Some Things I’ve Been Reading


I don’t just read comic strips around here. It seems like it, I grant. But there’s other things that catch my interest and that you might also like.

The first: many people have talked about what great thinkers did during their quarantine-induced disruptions to their lives. Isaac Newton is held up as a great example. While avoiding the Plague, after all, he had that great year of discovering calculus, gravity, optics, and an automatic transmission that doesn’t fail after eight years of normal driving. It’s a great story. The trouble is that real thing is always more ambiguous, more hesitant, and less well-defined than the story. The Renaissance Mathematicus discusses, in detail, something closer to the reality of Newton’s accomplishments during that plague year. This is not to say that his work was not astounding. But it was not as much, or as intense, or as superhuman as inspirational tweets would like.

If you do decide the quarantine is a great chance to revolutionize academia, good luck. You need some reference material, though. Springer publishing has put out several hundred of its textbooks as free PDFs or eBooks. A list of 408 of them (the poster claims) is here on Reddit. This is not only a list of mathematics and mathematics-related topics, and I not undrestand the poster’s organization scheme. But there are a lot of books here, including at least two Introduction to Partial Differential Equations texts. There’s something of note there. This could finally be the thing that gets me to learn the mathematical-statistics programming language R. (It will not get me to learn the mathematical-statistics programming language R.)

And, finally, the disruption to everything has messed up academic departments’ routines. Some of those routines are seminars, in which people share the work they’re doing. Fortunately, many of these seminars are moving to online presentations. And then you can join in, and at least listen, without needing even to worry about being the stranger hanging around the mathematics department. Mathseminars.org has a list of upcoming seminars, with links to what the sessions are about and how to join them. The majority are in English, but there are listed seminars in Spanish, Russian, and French.

I grant the seminar titles are filled with enough jargon to intimidate someone not already well-versed in the field. To pick an example set for the 22nd of April, my time, I’ve never even heard of Dieudonné Theory, prismatic or otherwise. Don’t let that throw you. I would expect speaker Arthur-César La Bras to bring people up to a basic understanding swiftly. It’s the seminars whose titles contain words you’re sure you know that are truly baffling, which is why I fear Alexandra Kjuchukova’s The meridional rank conjecture: an attack with crayons. If they’re talking about crayons it can’t be good.

Reading the Comics, January 17, 2015: Finding Your Place Edition


This week’s collection of mathematics-themed comic strips includes one of the best examples of using mathematics in real life, because it describes how to find your position if you’re lost in, in this case, an uncharted island. I’m only saddened that I couldn’t find a natural way to work in how to use an analog watch as a makeshift compass, so I’m shoehorning it in up here, as well as pointing out that if you don’t have an analog clock to use, you can still approximate it by drawing the hands of the clock on a sheet of paper and using that as a pretend watch, and there is something awesome about using a sheet of paper with the time drawn on it as a way to finding north.

Dave Whamond’s Reality Check (January 12) is a guru-on-the-mountain joke, explaining that the answers to life are in the back of the math book. It’s certainly convention for a mathematics book, at least up through about Intro Differential Equations, to include answers to the problems, or at least a selection of problems, in the back, and on reflection it’s a bit of an odd convention. You don’t see that in, say, a history book even where the questions can be reduced to picking out trivia from the main text. I suppose the math-answers convention reflects an idea that there’s a correct way to go about solving a problem, and therefore, you can check whether you picked the correct way and followed it correctly with no more answer than a printed “15/2” as guide. In this way, I suppose, a mathematics textbook can be self-teaching — at least, the eager student can do some of her own pass/fail grading — which was probably invaluable back in the days when finding a skilled mathematics teacher was so much harder than it is today.

Continue reading “Reading the Comics, January 17, 2015: Finding Your Place Edition”

Me and the Witch


The Google Doodle for today (the 16th of May) commemorates Maria Gaetana Agnesi, an 18th century Italian mathematician/philosopher who became a professor at the University of Bologna, studied (among other things) the curves named after her, and wrote several textbooks including, if Mathworld is correct on this point, the earliest surviving mathematical work (Instituzioni analitiche ad uso della gioventù italiana — Analytical Institutions for the Use of Italian Youth) known to be written by a woman .

I remember where I first encountered the Witch of Agnesi, though: it was in seventh grade, in the midst of my own pre-algebra textbook. The book was doing its best to describe how to plot curves, although at the seventh-grade level that’s pretty much just straight lines. It tossed off a mention, though, that there was this woman, Maria Gaetana Agnesi, and a curve named the “witch of Agnesi” because of its strange shape, and gave a formula describing the relationship of points on the curve as y = \frac{8a^3}{x^2 + 4a^2} which is correct but a struggle to parse if you’re still at the y = 4x - 2 stage of things, particularly since it didn’t include a picture of the curve and I was still at that point vague about the use of abstract coefficients like a in equations. (I’m not sure if I was just slow on the uptake or if the book hadn’t described it at that point.)

Still, I did my best working out what the curve might be (I had a fuzzy impression that it might be the shape of a witch’s hat, which, for the right parameters and if you’re willing to be loose in your interpretation, isn’t too implausible), by picking a couple easy-looking values for a and then more easy-looking values for x and trying to plot the curve, but I was never back then satisfied with the results.

I admit now I wonder if the textbook hadn’t left the plot out on purpose, since I’m sure I wouldn’t have thought so much about the curve if I could just see it. But I also have suspicions that the footnote was just there at all because it allowed a chance to legitimately mention a female mathematician in a context that would make sense for students at that level, without much thought about whether a picture would help matters any. Most of the contributions of female mathematicians prominent enough to get named for them tend to cluster around more modern times and thus around higher-level materials; there’s no explaining Sofia Kowalevski’s existence and uniqueness theorems for analytic partial differential equations to a seventh-grader.