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How to respond to "unfair to write English" comments?
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 past semesters, on the first day of the course I have a slide with this quote:

Writing Proofs in English
“The 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. 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 a bit 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 with 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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In books by the Nicolas Bourbaki group the proofs have been written in French (with a lot of math symbols)

I just want to thank you for making explicit that mathematics, as usually taught, is over-grounded in obfuscatory symbology. For every student who bristles at the English issue, there are three who have been entirely denied mathematics education because the field would rather manipulate discrete Greek letters than present ideas in natural language. If the rest of your course emphasizes conceptual understanding the way that you seem to imply here, I am sure it is to the benefit of all your students.

I remember this discussed on Mathematics years ago. I don't agree with "The best notation is no notation", imagine writing code in that way. Notation has concrete and well-defined rules and meaning, English words do not.

@IS4: Thanks for pointing out that thread (I'll add it to my question shortly). I think it's useful to note the several highest answers and consensus are saying that, yes, math papers are mostly written in English. And that the OP's original observation is that none of their various undegrad/graduate textbooks ever used any special logic symbols.

"This seems unfair to students who have poor English skills" Response: That is why we have a TOEFL requirement. and then move on.

@DanielR.Collins True. I come from a non-English country and studied math in my native language my whole life, so perhaps the situation is different in those cases.

Imagine writing code in that way, indeed. It would look like COBOL.

For writing proofs, full knowledge of English is not necessary. Most proofs can be written using a single tense. It is sufficient (and often advisable) to keep the structure of sentences very simple; that is very similar to how logic statements are written using math notation. Arguably, this exercise requires students to use only a small and simple subset of English level. Most students are expected to have it by the admission requirements of the course they signed on.

Funny how full knowledge is not necessary at research and at the top-level (see, ehm, hear the average English level at conferences), but how relevant is "local language" to get good grades in the modern teaching of mathematics at the lower level (high school, college, BSc and MSc ...).
Source: personal experience at international conferences, personal bad english.

@EarlGrey I find your comment interesting because (to me) it simultaneously suggests that 1) English skills do not need to be perfect, but 2) since English is the lingua franca of much professional communication there is a working skill level that is essential.

(+1) Especially for It is sufficient (and often advisable) to keep the structure of sentences very simple.

@pjs absolutely, after URSS dissolution, English is the (only?) lingua franca for science. Russian was also a lingua franca, in the 70s it was not uncommon to have Russian books and papers discussed in East Germany or in Czech Republic. Much of the Russian knowledge and skills have been imported into the western world.
Nowadays, even commercial blogging is done in English instead of, let's say, German, to reach a wider audience.

Nobody, at any conferece I attented, was unable to speak english. Yes some people had a strong accent but everyone was able to follow the talks which were held in english.

I think you guys missing the point. There is a big difference between "can", "reliably can" and "effortlessly can". For a native speaker, talking to a piece of wood in their mother tongue is easy, and Halmos's point is to encourage this natural, effortless state vs using symbols. For most foreign students, it is not an effortless, natural conversation, with free flow of thoughts.

@stupidstudent A colleague went to an "international" conference in St. Petersburg in the early 2010s.  Almost all presentations were in Russian.  After my (Swedish) colleague presented in English, an old Russian scientist approached him and said in very broken English that he thought from the plots that my colleague's work looked very good, but that he hadn't understood anything my colleague said.  So — I agree with you for most conferences, but there are still exceptions.

@stupidstudent Nobody at any conference until you get someone at a certain conference ;) .  Your argument is valid until proven contrary ---> you have to visit every conference in the world and attend every talk and every poster to be sure about your statement!
Try harder, try at the poster session, try at conference outside IT subjects ...

I'm marking this as the selected answer, because it will definitely be part of my response in the future, and it's by far the mostly highly upvoted at this time. I would encourage readers to check out several of the other answers below, because they provide many additional great points. I've added an answer of my own to compile my favorite pieces (likely much further below).

Certain paper reviewers commenting "The English is in this paper does not seem to be native usage" seem to disagree with this idea

@AgnishomChattopadhyay Some reviewers are power hungry individuals, allowing their insecurities and biases  to compromise their academic judgement.

Your experience resonates with me. In my classes I also have many students with imperfect English. I have often noticed (including as recently as a couple of weeks ago) that when I give lengthy word questions explaining a complicated real-life problem and asking to model it mathematically, some students struggle to understand what they are being asked to do due to language difficulties; and this is despite the fact that the question is written in grammatically correct, plain English, and I even make a conscious effort to edit the questions and “water down” the level of the English by removing complicated words and phrases to the extent possible.
Although I haven’t gotten pushback and don’t believe I have anything to answer for, thinking about this issue over the years has led me to conclude that there is a real problem of students who come to US universities with an incomplete mastery of English being at a disadvantage — often a significant one — because of their language skills. And I’ve wondered what I can do about it. For example, consciously trying to speak and write with slightly less complicated English words and phrases than I might be inclined to do if I knew I was addressing only native English speakers is one remedy. But it is a small and mostly (as far as I can tell) ineffective one. The students who were going to struggle are still struggling.
Now, whether or not this is “unfair” is a complicated ethical question and I don’t think it is my place to answer it. But one thing I’ve come to believe is that, at least, to the extent that it is unfair, the unfairness is a systemic kind of unfairness that is built into a university system that admits a large number of foreign students and expects them to handle an environment in which knowledge of (high-level, academic) English is assumed. In other words, it is not me who introduced the unfairness, and it is not me who has much power to do anything about it.
At the end of the day, my job is to teach mathematics, using English as the language of instruction, and that is what I do. If the subject I’m teaching involves writing word problems to teach people how to model and interpret real-life problems, that is what I will do. If the subject requires students to write proofs verbally, that is what I will require (though grading will be done based on the mathematical correctness of the answer and not based on correct grammar and spelling). There just isn’t any other way.
When a student says to you that what you are doing is unfair, tell them that you are simply teaching the subject you were assigned to teach as it should be taught by a qualified instructor. Ask them what they are suggesting that you do instead. My guess is they will not be able to make a coherent suggestion, and perhaps that will lead them to understand that the problem is more complicated than they realized.
Also: tell the advisors at your college not to tell students that mathematics does not require strong language skills! That is a horribly false and misleading thing to tell people and can obviously set them up for trouble and disappointment.

