Some good ideas that I’d love to see implemented. (I would do them, if I were more of a hacker and had time to spare. Let me know if you’re interested in helping make any of these work!)
See a list of ideas by many people at http://hackathonprojects.tk/
These wikis are designed to help learners navigate new subjects.
And another one:
Program an AI for Hanabi. Have it follow the conventions and use human style deductive reasoning (imagining how the next turns will unfold and using that to update its play). Unlike other games this kind of deductive reasoning would actually help (rather than just doing something like minimax). See http://boardgamegeek.com/thread/939952/hanabi-style-game-online-play and https://github.com/Quuxplusone/Hanabi.
Program a 2-D adventure game engine in Elm, and then build games on top of it. (Start with a clone of something, ex. BlockWorld.) The functional style makes it easy to specify the behavior of different actors. Make it Turing-complete (cf. Minecraft, Dwarf Fortress). Add a premise/story (ex. Nell’s story in The Diamond Age). See https://github.com/holdenlee/elm.
Formalize “problem-solving” type problems (e.g. Engel) in Coq, and write an automated theorem prover in Gallina to try and solve those problems.
Create a (natural) language based on functional programming that “type-checks” and actually implement it in a programming language. (How can we build a parser if the sentences aren’t perfect grammar? Check nearby possibilities?)
Build a Penultima server which allows users to submit their own rules for pieces by writing functions (e.g. Actor -> Location -> Maybe Board, i.e., given an actor and a location for it to move to, return Nothing if it is invalid and return the resulting board otherwise). For a game, the site chooses a random submitted rule for each of the pieces. Rules can be upvoted and downvoted (so they will appear more/less common). The site keeps track of which users have played with which rules to prevent repeats. (At the minimum allow standard fairy chess piece moves http://en.wikipedia.org/wiki/Fairy_chess_piece. For an implementation of a game in Haskell that also allows rule changes, see Nomyx http://www.nomyx.net/.
Backchannel for online lectures – A simple customizable interface that has a video (possibly from YouTube) on one side and a list of questions and comments that people have about the video on the other side. At any time, a watcher can pause the video and type a question or comment, and it will be arranged chronologically in the document, with the video’s time stamp. People can upvote and downvote questions and comments. –This is a vast improvement over online lectures with no interactivity, and addresses several concerns over the “online lecture”-ification of classes as well as flipped classrooms: specifically, students cannot ask questions in real-time, and hence there is no personalization of the lecture, and no ability to go on interesting tangents. However, neither does in-person lecture accomplish this completely because there are too many people and one instructor. Now students get to ask ALL their questions, in a time-specific manner, and a teacher can address them during class (or by commenting on the questions). This also provides the instructor with very specific feedback to improve the online lecture. –Maybe some online courses already have this feature. (Does EdX do this? If this is an immediate improvement.) I imagine that someone could turn a YouTube video into a commentable video in this sense just by dropping a YouTube link at the website, possibly setting a password for students. This immediately makes the existing wealth of educational videos available vastly more powerful.
I imagine this extending to other media besides videos. What if we did the same for every major textbook, ordered by page number? Reading a textbook no longer has to be a very independent activity; you could be connected to the corpus of all questions and ideas that other people have had while reading the textbook. A reading group’s best friend!
(And what if we could make the comments/questions not linear, but graph-like?) 1.education <-> Piazza <-> TodaysMeet <-> Concrete Mathematics, Graham, Patashnik, Knuth (one of my favorite math books; they incorporated class comments into the margins of their textbook)