The n-Category Café

Cranks. With the ease of the internet, they’re around a lot more than just in unsolicited manuscripts in your mailbox.

No matter what you say, no matter how innocuous, there’s going to be someone who will take dire offense to it, and will not hesitate to let you know. What you need to know as a blogger is that just because one attacks you it doesn’t mean there aren’t a hundred people silently agreeing. Politely, firmly turn the crank aside and ignore him (or ban him if you know how) if he keeps coming back.

That wordpress.com allows LaTeX in the body text.

I was also asked to contribute a piece, but I think it would be more in the spirit of the maths blogging enterprise if I comment here instead.

I’m of course very enthusiastic about blogs as a medium for mathematical communication; it seems to fill in a niche between formal mathematical publications and informal seminars and conversations, as it combines the durable availability of the former with the interactivity of the latter. In particular, it seems to be the best place so far to put “folklore” and other iotas of mathematics that are individually too trifling to publish (at least, until the maths wikis build up more momentum).

Blogging is quite labor-intensive in the short term, but I find it has some time-saving effects in the long-term. For instance, I have found myself having to give the same speech about some mathematical topic to multiple graduate students over the years; it’s more efficient to put up a blog post on it and then to point all the students at that (and come back if they have more questions). Plus, the post gets enriched by further comments from other readers. In a similar spirit, I have found that one of the most efficient (and enjoyable) ways to learn a subject properly is to blog about it thoroughly.

There are other unexpected side benefits too - my papers get proofread a bit more, the references become more complete, and I learn all sorts of random bits of mathematical culture and knowledge that I wouldn’t otherwise be exposed to.

There are some non-trivial issues though. For instance, it is very possible to say something stupid (mathematically or otherwise) on a blog, which could then exist permanently on the internet for, say, a future employer to read about. I think this deters many mathematicians from participating, but it really shouldn’t; these free-form discussions shouldn’t be held to the same level of accuracy as formal publications. This may be a poor analogy, but it’s sort of like the difference between scripted comedy and improvisational comedy; one can slip up in the latter and not affect one’s reputation for the former (in some ways, it can even enhance it, if one recovers well.) Certainly I have great respect for many of the commenters on my own blog just for contributing their own thoughts, even if (or especially if) they are not in polished form.

I’ve had occasional issues with cranks, but one can simply delete any worthless posts, or in extreme cases, ban IP addresses and the like; this is the blog owner’s prerogative, and those posters are free to start their own blog if they want a forum.

LaTeX support is of course essential. Luca Trevisan’s LaTeX to Wordpress converter (with its automatic equation numbering, etc.) is particularly good for extended blog posts, though of course not applicable in this particular blog.

I think I’d sum things up by saying that mathematicians need to know that blogging is now a serious part of mathematical culture, so if they are not having at least an occasional look at what people are saying on their blogs, then they are missing out. And many other mathematicians are missing out on the interesting comments that they could (with very little effort) be making.

A more specific comment I might make is that there is a gap in the blog market that’s waiting to be filled. A blog is a great place to put ideas that are interesting and informative to many people but not suitable for a research paper. But the people who are writing posts of this kind are not covering all areas of mathematics by any means. I don’t want to say which areas are not covered in case I forget about a blog that does in fact cover an area I mention, but I can pretty well guarantee that a blog that had posts that explained ideas from parts of maths that are far from analysis/combinatorics/computer science in an accessible way would attract a huge number of hits.

Having said that, a mathematician who wants to set up a blog like that has to know how to write in a certain style: informal, but also precise enough that non-experts can follow what is being said. But such people exist, and they should consider blogging, because the market has not reached anything like saturation point.

I’m posting anonymously for various reasons that’ll probably become clear later on, although I suspect a select few people will still be able to guess who I am.

I have a mathematical blog, not as widely read as this or Terry’s, but with its share of followers; I also read and participate in a fairly wide selection of other math blogs.

First, the good things about mathematical blogging: like Terry said, blogs are currently the best place to write things that aren’t suitable for mainstream publication and are too trivial or nebulous to go on the arXiv or on a personal homepage. It’s also nice that one can discuss topics not directly related to research online – things like history, pedagogy, or career advice.