This answer somewhat assumes every person struggling with English is a foreign national here by choice - I'm not sure that's the case (especially at the community college level, especially so for Daniel, who's in Brooklyn)

@AzorAhai-him- I’m confused, do you mean “a foreign national here by choice” in contrast to “a foreign national who is here not by choice”, or something else? I’m not seeing where I assume whether people are here by choice or not.

"the unfairness is a systemic kind of unfairness that is built into a university system that admits a large number of foreign students and expects them to handle an environment in which knowledge of (high-level, academic) English is assumed" seems to say that there's only students with language problems because universities are admitting them for that sweet int'l tuition. What about refugee students? Or for example, someone who who immigrated as a 16-year-old? I don't disagree with your answer in general

@AzorAhai-him- okay. In case it was unclear, the main point I’m making is that students with poor English are at a disadvantage and that this puts instructors in an awkward situation of wanting to help those students to some extent but not having any practical mechanism for doing that without compromising academic standards. This applies equally to all students with poor English regardless of their particular status or life history. In practice, I suspect that foreign students are the main population for which this discussion is relevant, at least at my institution.

"Ask them what they are suggesting that you do instead" I think that this is a key point that should be given more emphasis. If there are reasonable adjustments that OP can make to assist students who are less fluent in English, then I would argue that OP should consider making them. But it sounds like OP is already doing that by sticking to simple language. I don't think it's reasonable to expect an English-language course to entirely avoid the English language.

It seems to me that at least part of the problem with students coming to
English speaking countries is that there seems to be widespread cheating in language exams. My experience is that three times I was closely involved in cases where a person had problems passing TOEFL or a similar exam, and in all three cases the persons were fluent in English and could even discuss their case with the faculty authorities. At the same time, I have often found students who come with a good grade in TOEFL, but cannot communicate, neither orally nor in writing.

@MartinArgerami interesting. Well, if a student cheated about their English skills to get in then they obviously don’t have a leg to stand on in claiming unfairness. So yes, this issue apparently touches on various other things that are wrong with the US higher education system, but are essentially tangential to OP’s question.

@MartinArgerami: I was just discussing the same thing my partner (who also served as adjunct faculty) over lunch today.

to speak and write with slightly less complicated English words and phrases than... ifI knew I was addressing only native English speakers - I've actually been shocked at the large number of US domestic students I've had who get lost when I use polysyllabic words in my math classes.

@MartinArgerami ... or maybe those tests are crap measuring someone's language skill, and the whole test-based approach is a big mistake, but hey, who am I to judge.

@Kimball Could that be because you're using words like "polysyllabic," which are not at all part of the vernacular? Sure, as a native speaker, I can tell immediately what it means, but why use obscure words when it isn't necessary, especially in a math class? If it were a literature or linguistics class, that would be a different matter, though, of course.

@Greg: I have no love for those exams, quite the contrary. But I'm certain that those students that come to my office and just cannot formulate a simple question, would not pass the language exams that I have witnessed, that said students supposedly passed.

@MartinArgerami Just curious: How many languages do you speak? How many such tests have you tried/seen? In my opinion, most of these tests are dumb and enforcing bad learning habits. I know many who passed these tests for the sake of passing these tests, without cheating, but without speaking good English.

@Greg: my native language is Spanish, and I immigrated to English speaking Canada in my 30s. My first experience in an English-speaking academic environment was at age 30. Three people close to me had to take IELTS (two cases) and TOEFL (one case). All three failed repeatedly and took several attempts to pass. All three had been living in Canada for years and had passed university classes with good grades. Opposite to this, the students I assume cheated are students that come to my office and cannot ask "when is the test?" or similarly simple questions.

@MartinArgerami Good argument, thank you: so you yourself agree that these tests are very poor at assessing language skills that are needed in an academic environment or in other real-life scenarios. Your only problem is that you automatically assume that people are cheating who are already aware of this fact and actually preparing for the test.

@Greg: my experience was with people that were preparing for the test, they were already fluent in English, and still the test was very hard. While I agree that the tests are bad, I don't agree that a person who cannot form any coherent sentence in English can pass them without cheating.

What language is used in courses within Germany? Is there an expectation of "dumbing down" the German grammar in order to more fully embrace foreign students' understanding of the materiel? (My point being this is NOT a US problem, nor an English-language-specific one either. If you attend a college/university in a country other than your own, then be as proficient in the language used as possible.) Going to Germany understanding no German is a problematic as coming to the US and lacking ESL skills.

@CGCampbell Good point, but unlike many American or UK universities, German universities do not have profit as the sole focus and rely less on the $$ coming from students from Asia.

