There is so much that is peculiar, irregular, silly, or downright twisted in mathematical verbiage that, certainly, we could all benefit from some soul-searching on the language of our culture. Some of mathematics usage is confusing (e. g. overuse of “normal” and “regular”) and some irritating (personal peeve: persistent classroom use of “guy” to refer to mathematical expressions – I know anthropomorphization makes things friendly and all, but I’m not sure that thinking of all mathematical objects as “guys” is good for our ongoing gender problem). And then there are other things that just floored me the first time I heard them (um, “clopen,” anyone?), not to mention our obsession/affliction with eponymy and its discontents. There is a dissertation in linguistic anthropology waiting to be written on mathematical usage, and perhaps several that already have been.

It would be all well and good to litigate the social and political aspects of mathematical speech, but who really has the time?^{ 1 }This is a graduate student blog, and, you know, life is already hard enough, so we must have some recreation. Proposed solution: **the mathematical crossword puzzle**, or more accurately, crossword puzzle with a strong mathematical bias – a venue to examine and lightheartedly ponder our field’s history, culture, language and content without needing to delve into heated public debate. On the other hand, maybe the chance for debate is sort of the point.^{ 2 } Entertainment which is presented as critical thinking and that leads to higher-level critical thinking is a high kind of art.

I suppose, based on my own experience, that many crossword solvers will relate to the experience of hating puzzle-makers for clues that make no sense, are elitist, presume familiarity with arcane or dated bits of culture, etc. To draw a parallel, I submit that this is exactly the sort of experience many students are having in math classes, at any level. That you are the kind of person that is willing to put up with being treated with such pomposity and contempt, until you are suddenly on the other side of this diode-like arrangement, is something one might infer from the fact that you are in mathematics graduate school and reading a math blog to boot, which is to say: I bet the intersection of math-o-philes and cruciverbalists is not so small.

But! We must do better than our teachers by seeking to not alienate, condescend, and exclude, and in order to get there first we must try. As a long-time-solver-first-time-constructor, let me say the following:

- Constructing is hard! Harder that you might think, harder than I thought at least. The junky, off-putting clues you find in crosswords are much more likely due to (i) the jams a maker finds them- self in while constructing and (ii) laziness at dealing with these jams, than they are to any kind of elitism or snootery.
- Regarding the handling of such jams, no matter how hard you try you are still a victim of your own biases. There is perhaps no way around this, at least not on an individual level. A diversity of backgrounds among puzzle-makers and solvers (draw the mathematical analogy) will lead to a richer and less homogenized and consistently frustrating experience. This is the general nature of the criticisms levelled at the New York Times editorialship by Rex Parker et al., and it leads to a big and important conversation on power, privilege, who’s being represented and who’s being excluded. I have made a best effort at inclusiveness in the theme and content of this puzzle, which I’m sure is still abjectly deficient in some respects.
- This puzzle has a few more black squares than is typical/admissible for your average newspaper puzzle. Here’s my accounting for this: many puzzles are built around a “theme,” a collection of clues that are linked by some common feature. Clues in this set are called “themers.” I tried to cram too many themers into this one, and in order to cope with the resulting jams, I had to black some stuff out.
- I couldn’t (and this is maybe a relief for solvers) find a way to reasonably make all of the clues mathematics related. So some are intersectional, and some are out of left-field. I learned a lot of trivia while making this, and my hope is that you might learn some too.

I hope you enjoy! If you are moved to create your own math-puzzles, I am also sharing the kinda janky LaTeX file I used to make this one, in case it helps.

^{ 1 }Maybe the same people that spend time making crosswords, ahem.

^{ 2 }Regular NYT puzzle solvers may know the boisterous commentary of Rex Parker and others in the puzzle blogosphere.

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I’ll never finish it, but it’s lovely.