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I moved away and am now planning to communicate with a friend over the internet and talk about mathematical subjects (e.g. via Skype). However the text blocks like "\int_G\omega..." in a chat window become more or less unreadable. It would be helpful to have a script like here on StackExchange, which translates the formulas.

Is there a good web page where one can write TeX code such that the other person sees changes live, or at least after pressing F5?

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There is GmailTeX, and an associated "plug-in" for Gmail Chat. I've only ever used the plain GmailTeX, but it seems to work pretty well. –  Arthur Fischer Jul 30 '12 at 8:03
    
Or consider chat with screen sharing; I don't know if.Skype has it but Google+ hangout does. This can be used either in combination with TeX processing software on your end, or (with a stylus and touch screen) to hand-write the formulas. –  user31373 Jul 30 '12 at 12:41
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This question (and also some links mentioned in the comments there) might be interesting for you: Chatting about mathematics (with real-time LaTeX rendering). –  Martin Sleziak Jul 31 '12 at 9:06
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You might also find something useful at TeX.SE, see e.g. Simultaneous collaborative editing of a LaTeX file and Compiling documents online. –  Martin Sleziak Jul 31 '12 at 9:09
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When I need it, I use writeLaTeX - there is a bit of lag, but overall it works.

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