This, here, is me trying it out. With any luck, the appearance of a new toy will get me back to actually blogging some more – it’s been winding down a bit much here lately.

He has, recently, written a post inspired by the xkcd comic on purity in the sciences. The comic is funny, and rings true, but Ben brings up a severe criticism of the premises of the comic that rings back to my own years as a hotheaded undergraduate.

You should read all of Ben’s post, but if you don’t, you should at least read the following:

And I think one of the key points here is this: mathematics is not science. Mathematics is often lumped in with science, and is often used by scientists. Mathematicians often know more science than normal people, and certainly scientists know more mathematics. But mathematics and science are fundamentally different activities, as different as making a gun and fighting in a battle. I mean, no one would claim there are no links between those occupations, or that gun-makers don’t pay a lot of attention to how guns are used, but not even a child would mistake one for the other. Putting mathematics on a continuum of purity with sciences is like putting it on a continuum with disciplines of art ordered by “highbrow-ness” (actually, I would argue that the latter captures the nature of mathematics better).

The critique here is pretty close to my own age-old hobby horse: the epistemology of mathematics is fundamentally different from the epistemology of the sciences. I used to use this as an argument for transferring the Department of Mathematics at Stockholm University from the Faculty of Sciences to the Faculty of Humanities. Nobody really took me serious back then. However, the basic ideas underlying it all reoccurs: both in Ben’s post, and in Pozorvlak’s excellent shot at classifying academic disciplines by their epistemology. Pozorvlak expands on his treatment of it all, but if we restrict it to the case Ben discusses, his point is basically this:
Mathematics deals with statements that can be proven.
Science deals with statements that cannot be proven, but can be falsified.

These two types of statements lead pretty immediately to different ideas of what truth is – and what knowledge is and all sorts of deep philosophical (as in cannot be proven, cannot be falsified, cannot even find circumstantial evidence for) questions dealing with the meta-level of academic research.

Nowadays, my University has the Mathematics department placed in the Faculty for Mathematics and Computer Science – and I have much less objections to this state of affairs.

Now, in a post just a day or two ago, Ben Webster of the Secret Blogging Seminar called for RSS feeds for the Mathjobs listings.

Imagine my surprise – and probably that of most the readers of the Secret Blogging seminar – to see, the day after posting, the following reply from Diane Boumenot at the AMS:

Hello all. First of all let me say, thank you for the kind words. Also, if you want to send suggestions to Mathjobs.Org, that can be easily done through the web site. However, thanks to Google Alerts and a willing programmer, your request has been received and acted on. As of this morning you can get an RSS feed through the View Jobs page of the Mathjobs website.

Thanks for the suggestion. Thoughts/ideas are always welcome. I will pass the one about Current Publications along to the publications division.
–Diane Boumenot
Manager, Membership & Programs, AMS

Dear Diane. Dear AMS. You’re doing a good job already. This amount of community awareness and swift responses is heartwarming, impressive and thouroughly amazing. Much love!

January: I decided on a whim to look in at the Dilbertblog, where the top post at the moment has Scott Adams calling all atheists that discuss on the net irrational, using a rather neat strawman carbon copy of most discussions of faith between believers (i.e. mostly Christians) and atheists he has seen on the web.

February: The second carnival of mathematics is up over at Good Math, Bad Math.

March: I just met up with the workgroup in the Deutsche Mathematikervereinigung (German Association of Mathematicians) with interest spanning “Information and Communication” – which turns out to mean that they care about libraries, about communicative tools for mathematicians, and spend their time thinking about these things, and meeting at conferences.

April: The website/forumsite Mathetreff, run by the Bezirksregierung (region government) Düsseldorf, just performed a mail interview with me.

May: In about 23 hours, I’ll step on to the train in Jena, heading for T’bilisi, Georgia.

June: Too harried to blog.

July: … or another bout of more-or-less shameless self-promotion.

August: Trying to make the time until my flight leaves tomorrow go by, I played around a bit with the proof assistant Coq.

September: No mathematical content today.
Note: The first september post consisted of a CAS interaction dump. Not fun to quote, so I took the second post.

October: In a conversation on IRC, I started prodding at low-order wreath products.

November: In a recent column at The Chronicle of Higher Education, the columnist writes:

December: I just received my first ever referee’s report.