Being at a disadvantage due to a lack of necessary skills does not seem unfair to me. The ability to communicate clearly in written form is an essential skill for pretty well everything that we hope that our students will go on to do in their later life. Thus, it is a skill that we should actively encourage them to develop, by pretty much the same methods that we encourage them to develop, say, mathematical skills. That includes methods such as assessing them on that ability.
Just for reference, my department explicitly awards 20% of the available marks on each assignment (not including exams, because expecting people to re-draft work under time pressure is unreasonable) for "clarity of written communication". Neither this, nor a more implicit approach, is unfair: it is an assessment system rewarding better results to more able students, which is precisely what assessment systems are supposed to do.

I agree with you, but it is worth keeping in mind that someone with English as a Second Language is at a disadvantage for reasons outside their control (whether it is arguably fair or not). I can muddle through a basic conversation in Spanish, but I would have a hard time doing anything mathematically in Spanish more complicated than making change.

@TimothyAWiseman On the other hand, choosing to attend a university in which the instruction is in a language that you do not speak very well is generally within your control. At least in my country, quite strong English skills are (theoretically) required to study at university, so anybody studying here without such (and there are a surprising number) actively cheated on or otherwise bypassed the necessary tests.

@TimothyAWiseman it is absolutely in your control to not attend uni that uses a language you don't understand. it's not something they keep hidden from you and then woah surprise, they use english in the US.  The english in a math course is, or should be, the least of someone's worries if they are weak in that area, because it's not like it gets any easier in the English lit course.

@eps A lot of foreign students in the U.S. come for grad school. There are no English Lit course requirements for, say, a Master's or Ph.D. in Computer Science. Granted, you do have a point with regard to the case of this particular question where it's a Freshman-level undergrad class, which such courses would indeed be part of the required curriculum.

Frankly, I wouldn’t be surprised if changing “English” to “Plain Language” was sufficient to quell students’ concerns. It neatly sidesteps their manifest discomfort with the language itself. I doubt the manifest objection is the whole story—STEM folks always bristle at problems you can’t just calculate—so maybe you’ll even have more interesting and relevant conversations.
If you still hear objections, why not provide some resources? From the lowest level of personal effort to the greatest: You could refer your students to an on-campus writing clinic. You could offer a list of texts you found particularly illuminating when you learned to express complex mathematical ideas in writing. Or you could make sure students who were struggling knew you were available to discuss their work during office hours.
The responses others have offered are oriented towards winning your conversations with your students. It’s true there are larger structural problems in play for which it would be unreasonable to hold you responsible. The observation that Kids Today demand license and call it liberty is also hard to dispute. But your class isn’t about that, and your students aren’t an expedient means to proving a broader claim about society.
Your question makes it clear that you take your students’ education seriously and believe you do them a service by pushing them. Good! That’s demanding work, and too few academics are interested in doing it. But whatever else it may accomplish, making “Life is unfair” the hill you die on doesn’t teach them anything they didn’t know already.
(It also seems way more exhausting than pasting a couple hyperlinks into your PowerPoint, but that’s between you and your clipboard.)
The quotation is meant to be a little uncomfortable—counterintuitive, surprising, thought-provoking. Discomfort is an opportunity to learn. For that purpose, “English” is the single least interesting and relevant word you’ve got.

+1 as well, thanks for writing this. As a side note, I will say at the moment I'm hamstrung in some ways by distance learning -- formerly I was told my students could walk into the writing lab, whereas currently online writing-lab tutoring is gate-kept, requiring registration in an English course. Totally agreed that "life is unfair" is the about the weakest possible response, and I'd never say that.

(+1) for I wouldn’t be surprised if changing “English” to “Plain Language” was sufficient to quell students’ concerns, which is a nice and very easy fix to the sensitivity issue that might be the cause of many of the student complaints.

@DanielR.Collins That’s so frustrating—you’d think someone in the school’s administration would notice that students enrolled in an English class probably already felt pretty comfortable with their English.
Sorry to have aimed that “life isn’t fair” bit at you. It was the most popular comment at the time I responded and that soured my sense of the tone.

@DanielP.Shannon: 100% with you on both points!

A short explanation of my grading philosophy in this instance often comforts my ESL learners:

While I will not take off points for general English mistakes (for example with grammar), I do take off points for mathematical English mistakes, that change/obscure the mathematical interpretation of your response.

While this does not put ESL students on the same footing as native English speakers, both groups struggle with technical language in their early proof classes, and so this puts the emphasis on what it's my job to teach all of them: good technical writing skills.

This is essentially the answer I would have given. The answers shouldn't be graded on the quality of the English, as long as they're understandable and express the correct mathematics.

(+1) I didn't see this answer until I'd already written and posted mine, but this philosophy is behind pretty much everything I wrote in my answer.

For my university at least, English proficiency is a requirement for enrollment to the point that students who learned English as a second language are required to take an English test like TOEFL as part of the admissions package. Therefore, although it may sound harsh,

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.

is the assumption I make. (If I were to take classes or teach in a country that does not speak English, I would think it reasonable to have to learn the local language.) My class is not about reading, writing, or speaking English, so I will suggest students visit the university writing center if I notice them struggling.

(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).

I think that math work definitely requires less language skills than some other subjects where writing is a larger part of the answer, but students still have to be able to understand the instructor's communication and explain their answers.
As a side note, I sometimes see students trying to derive a result algebraically without understanding what the math represents, and I usually suggest they describe their approach conceptually before going through the technical details.

