Create a tablet app for exploring arbitrary mathematics as an improvement over paper. This is arguably the killer app (of using a tablet for content creation, not merely for content consumption) because mathematics can computationally effectively use a medium "smarter" than paper.
It probably wants several large tablets (to look at several things at once) and a stylus. And maybe a keyboard. Hmm... then it approaches a regular computer.
Mathematica probably has some good ideas, but avoid lock-in to proprietary software.
Inspired by Ramanujan's notebooks, which were originally worked out on a tablet-like slate with slate pencil.
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