Tuesday, June 12, 2007

Book writing

I have now started working on a project I have considered for a long time: a reference book. I'm not doing this alone, but even the little bit that I have to do myself feels like very hard work.

First of all, it is in some sense as hard as writing a research paper; many theorems are not proven in the literature, or they are proven but the proof is too technical and you start looking for easier proofs, or they are stated as "obvious" but turn out surprisingly difficult to write down in detail.

Plus, there's the difficult choice of how much to include; you cannot produce a book that no one will have time to read. In the moment we are trying to achieve a compromise, carefully labeling the material to distinguish core stuff from technical details, included only so that advanced users can find the necessary references.

Finally, you have to find meaningful examples and exercises. When you write an advanced mathematics book, it is tempting to stick to the "Definition-Lemma-Theorem-Corollary" format. But it is never a good idea. You need to give exercises, so that the reader can get hands-on experience of the new material, and examples, to connect what they have learned with what they knew before. In this particular case, it is likely that the book will be used as a reference by researchers with somewhat different backgrounds, so we need even more examples to accomodate them all.

We (here it means "me and coauthors") have decided to actually write two books: a more elementary one, which should be ready next summer, and an advanced one, to be finished in summer 2009. I do hope that we will manage, since now all the authors are either done with childbearing or not interested in it.

I am impressed by how some people either have an immense spare time or can write well fast. For instance, I am seriously considering telling my students to use The Unapologetic Mathematician as the main reference for category theory. He has written a number of beautiful, elegant posts, developing the subject in just the right degree of generality.

If I tried to do anything like that it would take me ages. And without outside help, it would never be as good. On the other hand, I am apparently the only one in my bookwriting project who is able or at least willing to take a particularly elementary approach (technically, I would call it more geometry, less algebra). So I think I should insist, however hard I find it.

Maybe I should do like See Jane Compute, and keep a sidebar with accomplished tasks. At least I would have three tasks accomplished before the deadline (namely C#1, C#2 and C#3).
I think they are unique wih this property: everything else I do, I am always late.


John said...

Firstly, I wish you well with your attempt. I hope to someday write one of those things myself. Who knows, one may eventually be adapted from my scribblings onlines.

I also must thank you for your kind words. As for how I do it.. it's a little of each. These days I spend most of my time moving out of my apartment, and my weblog is a welcome distraction. However, I don't really spend all that much time on the actual writing. To whatever extent it's good it comes out quickly once I sit down to actually write, and using this platform to build a reputation for myself is plenty of motivation to sit down at least once a day.

That said, there's a certain amount of luck in there as well. I hadn't planned to prove Baez' assertion about groupoids with faithful functors to groups when I sat down to write that post, but it just seemed the natural direction to go, considering what I'd said before and what I'm looking to say in the future, and I just followed what seemed the natural course of things.

If there's a Tao of mathematics, there may be a Tao of mathematics writing as well. It's easy to say, I know, but don't try too hard with your writing. If you do you'll just end up hating it. Find the natural course and just let the book write itself.

estraven said...

Whenever I let myself write freely I end up with the empty set. It is a kind of Penelope's activity: I write, and cancel, and rewrite, and recancel... it never converges. I must learn to stop canceling. Thanks for the encouragement.