I’m hosting the Carnival of Mathematics tomorrow, which is a little strange for me, since this is not actually a math blog.

Why not? I’m a mathematician, after all, and I spend the majority of my day thinking about math — so why don’t I blog about it very much?

I once had a conversation with a colleague of mine in mathematical physics about people who announce important results and then take a long time writing them up. I was complaining about such people, and my colleague was defending them. There are good arguments on both sides, of course. On one hand, if “everyone knows” that X has proved Y, nobody’s going to work on Y — but people may also be reluctant to prove things that depend on Y, since the proof hasn’t appeared. So a whole area of inquiry can get stuck. On the other hand, when things are rushed into print, there can be mistakes, or just inadequate explanations, and once the paper’s published it may be a long time before the author or someone else writes a really readable version. Anyway, my friend and I went back and forth on this for a while, and finally he said, “But really, why is it so annoying to you to have to wait a month or two to see the proof?”

And that’s when the lightbulb went on. For him, “a long time” meant “a month.” For me, it means “two years.” Physics is fast. Math is slow.

And I *like* that about math. I like that I don’t have to anxiously scan the new number theory postings on the arXiv each morning for new developments, and I like that I’ll never have to finish a paper by nightfall in order to avoid being scooped. In math we let our ideas simmer a long time before we share them with our colleagues, and even longer before we make them public. We’re contemplatives.

Math blogging, in some ways, works against that. If I blogged about my mathematics as it happened, what you’d see is a lot of first drafts, and a lot of “whoops! I take that back.” Wouldn’t you rather just read my paper, when I carefully, thoughtfully, and eventually, write it?

Two remarks:

- This is really an explanation of why I don’t blog about math I’m working on. It doesn’t apply to blogging of the form “Here’s a recent paper someone just posted on the arXiv, and here’s why I think it’s interesting,” a la Not Even Wrong. This kind of mathblogging is an unmixed good and maybe I’ll start doing more of it.
- An interesting counterargument might be something like: “Blogging about your mathematical ideas makes those ideas available to people outside your circle of elite research universities — since you do talk informally about these ideas with your colleagues inside this circle, it’s undemocratic and bad not to make them available to outsiders.” I haven’t decided whether this counterargument makes sense or not.

If it’s not too late, here is a submission for the math carnival. It’s mostly elementary or middle school level, but the last puzzle may challenge older students.

One thing I’ve liked in some of the few posts about math I’ve already done has been to be able to explain (or point out simply) a few things about a finished paper which I found interesting/amusing/enlightening while writing it, but which are not necessarily apparent when looking at the paper itself (e.g., recently, it was just an amusing way of keeping track of dependencies on variables in a lemma which is in no way important to the main ideas of the paper).

Here “finished” is an important keyword, and it is meant in the sense that the paper has been submitted for publication and is therefore in a state where I am comfortable with other people reading it. I don’t particularly feel like discussing vague ideas online when I am working on them.

About the problem of people not finishing to write something: in a paper in (I think) GAFA 2000, Novikov comments on the state of topology at some point in the 70’s or 80’s, where a few important theorems did not get written up correctly. There was a story a bit like the following (I may have misremembered some details): at some point, a “new” proof was proposed of one of those theorems (say Theorem A), but the authors did not realize that they applied another one (say Theorem B), the (unpublished) proof of which depended heavily (and hiddenly) on Theorem A…

I think that most important part of writing about math is making it readable to those who don’t get it.

If my co-worker had a dime for every time he hard that all of the winners in the Wisconsin Lottery were from [INSERT REGION WHERE PERSON DOES NOT LIVE].

If only people with mathematical training could disabuse people of these false notions and logical fallacies regarding mathematics, probability and functions.

Meanwhile… http://www.slate.com/id/2185975/ this is too complicated. Most people would be happy with method. The square of the difference in score is greater than the seconds remaining, the lead is safe.

I think it’s understood that when people blog about their ideas of a technical or even non-technical nature that they are not writing for the ages; that they are allowed to change course or even contradict themselves at a future date.

Blogging is expressing your current notions so that other people can look at them, maybe give helpful feedback, maybe get inspired by them to do something different. In the language of the philosophy of science, blogging is within the “context of discovery” rather than the “context of justification”; it corresponds to scribbled notes rather than published papers.

What’s more, although the scribbled notes may be harder to follow than the published paper, they may also be easier. Somehow I suspect that it’s at the final polishing stage that people go through and replace talk of subsets with talk of functions to the truth values, or define that very simple thing, a group, in the complicated phraseology of model theory. (Both examples due to Quine.)

Now you may be the kind of person, like Andrew Wiles or Douglas Hofstadter, who can’t stand the notion of anyone looking over their shoulder, and don’t want to present their professional ideas until they have total control over the what, where, and when. But if not, then do let us in!

(I’m not even speaking for myself, since Mathesis loves me far less than I love her, and I probably will have no faintest clue about whatever you say about whatever hypertwistoploppic pseudotheomorphisms you are working on these days. I’m speaking for the interested world at large.)

I buy it. A blog where a mathematician writes, but not a math blog.

For me, a math teacher blog is possible – but there is (naturally) a huge difference in tempo.

Jonathan

Hi Jordan!

While I personally would love to see posts here about maths, you hardly need to justify it if you decide to do something completely different with your blog. I will point out, though, that unlike formal mathematical journals in which it is difficult to retract or amend anything that you publish, in a blog you can correct errors in a matter of seconds, and so one does not need to devote the same type of painstaking care and attention to detail to mathematical blog posts as one does to mathematical papers. Mathematical blogging seems to be sort of a blend between the formal world of mathematical publication and the informal world of mathematical discussion; I think the format has great potential to be the “best of both worlds” in many respects.

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