Writing history posts for the math.SE blog

Question

The Mathematics stackexchange has a blog featuring short expository articles about interesting pieces of mathematics. The articles are user-written. Now, I think part of our mission as a community, especially if we want to grow, needs to be to promote interest in the history of math and science, especially among other SE users. I thought maybe we could write some interesting blog posts to draw attention, perhaps we could also ask permission to link to HSM at the end, which I'm sure wouldn't be a problem, there's no reason math.SE should have a problem with promoting a sister site.

The style of the math.SE blog tends towards quite novel topics, the kind of mathematics that I'd usually call "cute" - ie, immediately accessible, at least in terms of why it's interesting. For example, the "stable marriage problem", or tetration. Thus, historical articles should focus on topics interesting to people without a pre-existing interest in history. I've left a few of my own ideas in an answer below.

The same sort of thing could be done for the physics SE, of course. Does it have a similar blog? Can we propose starting one?

Answer 1

Here are some ideas that might at least provide some inspiration. Notice that all of these ideas have technical mathematical content as well as historical content, which I think is important for an audience that might not be that interested in history. It's all more in keeping with one of my personal mission statements of promoting the idea that reading about the history of modern concepts helps you understand those concepts better.

1. The idea for the blog posts actually hit me when I sat down to read Euler's textbook on calculus (which has an English translation by Blanton!) and realized for the first time how absolutely demented some of the old appeals to the concept of infinity were. I knew it was non-rigorous, but I didn't think it would be this bad. An article of "highlights" of some of the most egregious and less well known arguments (everybody's seen his derivation of $\sum n^{-2}$) in Euler's work, along with discussion, would probably be very entertaining and enlightening. Someone with more knowledge of the period might also be able to explain what might have been going through Euler's head, and why the arguments may not be so non-sensical as they at first seem (or maybe they really are non-sensical, but then again the results are correct).

2. In a similar (that is, mildly iconoclastic) vein, I believe some of Cantor's writings on his theories are fairly bizarre, including explicit appeals to god and religion. An analysis of the same type could be very interesting. In particular, I'd love to see some of the famous anti-Cantor quotes ("I am not sure if in Cantor's writing there is more philosophy or theology, but I am sure there is no mathematics there.") put into their proper context.

3. When studying measure theory recently, I found some historically-oriented lecture notes, and I was interested to see that Lebesgue wasn't the first to define measure, and that the problem of rigorously defining length in the context of $\mathbb R$ had been around for a while. Indeed, we call sets Borel measurable because Borel had provided another definition of length earlier than Lebesgue. It was especially interesting to see how geometrically motivated a lot of the constructions were, such as Lebesgue's "outer measure" concept. An exposition on this more intuitive, geometrical side of measure theory could be interesting.

4. Early definitions of a group were quite different from the modern one, often leaving out inverses in favor of posulating the cancellation law, and Cayley's original definition was actually more like what we would now call a free group (with defining relations). An exposition on early definitions and how they relate to our point of view could be instructive. Similarly for rings and fields etc, of course.

5. I've been reading about projective geometry recently, and I believe a lot of the subject stems essentially from one man - Desargues - who wrote a small number of texts on the subject in the 1600s or possibly 1500s, I'm too lazy to double check. In any case, the very concrete subject of the books (I think they were basically handbooks for working artists) would make them a good, accessible subject for an article.

Answer 2

Putting a status-declined on this question feels a little too mean, but the Math SE blog (along with most other SE community blogs) has been shut down, so the original aim of this question is kind of... obsolete... now.

You're still more than welcome to start a community blog through a third-party service, though, if there's interest! Worldbuilding SE has the awesome Universe Factory, and the post I linked above has info on a few more.

Answer 3

I believe JackM's answer already covers a wide range of interesting mathematics, so we should think about posts in other topics. To his list I'd like to add some of my personal favorites, whose answers could be compiled into a post or extended by the OP.

1) I think something in the spirit of the accepted answer in here should be added: Which school of philosophy motivated thinking about spaces of higher dimension? I really enjoyed that read.

2) Answers in here are also GREAT: Whose shoulders did Newton stand on? IMO Geremia's answer was way more on point than the others (I even bought one of the books he cites). Everyone interested should read the whole thread though.