Another advantage, particularly for those of us without the stature of a Terry Tao or a Tim Gowers, is the meritocratic nature of blogs and the Internet in general; a bright high-schooler or undergrad has the opportunity to contribute as much to a discussion as a tenured Harvard professor.

There are some disadvantages, though. The anonymity of the internet (and the ability for anyone to comment) can lead to cranks, but it also can lead to flame wars. (Read the anonymous comments on some of Lance Fortnow’s more contentious entries some time.) Blogging and contributing to blogs isn’t for the faint of heart or ego; particularly if you wade into discussions of non-mathematical topics, you and your strongly-held beliefs are liable to be attacked, and not necessarily civilly.

Keeping with the ego theme, I have to admit: it can be hard not to view blogging as a popularity contest. When Blog X links to Blog Y but not your blog, or when Dr. W leaves a terse note in reply to one comment of yours while effusively praising every word Professor Z writes, the natural human response is envy. Of course, this is by no means confined to the blogosphere, but it would be unfair and untrue to suggest that the math blog world is some sort of harmonious Platonic meritocracy.

In conclusion, maybe the best analogy for the blogging world is the conference hallway; informal, surprisingly fertile, and often more enjoyable than the stuffy talk given in the lecture room, but at the same time inhospitable and occasionally petty.

In arguing the case for blogs to newcomers it may be useful to give an idea of the time it requires on a daily or weekly basis, and also to provide figures about the average number of readers, and of commentators, of a typical blog post. The pros and cons of both single-author and multiple-authors blogs might also require some explanations.

A side remark I’d like to make is that even though most mathematicians understand english well-enough to read a paper and talk to colleagues, maybe some of the non-native english speakers who live say in Europe or Asia perhaps find it a bit difficult to follow quick replies and slang words, and prefer moreover not to write in their not always perfect english (while on the other hand blogging itself in their native language would be no problem to them). This might explain that some subjects are not well represented as yet.

Here’s a few quick thoughts. I’ve repeated a few comments made earlier, where it seems like there may be value in hearing the same comment from more than one person.

* There are many free blogging platforms. A good one is wordpress.com, and it has the benefit of allowing LaTeX.

* It’s not clear how long any of this will be preserved. Will the material in our blogs still be around in 20 years time? What happens if wordpress.com or other services go bankrupt? The Wordpress software itself is open source, so it’d probably be possible to move to another host, but this is potentially a worry.

* Regularly allowing anonymous comments sometimes really brings out strange behaviour, behaviour I wouldn’t have believed if I hadn’t seen. I don’t like pointing out examples — it feels like I’m criticising the blogs involved, which is not true (there are some wonderful blogs with awful comments) — but you can probably easily supply your own examples.

* To address the previous problem, when people submit comments I require people to enter an email address, and I hand-moderate the first comment from that address. If I allow it through, subsequent comments are passed through moderation automatically. This is, I believe, the wordpress default, and seems to strike a happy balance between allowing comments through, and suppressing rude or unproductive comments.

* With that said, the comments on many blogs are simply astonishingly good, adding all sorts of extra insights and perspective to the original post. Polymath1 is an extreme example, but it’s at the end of a continuum: I’ve seen many wonderful comment threads here, and on many other blogs.

* Handling comments is, in general, a skill that has to be learnt. I don’t know if anyone’s ever explained the elements of that skill, but a start is here: http://nielsenhayden.com/makinglight/archives/006036.html.

* The range of the blogging medium is still being defined. That’s exciting: blogs like the n-category cafe, the Polymath Project, and Terry’s blog are all helping expand the range of the blogging medium. There’s almost certainly a lot of potential in the existing tools that is not being realized. And, of course, many of the tools will certainly be enhanced a lot in the years to come.

* Some people will no doubt see it as crass, but I think there’s value in mentioning the audience sizes for some of the blogs. This is important for many reasons, but one is simply the fact of exposing mathematics to a wider audience. A lot of undergraduates and high school students are reading these blogs. So are many people in other professions - I see math blogs surprisingly often on the front page of sites like Hacker News (a site mainly for startup entrepreneur). The best mathematical blogs make mathematics seem astonishingly alive and important to people outside the profession, and that’s a very good thing. (When I was catching up on the Polymath1 comment threads I continually found myself getting tense, rather like I was watching a suspense movie. Perhaps my reaction was idiosyncratic, but I like to think it’s a response others might have, too.)

