mathematical media
Dec. 19th, 2006 07:36 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
guslI 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.
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.
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(no subject)
Date: 2006-12-20 02:31 am (UTC)But I really would like the ability to click on technical terms and have those terms defined. I'd also like the ability to click on a theorem number and be taken back to the statement of the theorem it refers to, because mathematical writers have this nasty habit of saying "and by Theorem X, this follows" and I wonder "what the hell is Theorem X?". Because I'm lazy, I don't go back to look and see what Theorem X was, but I would if it were easier to do so.
(no subject)
Date: 2006-12-20 04:38 pm (UTC)the main difficulty here is interpreting the written mathematical text into a formal language -- I would submit that the vast majority of texts don't map to any formal language without a lot of interpretation work. This seems like a career's worth of Ph.D. theses to direct.