| I've long wanted a series of interactive math ebooks that work that way. Each would take one interesting theorem, such as the prime number theorem, and work backward. When you start the book, it would give the theorem and proof at a level that would be used in a research journal. For each step of the proof, you would have two options for getting more detail. The first option would be at the same level, but less terse. E.g., if the proof said something like "A implies B", asking for more detail might change that to "A implies B by the Soandso theorem". Asking for more detail there might elaborate on how you use the Soandso theorem with A". The second expansion options gives you the background to understand what is going on. In the above example, doing this kind of expansion on the Soandso theorem would explain that theorem and how to prove it. Both types of expansion can be applied to the results of either type of expansion. In particular, you can use the second type to go all the way down to high school mathematics. If you started with just high school math, and used one of these books, you would get the basics...but only those parts of the basics you need to understand the starting theorem. Pick a different starting theorem, and you get a different subset of the basics. It should be possible to pick a set of theorems to treat this way that together end up covering most of the basics. That might be a more engaging way to teach mathematics, because you are always working directly toward some interesting theorem. |
Sadly, the monetization of this is tricky. Probably has to be an open source effort. Need some visionary like wales or khan, but they are very very rare.