You might find some interest a short essay I wrote earlier this year on the value of mathematical blogs — it’s at http://michaelnielsen.org/blog/doing-science-online/. The editors at Nature Physics liked the essay, and published a revised version earlier this year.

I’d agree with Terence Tao and Qiaochu Yuan that blogging is a productive way to learn a topic; I have posted multiple times on material that I vaguely understood but wanted to learn better, and now not only will retain it better, but will have a source to refer back to in the future. Since I know that other people will read the post, I have additional motivation to do a better job. I’ve also learned quite a bit from the comments.

I also think there is also plenty of room in the mathematical blogosphere for many new websites, since there are large areas of mathematics still not covered. It should not be hard to find a niche.

Group blogging offers the benefit of interactions between the individual bloggers and boosted activity. When the different bloggers have different mathematical interests, the blog can become more lively as a result.

Despite the title of the thread, I also think one more important point is the following: Mathematical blogs are not just for professional mathematicians. Students, too, can benefit from blogs; for instance, the opportunities to discuss mathematics in a high school setting are somewhat limited, but can be expanded significantly through both one’s own blog and comments elsewhere.

I like to think of math blogging as a notebook for thoughts. Except there are many many benefits you don’t get from an ordinary notebook.

1) You get other people’s comments (which often give insight into something you hadn’t thought of before).

2) The notes are typed.

3) The notes are incredibly easy to search.

4) Other people are reading your notes, which helps you find typos and keeps your writeup honest.

5) You never run out of pages or lose the notebook (there is the slight concern brought up by an earlier comment about a website going under).

There are probably lots more that I’m just not thinking of right now.

I believe that every serious (and/or fun) Math Blogger should:

(1) Make (if only for personal and students’ use) a list of their 10 favorite Math Blogs and 10 favorite Math web sites (these may intersect).

(2) Think through your constructive yet real competition with these. What is your objective regarding a sustained competitive advantage?

(3) Think through your real competition with your suppliers (guest-bloggers, ISP, blog host, software infrastructure, university or corporation or agency, paper and online journals, book publishers).

(4) Think through your real competition with your customers (i.e. readers, editors and readers of spinoff papers, books, TV appearances, etc.). If you are mostly free but also sell something (T-shirts, mugs, your books) then pricing theory is the way to optimize that component.

(5) Think through your real competition with government (taxation, regulation, copyright, trademark, patent, freedom of speech).

(6) Think through your real competition with changes in technology that alter any of the other items in the list.

I believe that if you fail to do any one of these, you will asymptotically lose market share (attention, eyeballs). If you do them all, you are not guaranteed to attain your objectives, but your probability will be larger.

I credit John Porter, Harvard Business School, for his classification of Competition, and I take blame for any misunderstanding thereof.

Two more points which I didn’t see on previous comments:

(1) Community: even mathematicians are people and have a need for bonding into communities. Blogs play a part in serving this need for community-wide interaction, especially when there are a several interacting blogs in the same field (like the case in TCS). This is particularly important for graduate students and for those in remote locations. (Remote from what? Usually remote from the US.)

(2) Really fast really wide dissimination of important or interesting new results. For example this year, in the TCS blogosphere, we saw much discussion of three neat results: Braverman’s, Moser’s, and QIP=PSPACE. Of these three, two became widely known before they appeared in a conference or journal. While I am sure that these are not THE best three TCS papers this year (whatever that means), these are great results that I got to know about even though they are outside of my own research field.

Well, also, you get the added bonus of writing a sort of “self contained blog-notebook”. For example, my notes on category theory has all the category names be links to where they are defined, because - knowing myself - I’d forget what nCobHomDom refers to…or why it’s called that.

With a notebook, I have to resort to color coordination and even then it becomes a rainbow as opposed to a useful reference.