Communicating academic work is a key part of doing academic work. Communicating in different forms (symbolic, graphical, natural language prose, computer code, ...) is essential to engage with different audiences. As an effective communicator of academic work, you don't get to choose what is best for your audience, so you have to learn to be effective in multiple approaches.

Who is 'you' in this answer? The lecturer or the students?

Both, but this answer should be read as a direct response to such a student comment.

You (Ian), as an effective communicator,  can edit your answer to make it clearer.

I, as a lazy student, am accepting the poor marks received for failing to communicate clearly.

In addition to the other good answers:
There are two somewhat separate questions here, or maybe three. One is about the way "natural" mathematical questions arise in an English environment. Another is about old-or-new English formulations of direct mathematical questions in a classroom setting. Another is about responses in either case.
For complaints about having to respond coherently, as though it demanded an inordinate level of English fluency: well, no, it doesn't. A very rudimentary style is sufficient, and perhaps even better than long compound-complex sentences that self-interrupts, etc. Hemingway, not Faulkner. But, yes, English-style sentences. Not strings of various nouns and verbs with neurotic periods and capitalization.
Comprehension is a harder question. But for kids wanting to work in the U.S., "even in Math or tech", the "secondary" skill of fluency in English can be a decisive competitive edge. There are lots of people with good technical background, but with communication problems.

Each unnecessary mathematical symbol has a universally-applicable English equivalent
Replacing symbols with words is easy. Your students can just learn a single phrase to replace each symbol, and use that whenever they would use the symbol. Avoiding symbols isn't the hard part of writing mathematics in English.
The hard part of writing proofs is writing with proper structure. Students need to present their ideas in a logical order, signpost how each idea relates to the next, and have an appropriate structure for their proof. Importantly, these skills are only slightly language-dependent. If a student can write a good proof in their native language, a word-for-word translation of that would probably be better than many proofs written by native English speakers.
Your course notes or textbooks contain many examples of the language used in proofs
Native speakers as well as non-native speakers often don't know how to write proofs. I tutor a mathematics course with a writing assignment, and our standard first-instance answer when students ask how to write proofs is that they should copy the style in the notes. Our university devotes two weeks of one of its courses just to writing proofs, and I've heard of a university with an entire course dedicated to mathematical writing.

+1 If I were in this situation I would create a chart of symbols in one column and the correlated words and phrases in a second column so a symbolic proof could be replaced by words. A lot of the difficulties of spoken and written English do not really crop up in mathematical English.

This is so much more concrete than mine! And the focus on structure is very insightful. Thanks for articulating this.

I would answer:
"It is, nevertheless, an essential part of the skill you are here to learn. It is no different in principle to students with a weak mathematical background due to their previous education. As with any other challenging circumstance a student may face, specialist help is available for anyone having difficulties with any part of the curriculum and who needs to catch up on prerequisites."
If this is a common problem, there ought to be language tuition available specialising in remedial technical/mathematical English. Or they could get in touch with older/former students with a similar language/subject combination, find a study group, etc. But as regards "fairness", this is no different to the disadvantage faced by students who went to bad schools that didn't teach them calculus, or complex numbers, or whatever. Everyone has their own individual hurdles. For one student it's calculus, for another, English. Ask yourself, how would you answer someone who said they were not taught some prerequisite bit of mathematics at their previous school and it "wasn't fair"?

"Ask yourself, how would you answer" I'd say they are correct.  It is unfair.

"Nevertheless" suggests that you accept the claim that it is unfair.

Consider the statement "Requiring students to exhibit a skill is unfair to students who don't have that skill."
The statement is true if the skill is not related to the course.  It is unfair for a course in, say, discrete mathematics to require that students exhibit, say, the ability to swim.  This is because one can do discrete mathematics even if one cannot swim.
The statement is false if the skill is related to the course.  If is fair for a course in discrete mathematics to require that students exhibit the ability to count.  This is because one cannot do discrete mathematics if one cannot count.
Is the ability to write mathematical proofs related to a course in discrete mathematics?  Yes, if the focus is on theory; no, if the focus is on applications.
Is the ability to write in English related to a course in discrete mathematics?  Yes, if the course is taught in English; no, if the course is not taught in English.
Tell your students that your course focuses on theory and is taught in English.

Edit: It has (correctly) been pointed out in the comments that even though one cannot do discrete mathematics if one cannot count, one can still do discrete mathematics if one cannot write in English.  The reasoning I used in paragraphs 3 and 4 is not the same as the reasoning I used in paragraphs 2 and 3.

Good analysis. But as for the conclusion that it is not unfair, I think the feeling of unfairness comes from the fact that English is actually not required to do math: there are mathematicians who don’t speak any English. The requirement to speak English is a practical requirement, a bit similar to a requirement that a student needs to be able to walk down stairs because the lecture hall does not have an accessibility ramp. So one can argue that there is a bit of unfairness here, at least if the student wasn’t properly made aware of the importance of coming with good English preparation.

@DanRomik Yes, English is not required to do math in the same way that, say, Swahili is not required to do math.  But if the course is taught in English, then I would argue that English is required to do Math in that course.  If a course is taught in Swahili, then a student who knows only English (and doesn't understand the teacher or the materials, and is unable to answer using Swahili words) should not complain that it is "unfair."  What would be unfair is to require a teacher (who is hired to teach in English) to learn Swahili just so that their student could learn math better.

