If you have written a paper with someone you have come across this question:

How do we collaborate efficiently?

You probably ask it every time you collaborate because the answer is always slightly different.  Maybe you can physically meet with them, or you run into them in the lunch room every so often or maybe they are in a different city.  They might be working on the same problem as you or a different section of the paper, etc.

Much of the time, math problems are multifaceted, with sub-problems, ideas, conjectures and various proofs and write-ups on the back-burner.  I have attended many meetings where parts are spent trying to recall these ideas and remember where the write-ups are.  Often, an idea that will be important later will rush by us because we have a good problem to work on for the moment.

If you are like me, you have a different presence of mind when you are working alone than when you are meeting with someone.  Without delving into the psychology of mathematical cognition (something which I profess to know little about, beyond my own experience), it would be great to be able to think deeply like we do when we are alone and to feel the often upbeat synergy that comes from developing our ideas together.

Lastly, taking WIKIs as an example, knowledge and meaning develop differently when our discussions are written, as opposed to oral.  A good discussion can be followed and contributed to with relative ease.  A discussion in writing, however, adds a persistence of ideas that is not possible when it is spoken (see McNelly, Backchannel persistence and collaborative meaning-making, 2009).  This changes the way the group builds its ideas (for the better, in my opinion).  Currently, written communications for mathematicians tend to include drafts of the paper, comments of some sort, messy fragmented emails and reply-emails, the occasional instant message, and chalkboard scratchings if you are lucky enough to be co-located. Drafts of the paper are persistent, but they are not easy to contribute to in the form of a discussion.  Email is persistent, easy to contribute to, but hard to follow when there are several authors and several threads.  The other methods have similar problems.

Enter Google Wave.

If you haven't heard of this, do not go here (way too long) and don't bother with this (too technical).  Instead, watch the video below with the following considerations.  Wave has these things called robots and gadgets that add functionality (think LaTeX support).  The dream is to be able to collaboratively build a document in real time with LaTeX preview support, and then copy it all to a TeX file and compile it when you are done! (I would also like to be able to go out and play basketball in the rain and not get wet.  Now wouldn't that be nice?)

Google Wave solves a lot of the problems I outlined.  In the same wave (that's what an individual thread is called) that you build your document, you can make inline comments and side discussions or documents of related ideas.  You can collaborate in real time, or asynchronously, together or far apart.  There are other tools that have similar functionality (subEthaEdit, LaTeX enabled wikis), but Wave is the easiest to start using and the most likely to become useful in other ways.

Google Wave presents a few obstacles:

1. The LaTeX robots and gadgets that exist as of this writing leave something to be desired.

• There is a wave discussion on this (two actually, but the first one exploded).  Find it by searching in Google Wave for "with:public tag:latexforwave", without quotes.

1. You or your co-authors may not know how to use Google Wave.

• Find a friend with Wave and get an invite.  Familiarize yourself by searching for "with:public" and participating in a few public discussions.  It may seem complicated, but the learning curve is not so bad.  There are a million blog posts about how to use Wave so I won't say anything here.

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