Better, if someone else blogs something useful, or some article on arXiv is relevant, I can directly link to it rather than having an ad hoc in-notebook bibliography system.

Just my two cents on something blogs add that notebooks don’t really have…

Perhaps the most common question I get asked is “how do you get time to blog” (and the second one is “where do you get your ideas from”.

Blogging does take time, no doubt, but it takes far less time than most people think. Terry’s blog is of course the perfect counter-example, with the density of material in each post, but it’s also the perfect exception. Most blogs aren’t like that, and yet are stlll quite useful.

When people ask about blogging, they always say, “but I don’t want to write about my cat”, or “I can’t write like Terry Tao” :). I think it’s important to emphasize (as other commenters have said) that the blogging medium is flexible enough to have many different successful models, and that the best way to find a model is to start a blog and experiment: soon enough you’ll find something that works for you.

Thanks for all the great replies! I’m happy that this subject has gotten comments from many people who don’t usually post here. I’ll try to put a link to this blog entry in my opinion piece on the Notices — there’s too much good stuff to summarize in 800 words. Plus, it’s a little example of the power of blogging.

Another thought is about visibility: most blogs have a “blogroll” of a select few other blogs, but it would be very nice to have a comprehensive directory of math blogs. A simple webpage on a moderated wiki somewhere would do, detailing for each blog: link; author(s); average level of exposition (e.g. high school to research; research-only,…); and of course math areas (rouhly, perhaps with MSC or arXiv-like tags).

For example I only learnt about Danny Calegari’s nice blog recently through Terry’s blogroll, and I’m sure I’ve been missing other great blogs for some time. It must be more than slightly non-rewarding for them to do high quality blogging yet receive very few comments and page hits: a semi-official directory may well improve that situation.

Will you talk about the capacity of a maths blog to open up lines of communication to other disciplines? It has been my hope from the start of this blog that the Café will facilitate a deeper engagement of philosophy with mathematics. Still a long way to go!

It’s probably also worth mentioning ways to make it easier to *read* blogs, considering your target audience: aggregating everything to Google reader, etc.

For mathematicians who know nothing about blogs:
Mention a couple to look at: Tao’s at http://terrytao.wordpress.com/, maybe AMS Grad Student Blog at http://mathgradblog.williams.edu/

Mention RSS feeds.

For mathematicians interested in starting a blog, tell them in detail how easy it is to get started using WordPress e.g.

Frank Morgan http://blogs.williams.edu/Morgan

http://math.williams.edu

Maybe the most important thing I get personally from mathematical blogs is some access to current mathematical research and progress in a (much) wider range of fields than my own. Of course there are some other sources for this type of information, for instance the Notices and Bulletin of the AMS, and the book reviews of various mathematical societies, but these respond usually slower to current events.

This applies already when one is simply reading blogs; but writing one also gives at least a chance of presenting some of my own interests, remarks and results, and getting people well outside of analytic number theory to have a look at them.

So in the long run, it seems that blogs are one of the best ways to compensate for the specialization of research.

I’d like to point out that a math blog also serves as a medium for interactive teaching. For instance, Terry Tao has been exceedingly patient and gracious in responding to questions from the public at large(quicker and more detailed responses if your screen name contains string like “student” or “beginner”, of which some professional mathematicians might have taken advantage). Where else can you have this level of accessibility to a world renowned academic?
Elite institutions such as MIT have been providing free access to many of their lectures online, but it’s esentially a one way thoroughfare. Academic blogs are the alleyways to get back to campus.

Now for a comment from the (semi) lay audience. Without blogs, I would have lost contact and inspiration with math. I live outside town, and the local Barvarian uni math library is closed almost surely when I manage to get around to get there. So I haven’t seen the library for almost a decade. One reason I left the PhD behind was my dreams of collaborative internets math paradise (meanwhile much come true) and the fact that they didn’t allow me a decent computer in my office while happily paying me a full Studienrat salary. It felt like being forced to scribe on clay tablets, while everyone else had ink and paper.

Certainly blog and blogging is an interesting phenomenon that I am quite curious about. It can be very interesting to look, also from a skeptical point of view, at mathematical blogging.