Also, writing mathematical proofs is not required to do math in the same way that, say, being able to write programs is not required to do math.  If the student only needs the math as a tool (for practical applications), then they could argue that it is "unfair" that they are required to write proofs.  But if the course is explicitly one that focuses on theory, then would you say that it is "unfair" to require that students write proofs?  If the course is explicitly one on how to write programs to do math, then would you say it is "unfair" to require that students write programs?

@DanRomik Anyway, you make a good point that my paragraphs 4 and 5 do not follow the reasoning in my paragraphs 2 and 3, and I thank you for that observation.  I'm leaving the computer soon, but when I return, I'll try to edit my post to include your comment.

@DanRomik (By the way, I agree with what you wrote in your answer and I upvoted it.)

Thanks. I don’t have a strong opinion about the fairness issue. I said “one can argue” because I think it is a valid argument, but there are valid arguments also in the opposite direction (as you and others pointed out) so in the end it doesn’t seem clear-cut to me whether it is fair or not, or whether that’s even an entirely meaningful question.

I first would recommend that you talk to the writing support services people at your institution, such as the writing center or the center for teaching and learning.  They will have some suggestions for you about how to approach this topic in a way that is constructive and useful for students.  I'm not in math, but I do have students who have challenges with standard written English, both immigrant and native born.
Here are some ideas I would suggest.

I always say that one of my learning outcomes is that you will improve your skill in writing. This is not a grammar class, and writing mechanics will not be an important part of the grading, but what will be important is that you get a lot of practice in professional writing in our discipline.

You can also add oral expression to this, and your example of explaining on a walk is a nice way of expressing this.  I would even consider adding something about that in your learning outcomes.

All the writing pedagogy people will tell you two things. One is that to get better at writing you have to write a lot.  The second is that revision is essential.  Create opportunities for your students to revise their writing.

Don't try to teach a grammar or composition course. You're not actually qualified for that besides the fact that you have math content to cover. If you can help students make small steps in their writing be happy with that.

Make sure you encourage students to take advantage of tutoring and other academic supports.  Remind them every week that this is an option so that using them becomes de-stigmatized.

Since you are a fellow CUNY person I would strongly suggest that you see if you can get a WAC fellow to work with you. They are generally excellent and have good training.

Update
I have been thinking a lot about your question.  I think we were missing the point (largely) because the students weren't asking about writing but about writing in English.  Here's what I've been thinking.
First I think you should reassure them that if they are doing math in their first language, that is normal. Being able to do math in a second language is the last or close to the last point of fluency.
What I might suggest is that you say they can write in their own language, but then translate into English if they prefer.  I'd have them hand in both along with the Google translate version so that you know they went beyond that (which is the obvious first step).   Your goal then, even though you won't exactly grade on it, is to help them get more fluent in English.I think you should stress to them how important this will be in the workforce.   You can also encourage them to write directly in English and say that you'll grade it to the same standard as the translated submissions, not expecting perfection.

+1 Thanks for this; I'm glad you shared it, as it may be helpful to others. In my case, most everything you've suggested is stuff I've already added/tried. When I've touched base with my writing center in the past, they seemed trepidatious, yet said they'd accept my students in the lab -- but currently that's impossible, because online English tutoring is now gate-kept by the need to be registered in an English course. I fear a WAC fellow would be very frustrated by my technical situation.

That's really frustrating about the writing center.  The thing bout WAC is (at least for us) they help you to think about how to be encouraging to students so they can overcome anxiety, among other things.

Thanks for that. I've been thinking about your 4th bullet for a day now. I think I would pose that writing math (while mostly in English) is a specialized, technical form of writing (including its custom grammar and composition), and arguably I'm better trained and qualified for that than anyone else on the premises.

Just to be clear: You're not a WAC fellow yourself, but that's a resource you've used in the past?

Correct. The WAC program is something I have used. But each campus organizes their programs differently, so you may not have that exact option. But I think if you have WAC coordinators you could ask them for a consult at least.

@DanielR.Collins  Updated this with some new thoughts.

Related: https://academia.stackexchange.com/questions/127116/how-to-write-papers-efficiently-when-english-isnt-my-first-language/127203#127203

Maybe something like:
"It is important to understand the motivation of why something is done as well as the underlying beliefs/assumptions the writer has made. The role of mathematics is to allow us to understand complicated relationships between aspects of reality, the symbols' role is to help reduce mistakes in logical reasoning and allow us to deduce counter-intuitive relations with a high degree of confidence. However seeing a formula, and understanding a formula, are very different things. The second of which is important for extending our understanding to more advanced mathematics and applying these formulas in new or innovative situations."
If you are working with computer scientists or physicists this ability to explain in words rather than just symbols is important since the mathematics is only a means to an end rather than a thing unto itself. For mathematics students you could find the counter argument that mathematics is separate from the rest of reality and so symbol pushing should be enough. But that fails to take into account that the mathematics that they are working with is being worked with in a fleshy ball of meat, living deep within reality. Something that doesn't work well with just symbols disconnected from reality and has a limited amount of memory. This leads to the need for any student to be able to chunk ideas together when they want to learn more advanced topics, this is much easier to do with verbal and intuitive explanations than just a bunch of formulas and relations.
As for the students who are really bad with English, get them to first write their response in English, then a second time in their native language and run it through google translate. You're not going to be testing them on their grammar so the mistakes google translate put in probably won't obscure the underlying understanding that much if it was there to begin with (assuming its a fairly well represented language). And since your language of instruction is English, then if they can't understand that they should be spending time improving their English, and this gives them an opportunity to practice using English in a highly specialised case which they probably wouldn't otherwise get.

