Why write papers?
Here is what Dror Bar-Natan had to say about that on MathOverflow:
Papers are written so that their author(s) can forget their content and move on to other things. Therefore when you write you should be very careful to put in enough of the big picture and enough of the details so you’d be able to reconstruct your thoughts 10 years later if you’ll need to, assuming you’ll forget everything but retain some familiarity with some basic principles of mathematics.
It’s nice to think that papers could be so useful in light of the recent publishing debate…
Haha, that’s a pretty self-centric point of view. We write papers so that ten years later we may remember them?
Joel David Hamkins wrote
I like to read my own papers from 10 years ago…sometimes I learn something useful.
Peter Krautzberger wrote
I like this statement. For me it also makes a very good point why we should separate scientific progress from publication. In fact, it reminds me of Claire Mathieu’s post reacting to the publishing debate spawned by Gowers: publish other people’s work. It’s the old “communicated by” idea taken seriously, we should never publish our own results – or, a little softer, we should never publish alone.
Reading Michael Nielsen’s book I’m starting to think that Shelah’s model is actually the future (though not as papers). We cannot afford the Wiles, the Grothendieck or the Perelman model of research.
François G. Dorais wrote
I’m glad Joel confirmed this. The more I think about this, the more I realize how great advice this is. My next paper will be tacitly addressed to my future self. That’s much less awkward than writing for an imaginary reader who may never materialize…
Peter, it seems there are some missing parts in your second paragraph. I’m assuming you don’t mean Michael’s textbook on quantum computing. What are these models you’re talking about? I don’t see any sense in which Shelah, Wiles, Grothendiek, and Perelman would constitute realistic models for run-of-the-mill mathematicians.
Andreas Blass wrote
Although the intended readers of my papers are other mathematicians, not myself, I agree with the advice to put in enough information so that the paper will make sense to me 10 years from now. It’s embarrassing to write “clearly,” “obviously,” etc., and later be unable to remember why these things were clear, obvious, etc. I hope that, by making things clear to my future self, who won’t remember my present network of ideas, I also make things clear to my present readers who (I expect) have not yet explored that network.
Andreas, That last remark makes me think: we should be writing papers to ourselves ten years ago!
Micheal replied to Andreas Blass
Great post! This reminds me a lot of how Stevo Todorcevic writes his papers. As few details as possible while still allowing the (dedicated) reader to follow along.
No, there wasn’t anything missing. It was just poor writing on my part.
I meant “Reinventing discovery”, Michael Nielsen’s book about how the web will change the way research is done. I just finished part 1, hoping to post a review at some point. It’s an interesting read so far, partially well known to me (e.g. polymath), partially surprising, partially confusing.
What I meant with “Shelah’s model” is the idea of massive collaboration, spreading and helping as much as possible. With “Wiles’s model” I meant the idea of hiding preliminary results for years so that nobody can scoop. We need a different attitude towards making influences transparent (and the tools to give credit) so that we can find ways to modularize research much further.