In conclusion – living in Germany affects me adversely. The number of first sentences that span the entire first paragraph of the posts I’ve been looking at is staggering.

I’m a latecomer to it, in part because I have a very hit-or-miss interest in new technologies. (I still don’t own a cell phone, for example, though I check my e-mail 4,000 times a day.)

Now. There are 24 hours in a day. 1 440 minutes. 86 400 seconds. Thus, checking e-mail 4 000 times in a day would require you to check your inbox every 21.6 seconds. Day and night.

Either the author is innumerate or hyperactive.

I took the initiative, and invited some of the relevant Powers That Be to start an -themed group blog: The Infinite Seminar.

I also perceived a lack of blog aggregators, so I started Planet Math Blogseminars to aggregate group blogs in mathematics.

While I was at it, I bought the blogseminar.net domain. I’d be happy to allocate subdomains of this to decent enough blogs that wants in on it.

Do we have the volume for a Carnival of Research Mathematics?

I find Weibel very readable – once the interest is there. It’s a good reference, and not as opaque as, for instance, the MacLane + Hilton-Stammbach couplet can be at points.

The interest, however, is something I blame my alma mater for. Once upon a time, Jan-Erik Roos went to Paris and studied with Grothendieck. When he got back, he got a professorship at Stockholm University without having finished his PhD. He promptly made sure that nowadays (when he’s an Emeritus stalking the halls) there is not a single algebraist at Stockholm University without some sort of intuition for homological algebra.

So, my MSc advisor, Jörgen Backelin, gave me a subject building on from things that he touched in his PhD thesis, since I was obviously interested in combinatorics. And as such, nothing fits me better than looking at Ext and Tor over monomial rings (corresponding to coordinate hyperplane varieties…)

The other Very Interesting teacher, Jan-Erik Björk, at that university held a course in homological algebra that I attended. It was very handwavy, but with enough of deep understanding underneath that some things just clicked into place.

The story goes on. All in all, out of my 5 years at Stockholm University, at least 3 was spent doing homological algebra in addition to whatever else I was doing, and they were spent in a tight clique of undergrads and early grad students that all shared a high interest in the subject matter. In my transcript, I have an imposing distribution of courses:

where one credit corresponds to one week of fulltime study, roughly. The +20 for homological stuff is for my thesis project, which was on homological algebra, but wasn’t a lecture course. I also have some 5 or 10 points of homological stuff I never got exams done for. So all in all, I spent about a year fulltime with only homological algebra (slightly more distributed in time), and a year fulltime with only algebra of sorts that were not explicitly homological in nature.

And as they say, practice does make perfect. I have, from the various lecture courses I took, an intuition for the category of chain complexes, and for the derived category. I have an understanding for the basics of model categories. I have studied Operads and PROPs with Sergei Merkulov, and seen what happens when you take the basic stance that “We want to equate a structure with its free resolution”, and then run for the hills with it.

The other week I was discussing my graduation plans with my advisor, and he asked what my Rigorosum was going to be about. I told him I expected to do it in homological algebra, and he answered that he wasn’t certain that there was anyone available who’d be capable to accurately test my knowledge of the field. He is a group cohomologist, and he outblazes me when it comes to intuition for that – and especially when it comes to the topological notions in the field.

I, however, am comfortable thinking about differential graded modules and dg-algebras, and doing homological algebra with these. And this seems to place me, possibly, as the single person in my state with a good working knowledge of modern homological algebra.

The things I talked about in the post this follows up on are current knowledge. None of it is particularily original, but the presentation is a result of my personal history. You might very well get similar presentations if you ask my course mates from Stockholm University – but then, that school has a very special athmosphere when it comes to homological algebra.

Connected to this comes the observation that by constructing calculus using the tricks used in synthetic differential geometry, we end up with – again – modules over , and some very fascinating discussions are sparked as to subtle and interesting connections between these two viewpoints!

How on earth I am going to keep up with the interesting sprouting discussion group blogs I shall never know. Maybe it’s getting to the point where we’ll start an -blog?

Enjoy.

There’s a secret blogging seminar going on. And the people seem to be writing interesting things – what little they managed to write before the hushed rumour mill started.

Here it is, translated to english, for your enjoyment.

MT: Dear Mr. Johansson, you are an expert on mathematics blogs. Thus first off a double question: What is a blog, and what do you do in your algebra blog?

