Create a program that is designed to parse and track projects and tasks from emails alone. The point would be to make it completely non-intrusive (albeit not entirely non-interactive). So for example, when composing a message to a client or customer you might be asking a question. You want a response (there’s a “task” outstanding that’s pending a decision or some action). You would simply BCC the special mailbox. The message would be parsed and tracked. When the user replies, the same program is monitoring your incoming mailbox items. When the message arrives it would attempt to interpret whether the task was complete or not. It could then fire a simple email to you indicating that it THINKS that the task is complete with a simple Yes/No form that would let you close the task or not and also possibly make notes or record anything of interest. Or alternatively you could manually complete tasks by forwarding the message to the same mailbox.
This probably is not incredibly value in its proposed form — I’m sure something similar exists. But it would be fun to work on and would be neat to see how smart you could train it to be. Introduction of learning algorithms that would adapt to particular users would be even better.