As discussed here the new Stacks project website allows you to leave comments. In this blog post I’d like to advertise this as a fun activity and as well discuss what kind of comments I’d like to encourage. Before we start a disclaimer:
Comments are not part of the Stacks project. When you leave a comment, it is just a comment and nothing else. Don’t worry about correctness, etc. It is just a hope that occasionally comments will be useful and the material will find its way back into the Stacks project, but we’ll see.
Comments pointing out mistakes: Perhaps the most obvious way to use the comment system to this is that it is real easy to point out mistakes. For example I just left two comments pointing out silly mistakes. While reading the Stacks project in pdf form, if you encounter a mistake no matter how silly, just click on the embedded link to the tags’s page in the pdf and leave a comment. Any misspellings, typos, latex bloopers, mathematical mistakes (of course there aren’t any!), etc are very welcome.
Comments giving references: Another type of comments would be one where you leave references to papers, books, mimiographed notes, and whatnot that contain results similar to the one contained in the tag. Here are two examples.
Historical comments: Part of the idea of the comments system was to have people put in comments like: “This result was first shown in 1966 by so and so.”
Sign-off: Another idea for the comment system was to have mathematicians sign-off on some of the results: “I solemnly declare this mathematical result to be correct”.
Typographical comments: You are very welcome to leave typographical comments. Usually these are easy to implement. However, there are a lot of peculiarities in the LaTeX coding which I for better or worse decided on when first introducing certain symbols and mathematical notation. We eventually have to drastically improve the handling of these in the Stacks project, and Pieter Belmans and I have some ideas about how to proceed. I’ll discuss this in a future blog post.
Comments on how to improve exposition and results: I’d love to hear your suggestions on how to improve the Stacks project.
If you’ve read this far, then I’m sure you see what I’m trying to say. But to give some impetus I am going to challenge you to find mistakes:
T-shirts for mathematical errors: If you leave a comment pointing out an actual mathematical error in a statement or a proof of a lemma, proposition, theorem, or a mistake in the text of a section or remark, then I will send you a Stacks project T-shirt while supplies last (currently I have 1 large and 3 medium T-shirts — I’ll update this until I reach zero). Make sure to leave a working email address so I can reach you to get your address.