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.
A grad student fellowship
4 hours ago