Duolingo for math
An idea I roll around in my head from time to time, not as an idea to be taken literally (i.e. not as something to implement literally), but as a tool to generate new ideas, is trying to imagine what a Duolingo for math would look like.
One problem with "duolingo for math" is that in math, if you want to think about a problem or a theorem or whatever, you often need to load a lot of things into your working memory. So even just being able to "play" requires this initial loading. Once you have loaded things into WM however, you can often play in a fun way, and mini-tasks like in duolingo can work well.
