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I apologize if my question is not appropriate for this site, but I am interested in the opinion of mathematicians... in fact I would like to learn as many different opinions as possible.

The question is how do you manage the ideas during research, possibly in collaboration? I know this sounds way too general, but here I am interested in the technical aspect, so by "ideas" I mean sketches of some computations, questions, observations etc.

For instance, when you have an idea of some proposition and its proof, do you keep it in mind or on a handwritten paper, or write in some LaTeX file and then put it on some file hosting service like Dropbox (or maybe you use service like JaxEdit, writeLaTeX etc.)? How do you share it with your colleagues when they are not available personally?

P.S. I think this question should be community wiki, but I don't know how to set this.

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