MJ: A blog, or weblog as the name started, is basically just a comfortable way to publish texts sequentially on the web. As such blogs aren’t much more than websites with administration aids. The interesting starts when you involve interactions – comments on the texts or easy linking between different blogs.

For this, there are both many different blog softwares, that make these aspects easy accessible and automated, and many websites that network blogs. Thus, it happens that farreaching blog debates occur, where through a networking site several blog discuss or even fight over some question.

I run two blogs myself. One is a sort of open diary – I write there to tell my friends about my life: thoughts, news, book reviews or quiz results from various web quizzes or other toys. The other one (ed. note: here) is a blog that I opened as I was about to start my PhD studies. It’s inspired by the english PhD student Craig, who on his blog Gooseania writes about his life as a PhD student in Mathematics. On this blog, I collect more deliberate texts than in my diary: thoughts on my own research, explanations and popular mathematics texts, as well as some political texts and programming discussions and aspects of theoretical computer science.

MT: What role do blogs play in mathematics?

MJ: So far, their role is not very visible. There is a theoretical physicist – John Baez – who has been writing a blog in Usenet long before blogging started as a phenomenon. He currently runs a research blog, where he and his colleagues discuss current research with a loyal and to a large extent research active readership, link to new articles, and basically perform their research programme in public. Furthermore, several wellknown mathematicians have started blogging – Terence Tao, the 2006 Fields medalist, runs a blog, and Alain Connes participates in a group blog about non-commutative geometry.

There is, however, more student blogs around than researcher blogs. The older generation of mathematician doesn’t’ seem to have gotten on the bandwagon quite yet. I hope that this’ll change in the next couple of years.

MT: Are there math-blogs run by pre-university students?

MJ: I think there would be, though I haven’t really seen any in my searches. There are many more undergraduates to be found though. For instance, the universities of Newcastle and Warwick have blog directories and centralized blog sites with both student and teacher participation.

MT: Do blogs matter among teachers?

MJ: Definitely! There are many blogging teachers – primarily in the USA – who write about their teaching experiences, about pedagogy, about students and about their thoughts and ideas.

MT: How do you start a blog?

MJ: Today there are primarily a few generic blog hosts that come in question. The biggest may well be Blogger and WordPress.com, whereby WordPress offers better possibilities to write mathematics with their integrated LaTeX support.

I hope, though, to start a project to build a german blog host geared toward mathematicians and mathematics blogs.

MT: How do you find interesting blogs?

MJ: The best method, in my opinion, is to find a blog that interests you, and follow all the links in the sidebar, and repeat this for each blog you find interesting among those. Apart from that, there are carnivals: regular postings with links to interesting blog entries following a certain theme. There is one Carnival of Mathematics and also a Carnival of Education. There are also some sites that list new posts, sorted into categories. The possibly biggest is Technorati, where a search with keywords such as ‘mathematics’ or ‘education’ will give plenty of interesting hits.

MT: Finally, a question about your work as a mathematician. What do you do in algebra?

MJ: There are methods to convert questions such as “How many holes are there in this object? How many bubbles?” into purely algebraic questions. These conversions exhibit very interesting structures, that also give tools for more areas than just the initial geometrical questions. I consider how to perform calculations with these structures faster and better using extra information that can be found in the structures.

MT: Why algebra?

MJ: I’m a mathematician because I see a deep beauty in mathematics. To me, this beauty is found in the structures and abstract connections. Thus, in the realm of languages I find grammar more interesting than vocabulary or learning to speak the language; and in mathematics the abstractions carry an attraction in its own right.

MT: Thank you.

Go there. Read. There’s a LOT of good blog posts there.

My blog is not very anonymous. It is occasionally personal, occasionally political and throughout a venting location for thoughts, and a place where I formulate myself in higher detail – so to speak a scratchpad, but public enough for me to allow others to read it.

I write it to formulate my own thoughts further, find possible errors, start discussions, or just jot down the viewpoints that illuminated some point of some argument for me. I do it in public because I thouroughly enjoy the conversations it sparks.

I can see the charm of anonymity, but I am way too much of an attention junkie to be able to stay anonymous for very long. This has come up in my career – thoughts about job applications in process, published on this blog, and even more on my livejournal, sparked questions at the hiring interview with the potential (and now current) employer about my writings and what influence the there formulated ideas would have on my actual poise toward my current job.