Rather than trying to respond to student reactions to that particular quote, it might be better from a sensitivity standpoint to simply give several examples with explanations, perhaps categorizing the examples into a few named types of poor exposition. Then, perhaps at some later time when students have had some experience in "writing mathematics" and getting feedback, you could present the Halmos quote in class and ask students to discuss what they think it means.
One type of poor exposition is excessive symbolism, which is discussed in Section 15 Resist Symbols of the Halmos paper (originally published in 1970 and reprinted many times since then). For example, one should resist the temptation to introduce notation in the statement of a theorem that is only needed to prove the theorem, such as "Theorem: Every point p in a bop-bee quasi-uniform space X has a proactive neighborhood." There is no need to include p or X into the statement of this theorem. However, I see this advice violated in just about every math paper I look at. Regarding excessive symbolism in general, see my answers to the Mathematics Stack Exchange questions Using the implies symbol in proofs and How formal or informal should math texts (written for different purposes) be?
Another type of poor exposition could be roughly identified with the linguistic term "structural ambiguity", and would include both incorrect and ambiguous uses of quantifiers, such as missing quantifiers, incorrect quantifier order, and what is sometimes called a hanging quantifier. It also includes more English-specific scope issues like "John sent a letter to each of his students" (Was the same letter sent to all students, or did each
student get a personalized letter?), and "Every researcher of a company gave a presentation" (Did all of the researchers belong to the same company?), and "big truck driver" (Does this refer to a driver of big-trucks or to a big-driver of trucks?), although these more English-specific issues might be too tangential and overload your students with too much information (and thus handled on a case-by-case basis as they arise).
Still another type of poor exposition is the incorrect use of notation and terms, and I'm sure you can give many examples. One type of ambiguity that ordinarily doesn't cause problems, but which might be useful to mention in light of your course topics, is the use of "and" when an order is involved, such as "the ratio of p and q" and "the difference of p and q" and "the quotient of p and q" (example in my present line of work and my comments about it). However, I definitely recommend not falling into the rabbit hole of being obsessively correct for your students, and instead stick to the most significant concerns. Some things in the answers/comments to Abusing mathematical notation, are these examples of abuse? are what I consider as obsessively correct for your students, and very many of the things discussed in this critique of Rotman's book An Introduction to the Theory of Groups, written by the author of this book, are what I consider as obsessively correct for your students. Probably a better term than "obsessively correct" exists, but this is the best I can think of now.
For the most part the examples I've given are of a logical and mathematical character, and I think most of your focus should be on these types of examples, and not on grammar issues specific to English, although of course when grading student work you should point out grammar issues if you notice them (except those students who have a huge number of grammar issues in their writing, and for those students you may want to seek the advice of someone locally, as suggested at the end of @Elin's answer).

There's so many great answers here -- so I'm submitting my own so as to organize my favorite observations for future reference. My answer in future classes will be a combination of these insights:

English proficiency was required, and tested, to enter the college.
Writing in natural language is an integral part of the subject, as well as any academic work.
The writing we do is in fairly plain, simple English. If one can write a cogent, simple proof in another language, then it's a fairly easy job to translate it.
The hard part is really understanding the mathematics, not the notation.
If someone is weak at writing, then it's good to get practice, which we provide.

This quote is not about English but about avoiding symbolism when natural language can be used. Paul Halmos was born Hungarian, and the best way to understand this is to imagine him discussing math in Hungarian with another Hungarian born prominent mathematician of his era, such as Paul Erdős or John von Neumann.
And this quote is generally misunderstood when applied to students.
Students (and mathematicians) should acquire proficiency both in using symbolism and in avoiding it. When one is unsure if an argument is valid one should be able to write it symbolically and that may help in verifying whether the argument is valid. Then when one wants to communicate an argument to someone else, avoiding excessive use of symbols helps.
Students should be encouraged to experiment with writing the same argument with more and with less symbolism. Students who are less proficient in the natural language required in the homework would have the added value of acquiring more experience in the use of that language.

If students have been assigned to write in English and they complain:

This seems unfair to students who have poor English skills

The correct response is

Some students learned English as a native language and other students learned some other native language, but everyone is expected to write in English.  Yes, this is unfair.
Most of the money and power in the world is associated with using the English language.  This is unfair to people who speak other languages, but nobody knows how to change it.
The best thing we are able to do about the situation is help students learn English.
Completing this course will help you learn English.  For example, writing proofs in English will help you learn English.
Many students who are English language learners are successful in this course and in this discipline.  (add examples)
The resources available to help you are ...

+1  The purpose of education is for people to learn new skills and to improve the ones they have.  A course that challenges students to practice and improve the skills they are weak in is the whole point of being there.

I agree with the students, and think that quote is used in the wrong context. I don't know why you'd discourage using standard notation. In my teaching I wanted the students to use the correct technical terms. More importantly, I tried to get them to understand that jargon for a complex idea is natural and not show-offy at all. It seems to me you're going out-of-your way to add English proficiency where it's not needed.
Jargon-wise (which I realize isn't the same as notation, but close) I was glad when students were finally comfortable replacing "rules for how the symbols have to be" with "syntax" or "the input value in the call" with "the argument" and so on (I taught lots of intro programming). I had plenty of international students and quickly realized that most plain English is chock full of idioms, complex tenses and other challenging bits. They're already stuck listening to my colloquial English explanations, which is torture enough. And it's not as if jargon is a crutch -- you have to understand it to use it properly.
That quote -- I think I know what it's about. Most new notations are bad. Alternate ones spring up and it takes a decade before the "obvious" best way takes hold. I've read papers on new ideas where they spent time on a notation which wasn't all that clear and wasn't used much. They could have simply written "let A-prime be a compressed version of A which adheres to the previously discussed requirements". I think the quote is saying: "if you have a new idea, just say it. A good notation will come much later once the idea is explored".

