I teach mathematics and computing, for example, our department’s discrete mathematics course. As is customary for that course, it’s used as the first foray into formal mathematics, including a heavy emphasis on reading and writing proofs throughout the semester (required for both our math & computing majors). In response to difficulties I’ve seen students wrestle with in prior semesters, on the first day of the course I have a slide with this quote:

Writing Proofs in English

β€œThe best notation is no notation; whenever it is possible to avoid the use of a complicated alphabetic apparatus, avoid it. A good attitude to the preparation of written mathematical exposition is to pretend that it is spoken. Pretend that you are explaining the subject to a friend on a long walk in the woods, with no paper available; fall back on symbolism only when it is really necessary.” – Paul Halmos, How to Write Mathematics

Now, the last few semesters I’ve done this I find that I regularly get pushback on this. For example, this semester I had a student write in the live online chat, something like, "This seems unfair to students who have poor English skills". And I’ve been kind of stumped for a short, solid response to that.

Note that I’m at a community college in the U.S., which is part of a large urban university, and about half of our student population is foreign-born. We have a TOEFL requirement for enrollment, but some students indeed have very weak English skills (I’ve had a small number that apparently needed every course lecture translated by a friend, and couldn’t communicate to me directly).

My initial instinct is something like, "You enrolled at a university where the instruction is in English, and has an English requirement for registration, so no one should be surprised at this." But (a) that seems wordy and byzantine, and (b) misses the underlying problem that people are led to believe that math work is entirely deterministic symbol-pushing, such that some people pursue it precisely because they think they won’t need strong language skills (in fact, some of our advisors explicitly say this to students).

Obviously, replace "English" here with "natural language" at whatever institution and location you might consider.

What’s the best, shortest response to student criticism that "It’s unfair to expect writing in English"?

Related from SE Mathematics: Why there is no sign of logic symbols in mathematical texts?

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