Some stories about becoming a mathematician

I have a peculiar little day with neither an A-to-Z, a recap, or a Reading the Comics post to publish. It feels illicit somehow. Well, let me share something which I ran across recently. It’s an e-book published by the American Mathematical Society, Living Proof: Stories of Resilience Along the Mathematical Journey. Editors Allison K Henrich, Emille D Lawrence, Matthew A Pons, and David G Taylor.

It’s a collection of short autobiographical essays from mathematicians. The focus is on the hard part. Getting to an advanced degree implies some a lot of work, much of it intellectually challenging. I felt a great relief every essay I found where someone else struggled with real analysis, or the great obstacle of qualifying exams. And I can take some comfort, thinking back at all the ways I was a bad student, to know how many other people were also bad students in the same ways. (Is there anyone who goes on to a doctoral program in mathematics who learns how to study before about two years into the program?)

There are other challenges. It’s not a surprise that American life, even academic life, is harder if you can’t pass as a heterosexual white male. A number of the writers are women, or black people, or non-heterosexual people. And they’re generous enough to share infuriating experiences. One can admire, for example, Robin Blankenship’s social engineering that convinced her algebraic topology instructor that she did, indeed, understand the material as well as her male peers did. One can feel the horror of the professor saying he had been giving her lousy scores because his impression was that she didn’t know what she was doing even as she gave correct answers. And she wasn’t the only person who struggled against a professor grading from the impression of his students rather than their actual work. There is always subjectivity and judgement in grading, even in mathematics, even in something as logically “pure” as a proof. But that …

I do not remember having a professor grading me in a way that seemed out of line with my work. The grade to expect if the grading were done single-blind, with no information about the identity of the exam-taker. But, then, I’m white and male and anyone looking at me would see someone who looks like he should be a mathematician. I think my presentation is, to be precise, “high school physics teacher who thinks this class just might be ready to see an amazing demonstration about something we call the Conservation of Angular Momentum”. That’s near enough to “mathematician” for most needs. This makes many of these essays, to me, embarrassing eye-openings.

So I think the book’s worth reading. And it is a great number of essays, most of them two or three pages. So it’s one you can pick up and read when you just have a few free minutes.

What Lewis Carroll Says Exists That I Don’t

I borrowed from the library Symbolic Logic, a collection of an elementary textbook — intended for children, and more fun than usual because of that — on logic by Lewis Carroll, combined with notes and manuscript pages which William Warren Bartley III found toward the second volume in the series. The first part is particularly nice since it’s text that not only was finished in Carroll’s life but went through several editions so he could improve the unclear parts. In case I do get to teaching a new logic course I’ll have to plunder it for examples as well as for this rather nice visual representation Carroll used for sorting out what was implied by a set of propositions regard “All (something) are (something else)” and “Some (something) are (this)” and “No (something) are (whatnot)”. It’s not quite Venn diagrams, although you can see them from there. Oddly, Carroll apparently couldn’t; there’s a rather amusing bit in the second volume where Carroll makes Venn diagrams out to be silly because you can make them terribly complicated.