Short and to the point

This is not unfair. The college has a TOEFL requirement for
enrollment, and any student work will be graded in English only.
Algo, the guidelines ask for simple English, so it's beneficial to
people with no mastery of English.

I don't think immigrants have to take TOEFL, this is not people coming from abroad to go to college.

Hopefully a professor commenting on the English requirements will not be writing "algo" instead of "also".

The original slide doesn't push the reader to use English.  Pretend that you are explaining the subject to a friend.  This pretense could be done in the favorite language the two of you share.  It doesn't have to be English.  There are many languages that are just as well suited as English for this purpose.
Now the question becomes how to communicate with the professor.  If the best language for this purpose is English, then that's the language to use.  This may not be fair, but it's useful.
It may put some people at a disadvantage.  They may have to work harder to polish their English communication skills.  This could serve them well later on.  Another solution is to find a different professor who teaches the same course, but in the student's first language.

as an aside, during part of my career, my assignment was to travel to Mexico or Puerto Rico and teach short courses in database design in Spanish.  Concepts from relational mathematics are very useful in this context.  I found that learning how to express these concepts in my second language gave me a deeper appreciation of the concepts themselves.

This is an overreach, but I suggest that instead of just formulating a counter-response, you spend a class or two familiarizing the students with the required terms/words in their English sense (rather than the strictly mathematical sense).
Many non-native English speakers struggle to build an intuition for slightly abstract math, because they have never used the words manifold, convergence, degenerate etc. in their daily life.
Exposing students to these terms in the preparatory part of the course will help allay anxiety and also implicitly convey that appropriate terminology/syntax is required in the course. Maybe that can be made explicit as well. If the course schedule doesn't permit these extra hours, you could consider circulating handouts and having a non-graded quiz on the same.

I've had a small number that apparently needed every course lecture translated by a friend, and couldn't communicate to me directly

If they can't communicate in even the most basic English, I have a difficult time understanding how they could pass TOEFL to begin with, unless your university's entry mark for TOEFL is in negative territory.
Anyway, you seem to think that this is something that's your responsibility and something you can and should do something about. It's not. If students are coming into an English university, with courses taught in English, then they had better bloody well be able to keep up with the English that the instructors are using.
The simplest way to explain this is by turning it around on them, so:

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

"If I had chosen to study at an institution that uses <student's native language> for instruction, and I lacked a fundamental grasp of that language, would it be valid for me to claim that it is "unfair" that I cannot understand the instruction being given?"
If they answer "no", they have defeated their own argument.
If they answer "yes", get them to articulate why, because either they are just being difficult, or their reasoning will be unsound and easily defeated.

@AnonymousPhysicist How is not having a choice "inappropriate"? Your argument makes zero sense.

That's not what I said.  Your answer denies the truth, which is that most student's choice is between studying in English and not studying.  Your answer, in the second to last paragraph, implies students chose to study in English when they could have chosen to study in their native language.  Therefore, your answer is very inappropriate.

@AnonymousPhysicist I was doing nothing more than outlining a hypothetical situation as a way to challenge the student's assumptions and viewpoint on the matter. It's a standard and scientific way of constructing argument and there's zero implication there, only your assumptions.

@AnonymousPhysicist Further, if you're going to post a comment that attempts to make a point but does so poorly, don't get upset when people don't get that point. Don't delete that comment after its poor quality becomes apparent, it makes you look dishonest. And especially, don't delete that comment, then chastise someone who responded to it, for missing the point - that you failed to adequately make!

I deleted it because it was not written clearly.  I am only criticizing the answer.

Regarding your rhetorical question “if I had chosen to study [etc]”, I would say that if the non-English speaking university admitted me despite my lack of necessary knowledge of the language of instruction, thereby misleading me by implying incorrectly that they consider me qualified to succeed in their course of studies, I would actually have some valid reason to complain. Whether it makes sense to use the word “unfair” in this context is a tricky semantic question, but the point is the answer to the rhetorical question is less obvious than you might think.

@DanRomik That sort of complaint should not be directed at an instructor, but at the university administration.

This is certainly a response, but one that borders on the obnoxious, for reasons that are possibly not clear to you. I'm glad to elaborate in chat if you're interested.

@DanRomik university admissions processes are complicated and far from perfect. I wouldn't act as if they are perfect.

I would turn this on its head: 1) English is a basic skill you need in all paths of life - especially but not only in an English speaking country. 2) Some natural language is specifically needed to communicate about math and in your course that is English. So English is a two-fold requirement, thus it is fair to use it and request using it and in addition, using it also supports acquiring and improving the general skill of communicating in English. Languages are far better acquired if they are actually trained in different settings than solely in language courses. So you do your students a favour in helping them improve their English alongside learning math.
I've studied in a country where English is a foreign language and yet the same argument was provided there (university-level/college) for why the majority of classes was in English. Sure there were nay-sayers, too, and they were guaranteed enough courses held in the country's official language to pass their Bachelor's degree without having to go to an English language course, but few used that offer and there it was English or official native language of the country which likely in your case is English, too.

