For those of you following the long OT comments discussion on graphics programs, let me second Chris’s endorsement of Tikz. It is by far the best LaTeX graphics package I have ever used. I couldn’t possibly compete with the manual (what other manual starts with 3 fantastic tutorials?), and this page of examples. I have a certain affection for xypic, which has served me well over the years, but Tikz is just lightyears ahead. That is all.


Mathematicians beat pornographers!

For years, whenever I ran a web search for something involving LaTeX, I would throw the word “typesetting” into the search terms in order to screen out the p-o-r-n. I just checked, and this is no longer necessary: Even without safesearch, the first three pages of google hits on “latex” contain only one allusion to the material’s use in fetish wear — and only three references to the rubber material at all.

It is great that google now thinks I am more likely to care about quality typesetting than about rubber clad women. But I wonder whether this is smart behavior on google’s part. It seems to me that a really smart search engine would realize that people searching for “latex” fall into three or four distinct camps — mathematicians, materials scientists, fetishists, and perhaps some group I’m not thinking of — and offer me a few hits focused on each group. And that, in turn, made me wonder how I would design an algorithm to do such clustering. Any ideas?

Math stimulus

Update: For a different take see David’s comment.

Peter Woit made an excellent point in the comments that I want to bring up to the main page and expand on:

In math, a short-term increase in NSF funding of conferences and summer salary is hard to justify, but more money for postdoc positions and graduate student fellowships to keep people employed as university budgets get cut is something that makes a lot of sense.

I think this is exactly right. The main purpose as I see it of a stimulus package (and I admit I don’t really understand stimulus stuff well, it’s not like universal health care where it’s pretty obvious what we should be doing cause you can just travel and see it) is to keep people employed and spending the same way they would be if the economy weren’t tanked. The single best way to do this is to keep people employed in the jobs they would have in a normal economy. This is why state aid is such an obvious component of a stimulus, it keeps school teachers and other state employees at the same jobs they had before the recession and the same jobs they’ll have after the recession.

In math what are the jobs people are losing because of the recession? Yes graduate students and postdocs as Peter points out. But even more than either of those it’s starting tenure track jobs that are getting cut. A quick perusal of the math jobs wiki shows that many more of those searches have been cancelled.

So if I were running the NSF and the math portion of the budget was expanded I would try to increase the number of graduate student and postdoc fellowships (but not their pays, no matter how much I personally would enjoy a pay raise), but my first priority would be to start a program whereby schools can get several years of bridge funds for making new tenure-track hires.

Springer folks?

So, my last post got a pingback from a blog called “Topology and Geometry”. The post was entitled “for the springer folks,” and I couldn’t help but think to myself “Wait, there’s a blog out there with a serious enough constituency for springer fibers that they get their own category? Who are these people?”

As far as I can tell, this is the class blog for a graduate class at Northwestern (taught by a friend of the blog who shall remain nameless), part of which is covering Springer theory. It might be a little hard for those without the benefit of the lectures to follow, but is an interesting example of Web 2.0 in the classroom.

Of course, it’s also good that there is an account of Springer theory on the web, so I can link to it when I finally get around to writing up how to categorify Springer theory.

Not Even Blogging

Since we’ve been on a physics kick lately, you may want to scoot over and watch Peter Woit talking to Sabine Hossenfelder at bloggingheads.

Probably the most interesting part (to me, at least) is the discussion of the difference between math and physics culture.  I often have a vague sense that these differences exist (mostly in ways that make me happy that I stayed in mathematics), but often wonder whether I am making them up.  Well, one data point in my favor.

I’d also like to riff a little bit on the issues brought up by Sabine. I hadn’t encountered her previously (and I bet a lot of you haven’t).  For reference, she is a physics postdoc at Perimeter, who blogs at Backreaction.  She has some pretty strong words for the academic community as a whole, and how it directs research.   Continue reading

What is purity?

So, maybe I’m a little late to this party, but I wanted to comment on a recent XCKD (yes, Isabel blogged it first, though I added it to our del.icio.us before she blogged it). This arranged several scientific fields, by order of purity. Of course, the mathematician is standing at the far end of the scale (saying “Oh hey, I didn’t see you guys all the way over there”). The same point has circulated in saying form as

“Biologists defer to chemists. Chemists defer to physicists. Physicists defer to mathematicians. Mathematicians defer only to God”

(does anyone have an attribution for this quote? My Google-fu was insufficient).

Now, I think it’s clear that I love XKCD (one of these days, I’ll get my shit together and drive out to the Boston meet-up. Who knows, maybe next Saturday), but I can’t help but disagree a bit with the premise of this comic. I think it misses something pretty important about mathematics. Continue reading

More advice for prospective graduate students

Isabel Lugo had a nice post recently on advice for prospective graduate students. Although not all of her advice rang true to me (the first year of graduate school was pretty fun for most people I know), she makes an excellent point in comment 2 that I wanted to respond to.

Your mathematical interests will change during the first year in graduate school, because a lot of subjects “feel” different at the undergraduate level than at the graduate level, and there are some things you just don’t see as an undergraduate at all.

Personally, my favorite subjects in mathematics are:

  1. The representation theory of finite groups from Frobenius through Brauer
  2. Algebraic and Analytic Number Theory from Gauss through sometime in the late 1800s
  3. Quantum Topology from the Jones polynomial through the present

On the one hand you can tell from this that I like algebra more than I like geometry or analysis. This was something I was quite aware of as an undergraduate and beginning graduate student. However, all of these have something else important in common: they are/were all young subjects. With the exception of Euler’s prescient work on zeta functions, there’s not a whole lot of precursors prior to the beginnings I’ve stated above. You don’t see on my list anything like modern homotopy theory, ell-adic cohomology, the classification of simple groups project, or 20th century number theory. I went into graduate school thinking I wanted to do number theory because I love number theory up until about 1920. The lesson I should have taken from that is that I like younger topics in algebra, not that I want to do number theory. Older subjects feel different from younger subjects. You have more tools, bigger machines, but the most natural questions have already been answered and the field has moved on to harder things. But there was no way for me to know this as an undergraduate, because undergraduates don’t know enough to have been exposed to any material in an older subject.

There are lots of other key differences between fields: Do people do more theory building or problem solving? Is the topic dominated by a few giants’ research programs with other people following their lead or is it more each researcher having their own smaller programs? Is it on the intersection of multiple fields or more isolated from other fields of mathematics?

Obviously a first-year graduate student isn’t going to know the answers to these questions, but these are the sorts of questions that you need to ask yourself rather than just “which subject did I like as an undergraduate.”