This reminds me of email, an earlier revolution in human communication with profound implication on our life, in general, and on mathematical communication especially. (Also in this case it had mixed effects.)

Many things that were very difficult some decades ago regarding writing papers, communicating, and having quick access to information became too easy. It is not clear if this had much effect on where the real deadlocks for progress in mathematics are.

I am a maths graduate but not a mathematician. I read this blog to help motivate me to learn category theory and I read ‘good math, bad math’ for entertainment. These seem to represent two extremes of the Math Blog spectrum; the only things they have in common are exploring maths and being consistently interesting. Something like Todd & Vishal’s blog falls in the middle. I think the fact that you can potentially communicate with a wide range of inerested folks is the advantage, and the need to couch any exposition so that the discussion brings them with you rather than starting 5 miles above their head is the challenge. The payoff isn’t just that you get responses; if you increase outside general interest in your specialist area, that is also significant.

for those who read French, I would advise to take a look at the “Annales de Gergone” http://www.numdam.org/numdam-bin/feuilleter?id=AMPA_1810-1811__1_
It was the first journal of mathematics to exist, and was run by a single man Gergonne himself. He used to post his own mathematical discoveries or questions, and often non professional mathematicians (high school teachers, students…) either answered these questions or commented on previous contributions. Doesn’t it remind you of something?

One small point, which has already sort of been made. I used to put expository material on my web page, which has a webcounter. When I put similar, or in some cases identical, material on my blog, the audience was larger by one or two orders of magnitude. And the average quality of the comments is very high – many times I have thought that I had completely understood a topic, and then someone has contributed an insight that I had not had. I think some people think that all blog comments are like the strange ones one might read on a political journalist’s blog.

I think an important point is that mathblogging is only one of many aspects of online mathematics. Things such as the arXiv, the Tricki, the nLab, Wikipedia, various online databases, and new forms of publishing might possibly be the beginning of a major shift in how mathematics and science in general is done. Another aspect is new opportunities for collaboration, with for example the Polymath experiments and tools such as Google Wave. There are many interesting insights on all this in this other post of Michael Nielsen.

You might consider addressing head-on the sceptical things that some mathematicians say about blogs. Of course, you’re unlikely to hear those things from the people who comment here, but perhaps you know sceptics and could get them to articulate their views.

Some mathematicians think that blogs are a waste of time. Research articles are the serious stuff. Why don’t you stop pouring time into this ephemeral stuff and write papers instead? Some mathematicians say that what you read on blogs is unreliable. Some worry that if they post their ideas on blogs, other people will steal them.

I can’t remember what other criticisms people make. I’m such a convert that it’s an effort of memory. But I’m sure you can find plenty more negative opinions.

There are a few things which are initial deterrents to my wanting to start a blog.

First, and this has been mentioned a lot, the time that it would take to get up and running.

Second, mentioned a little, is that having a blog exposes you to seeming stupid. This especially applies to the sort of blog I’m contemplating, which would be a discussion of all the conjectures, half-finished projects and quarter-baked ideas I seem to have accumulated. My blog would contain a lot of dumb things, wrong ideas, and show off places where I’m stuck though lack of knowledge or skill.

Third, possibly not mentioned here so far, is the link - or lack of a link - between blogging and traditional academic publishing. As an early career researcher, I’m feeling a lot of pressure to get my publication count up, especially in “top” journals. OK, so what happens with citation and plagiarism? Say I put up some partial result on my blog, then I later go to publish and find that it’s already been published by someone else with no attribution to my blog? It could be a case of independent discovery, or it could be plagiarism. Do I publish, citing the dubious work? Do I try to investigate, or do I just let it go and work on other things?

Here are some concerns about mathematical bloggings (ML):

1) ML may sharpen attention inequality between mathematicians, areas, and problems

2) The inbalance in 1) will be, in part, based on issues which are orthogonal to mathematics

3) ML could make mathematical activity more entangled; harder for independent ideas to get thoroughly and independently studied

4) ML make it more difficult for non-English speaking mathematicians

5) ML may shift interest to informal (even vague) discussions of conceptual issues (or even gossip issues) rather than the technically and rigourous traditional way of doing mathematics

6) ML will blur the borders between research activity, pedagogical activity, and scientific journalism

7) ML will give incentives to “high rating activity” which maybe negatively correlated with high quality mathematics.

