Paul Michael Kielstra

I still haven’t taught a university course yet, and won’t for several years, but I’ve taken opportunities to teach where I’ve found them. I just finished teaching a week-long seminar for Chinese high-school students, entitled The Art of Mathematical Proof but mostly consisting of an introduction to group theory, at the Harvard Summit for Young Leaders in China (HSYLC). This post is my attempt to write down what I’ve learned, on the grounds that I would have had a much easier time if someone had pointed me to a post like it beforehand.

“Oh no,” said Adam. “We’re taking this too seriously. But surely it’s not non-degenerate?”

A friend of mine and I recently decided that it would be a good use of our time to determine how many dragons the USA could support. While exact numbers are obviously hard to come by, it turns out that the answer is about 4500. Here’s how we got there.

Internet, meet Civet. It’s a piece of software I wrote that lets you write very simple scripts to run programs over and over again with different parameters. It came out of a project I’m working on that involves profiling the performance of an algorithm to solve differential equations. I realized that it would be useful to have code that could run through dozens or hundreds of different setups and determine how many iterations the algorithm took to solve each, but without the overhead of a full testing or CI system. If you need to do repetitive experiments with computer software, you should check it out. But that’s not why I want to talk about it now.

As a junior mathematician, I feel strange writing this sort of post. Usually, I opine on things that it’s perfectly OK for someone at my level to write about: what it feels like to do math of any sort, specific tools a researcher needs when s/he’s just starting out, and so forth. Today, though, I’m going to be a little bolder than usual and argue that many papers and books today are missing something very useful: a full glossary of notation.

Recently, someone in an intercollegiate Facebook group asked how to tell if a journal were legitimate. I responded, and was surprised by the number of people who found it helpful (or, at least, helpful enough to Like). This post is an expanded version of that answer, in the hope that it could be helpful to even more people if it found its way outside Facebook’s walled garden.

Every so often, some wag will restart the debate over what is and what isn’t a “useful” degree. This might be someone on the internet, or it might be your father asking why he’s paying all this money for you to do East Asian Studies or Theater and Dance or Classics while your older brother studied Computer Science and now he’s pulling down $100 000 per year with benefits. Academics often weigh in to defend their own fields, often using phrases such as “[The thing I study] has never been more relevant than today”. The main divide seems to be between, on the one hand, the group that views education as job training and a college degree as an investment to be netted out against future earnings, and, on the other, the group that views education as teaching knowledge and good citizenship for their own sakes. I call these groups the plutophiles and sophophiles respectively. The sophophiles view the plutophiles as short-sighted money-grubbers with no sense of beauty, while the plutophiles view the sophophiles as pie-in-the-sky idealists with no sense of pragmatism.

Excitingly, I now have a new website. Hello, internet! My previous blog was great, but it was basically that: a regular blog without much room for anything else. I will be posting here occasionally, but I’ll also be using this site as a place to host a CV, link to my papers, and maybe carry out a few slightly left-field experiments.