I have decided to read a

mathematical textbook over the holidays, something I haven't done in a long time.

I keep wanting to click on terms that I don't recognize, to go to the definition.

Here's a useful programming/text-learning project: create a system that, given a mathematical document (LaTeX, PDF, scanned text), automatically turns it into a mathematical hypertext linking each technical term to its definition.

You can use a wiki to do the linking, as long as you have WikiTeX enabled to do the rendering. This should be a straightforward project if the original document is already in LaTeX. AFAIK, you can't put links on TeX-rendered images, but fortunately, terms that have definitions tend to be the kind that don't need any TeXing anyway.

For me, the next steps would be:

* variable substitution: the text lets the reader plug in values. This would be useful for understanding theorems.

* recognize whether a reader-given object satisfies a definition (along with a "WhyNot?" tool)

I think the main difficulty here is interpreting the written mathematical text into a formal language. Most people reading this are probably thinking about difficult questions, like which foundation they would choose. But the definitions that I have in mind could be decided with Prolog.

I should read

OpenMath applications to see what people are up to. They have

whole conferences on this stuff, so we should be seeing some progress in this area. I have to wonder why we don't yet see any interactive math books online (advanced, theorem-based math).

More ideas:

* interpreting diagrams as mathematical objects, which can (fail to) satisfy definitions.