage, in that since you have newly learned it, you'll have a better perspective from which to explain it to people who aren't familiar with the material.
If you want to practice writing, but you can't think of any fun (or... fun-like) ways to practice writing, it may be a good idea to practice in a way that isn't fun, instead of waiting for something fun to come along. If lack of motivation turns out to be actually problematic, then searching for a more motivating topic is a potential solution, but there are lots of other, potentially better solutions.