Perhaps the following advantage hasn’t been mentioned so far.

The blog I maintain is mostly for students and my posts mostly replies to questions. But I’ve found it to be practically very useful when traveling. That is, most research mathematicians are on the road quite a bit, and have to reschedule office hours frequently. The blog helps the students feel constantly connected, giving the mathematician a good deal of freedom of motion. As far as time goes, I think most of us have periods when we’re not quite focussed enough for research (say in a hotel room), and it seems not so hard to fit in some extra writing then. Of course there is also the fact that the same question doesn’t have to be answered twice.

Sorry to have come late to this interesting thread – I hope John, at least, is still reading.

I think that math blogs will flourish to the extent that barriers to entry, both real and perceived, get lower. To some extent that’s simply a function of it being perceived as a “normal” thing for a mathematician to do. More specific thoughts on this:

1. My own blog is quite a bit different from the “usual” math blog, if there’s yet such a thing. Namely: it’s really a personal blog in which about 30% of the posts are in some sense about math, and the rest is about books I’m reading, records I’m listening to, the baseball team I follow – you know, the stuff that 95% of all blogs are about.

On the one hand, I think this makes my blog less “serious” – on the other hand, WordPress makes it very easy for anyone who doesn’t care about my favorite baseball team to read only the posts tagged “math.”

I think many people who don’t feel up to the task of producing the amount of high-quality mathematical exposition per week that Terry does might feel more capable of, thus more inclined towards, doing what I do.

2. Writing good exposition suitable for newcomers to a technical field is very, very hard, and simply can’t be done in a short space. If I asked this of myself all the time I wouldn’t blog. Instead, I use blog posts about new papers I’ve noticed or talks I’ve seen as ways to record for myself what I take to be the main points, or what I want to remember. Sometimes these posts are legible to people outside a specific research area, sometimes not. I think this is OK and we should make sure potential bloggers know this is OK.

3. I rarely use LaTeX in my blog, just as I rarely use LaTeX in e-mails about math. Somehow this works for me as a psychological aid, reminding me that what I’m writing is supposed to be conversational and not something I’d write in a paper.

4. Someone asked above about the actual size of the readership of math blogs. Mine is very small compared to Tim’s or Terry’s or nCat – about 130 subscribers on Google Reader, between 200 and 300 hits most days, somewhere between 0 and 5 comments on most posts. It’s worth telling people that your blog doesn’t have to be mega-popular to be worthwhile; I’ve found my blog to be fantastically satisfying, and I don’t begrudge any of the time spent writing it.

5. Now I’ll throw in one piece of barrier-raising: I think the concern of “sounding stupid” is one that senior folks like me, and many other math bloggers, can safely ignore. But younger mathematicians are not at all wrong to worry about it. I’ve certainly had the experience of hearing that senior mathematician X has formed a bad opinion of young mathematician Y because of wrong or careless postings on Y’s blog.

On the other hand, any blog likely to generate this kind of negative reaction from professor X_1 no doubt increases Y’s name recognition enough to helpful at hiring time, when blog-reading hiring commmittee members X_2, X_3, and X_4 have some prior knowledge of Y’s interests and work.

There may be a difference between what math instructors need to know about blogging and what mathematicians need to know about blogging.

When I’ve looked around the math blogging world, there seem to be two groups of bloggers - those that focus mostly on the scholarship of teaching and learning math, and those that focus on high-level mathematical research.

Since you’re writing for the AMS, I suspect you’re focusing on that second group of bloggers. However, there are many useful math blogs out there who’s primary focus is to improve teaching and learning.

Personally, I blog to synthesize what I’ve learned and to share it with others to help flatten the learning curve.

I’ve been blogging about math, teaching, and technology for 2 years now over at Teaching College Math.

Blogging is a great option for some personality types: for people who generate ideas faster than they can write papers, especially for people who can lose their interest in a particular small subject very fast.

It takes me several months to write a paper, and several days to write a blog essay. By blogging I get my emotional reward, that I have accomplished something, much more often.