An experiment concerning mathematical writing

Update: comments on this post are now closed, since my latest post would compromise any further contributions to the experiment.

Most of this post consists of write-ups of proofs of five simple propositions about metric spaces. There are three write-ups per proof, and I would be very grateful for any comments that you might have. If you would like to participate in the experiment, then please state your level of mathematical experience (the main thing I need to know is whether you yourself have studied the basic theory of metric spaces) and then make any comments/observations you wish on the write-ups. The more you say, the more useful it will be (within reason). I am particularly interested in comparisons and preferences. For each proof, the order of the three write-ups has been chosen randomly and independently.

It would also be useful if you could rate each of the 15 write-ups for clarity and style. So that everyone rates in the same way, I suggest the following rating systems.

Clarity.

-2 very hard to understand
-1 hard to understand
0 neither particularly hard nor particularly easy
1 easy to understand
2 very easy to understand

Style.

-2 very badly written
-1 badly written
0 neither badly written nor well written
1 well written
2 very well written

I stress that ratings should not be regarded as a substitute for comments and observations, or vice versa. What I really need is both comments and numerical ratings.

I do not want people to be influenced by the answers that other people give, so all comments on this post will go to my moderation queue. When I have enough data for the experiment, probably in a week or so, I will publish all the comments (unless for some reason you specifically request that your comment should not be published).

The more people who participate, the more reliable the results of the experiment will be. I realize that it may take a little time, so thank you very much in advance to everybody who agrees to help. (Update 26th March: I now have over 30 responses; they have been very helpful indeed, so I am extremely grateful for those. If they keep coming in at a similar rate over the next few days it will be wonderful.)

Test

I am testing the WordPress feature that allows me to moderate all comments before allowing them to appear. This has nothing to do with the discussion on the last post. Rather, I want to be sure that the feature works before my next post, where it will be important for people to comment without seeing what others have said. So if someone could make a quick comment on this post, that would be helpful. Once I’m sure the feature is working, I’ll put up the post for which it matters.

In an ideal world, I would use the feature just for that post. However, as far as I can tell, my only options are allowing all comments, moderating all comments, or disabling comments completely on individual posts. Sending comments to the moderation queue on a post-by-post basis doesn’t seem to be possible, but if anyone knows a way, then I’d be very pleased to hear about it. Assuming there isn’t a way, then for a short while, all comments on this blog will be moderated, but I will try to approve comments on other posts regularly, so I hope this won’t be too annoying.

Update. Good job I did this test. I changed the relevant setting but didn’t click “Save settings”. Hence the three comments below.

Further update. OK, now it seems to be working just fine. Many thanks to those who sent test comments. I’ll put up the new post later this evening (British time).

Pierre Deligne wins the 2013 Abel Prize

I have just finished presenting the work of this year’s Abel Prize winner, who is Pierre Deligne. In due course, the talk will appear on the Abel Prize website. As in the last two years, I have also prepared a written version of the talk, which goes into more detail. However, even the written version leaves a lot out. It was intended for a general — that is, not necessarily mathematical — audience, though I had to assume at least some maths. If your level of mathematical experience means that you find it too elementary, then I have three recommendations for further reading. I found these slides of Kumar Murty about Ramanujan’s tau function helpful and interesting. I also very much like Brian Osserman’s article on the Weil conjectures, written for the Princeton Companion to Mathematics. Finally, Nick Katz did the laudatio for Deligne’s Fields Medal and wrote an excellent article on his work. (Another article that I stumbled on only recently that looks incredibly nice, which is not about Deligne, though it mentions him, but which sheds interesting light on some of Deligne’s work is Finding Meaning in Error Terms, by Barry Mazur. So far I have just skimmed through some of it, but I think I’ll be going back to read it in more detail.)

The work of Endre Szemerédi

A few years ago, Springer published a book called, The Abel Prize: 2003-2007 The First Five Years. A brief calculation will reveal that a second volume ought to be due soon, and that is indeed the case. I was asked to write the article about Endre Szemerédi, the 2012 winner, which I have just finished. I am glad to say that Springer’s policy with regard to this book is extremely enlightened: not only am I allowed to post my article as a preprint, but the entire book will be posted on the Norwegian Academy of Sciences website and will be freely accessible.

I was told to write the article as I pleased — the articles in the first volume are very different in style from each other — so I went for a style that was not unlike what I might have written if I had wanted to present several of Szemerédi’s results in a series of blog posts. That is, I’ve tried to explain the ideas, and when the going gets tough I have skipped the details. So it seems appropriate to post the article on this blog.

If you look at it and happen to notice any typos, false statements, wrong emphases, etc., I think it isn’t too late to make changes, so I’d be grateful to hear about them. Here is the article.