This is barely an answer, but having students with language issues is hardly new, and your college probably has resources for such students.  You should locate them, and guide your students to them.
You should look into what language assistance resources are available for students, particularly ESL students, at your community college -- maybe there is a writing lab or something.
If you can locate the resource, you should have a discussion about this issue with the person that heads this resource, and work out a plan for how to bring these students to a higher level in your course.

I've done that in the past and have it on my syllabus. I believe that to date no students of mine have ever made use of those resources. And it's been made worse in the current distance learning situation: the online English tutoring is gate-kept and only available for people currently registered in an English course.


text:
Received a mail from a collections agency
This is slightly long so please bear with me. This is for a friend and I'll be writing from his perspective.
I am an international graduate student at the University A. In 2016 when I was receiving decisions from grad schools about my applications, I got accepted into University B. I enrolled in a few courses(12 credits) while I was waiting for other decisions. Before I even requested an i20 (a document that international students request when they wish to go to a certain university in the US after being accepted by that uni) from B, I got accepted into A and went there instead for grad school, and consequently never requested an i20 from B.
This week I got a mail from a collections agency stating I owed 22k in fees for the courses I enrolled in all the way back in 2016. I checked every bit of mail, physical or electronic, that I may have received from B in regard to these courses in all my email accounts and residences, which I never did. In fact, the only emails that were found in my gmail were those of my failure to check in after my acceptance from them.
I contacted student accounts at B asking them about this issue and they asked me to get a tuition exception recommendation from the school of engineering. The school of engineering is recommending me for this exemption. The next step in this process is me submitting an appeal to the student accounts department.
This is where the issue arises. Student accounts states within its tuition exception process and guidelines document that appeals for tuition exception must be made within the same term as the courses. I am worried that they won't accept this recommendation from the engineering department despite them knowing the details of my case and never having raised this rule when I spoke to them earlier.
What recourse do I have if they refuse my appeal? I never requested an I20 from B which indicates I never checked in despite their emails to my gmail account they created for me. And most notably, they never sent me any course material or any TA emails for those courses, as is the norm for any courses that people are legitimately enrolled in. I don't have 22k to pay these people.

If I got mail from a collection agency stating that I owed some money that I don't actually owe, the first two things I'd do (I'm not sure about the proper order to do them) are to write back that I don't owe this money and to consult a lawyer.

I'm not sure I understand the situation. Did you enroll  and never attend or did you enroll and actually take classes? If the latter, why didn't you think you would have to pay tuition?

Adding to @AndreasBlass I think it is also very important if this is a simple mistake or if they intent to get the money from you no matter what. While I generally don't expect such a behavior from an university, some bureaucrats can be real assholes. But you can't know that in before. Maybe have you can have a simple telephone call to check? But I don't know the legal implications of telephone calls in your country, so you may wait for an expert answer :)

@SK19 I agree with most of your comment, but the fact that the OP got a letter from a collection agency, not from the university, indicates to me that someone wants to get the money (or at least some of it) no matter what.  I'm assuming here that the OP means the same thing as I do by "collections agency"; the sole purpose of such agencies is to get people's money (or make a deal to get part of it).

The collection agency could be trying to collect on behalf of the university (that might act reasonably if you can establish that you didn't enroll or properly withdrew after enrolling)  or the debt could have been sold to a third party (who will probably only give up when/if the costs of collection exceed the $22K owed.)

@BrianBorchers - Your comment is helpful up until the word "owed" at the end.  There is no money owed in this case.

@Flameofudun - You're putting the cart before the horse.  Let them give you or not give you the piece of paper you're requesting; then ask what to do about the piece of paper not having been provided. // Note, another possible explanation is that a shady collections agency was given (who knows how) a list of people who expressed some sort of interest in a particular school, and then they went fishing.  You could ask on Law SE but my guess is that if you ignore their letters, and tell them there is no one there by that name when they call, they will stop bothering you.  However, ...

... another approach would be to call their bluff and let it go to court.  If this were to reach court, you would go and explain things calmly to the judge.  The collections agency would not have the documentation they would need to extract any money from you, and this would be a simple thing that would not even require you to get legal representation. // Don't hesitate to work your way up the GWU administrative ladder.  If you get stuck -- try talking to the secretary of whoever's at the top. // If you're really concerned, at some point -- some lawyers will give a 15 min consult for free.

I'm voting to close this question as off-topic because at this point it's a hypothetical question.

@SK19 B is a respectable institution and I fully trust them to do the right thing. So I'm not pointing any fingers at their administrators. This is probably a simple misunderstanding.

Here are some educated guesses:  B has a collection agency which they regularly use.  They sell their bad debts to this agency at a (deep) discount and now that agency owns the debt.  They're taking a gamble that they can collect the debt.  (It is very possible that this "separate" collection agency is really just an office on campus.  But that makes little difference.)
I would write the collection agency and tell them that I have never set foot on B's campus and that I don't owe any money to them.  I would make a sentence like, "As an international student, I could not be enrolled at an American university without an i20.  If B cannot produce my i20, that is proof that I never attended there."  I would guess that at this point the agency would realize they lost their bet and go on to the next victim.
If not, things have entered the "nasty" stage.  I doubt it gets so far, but if necessary, write a letter to B accusing them of fraud.  Your premise is that they know that foreign students are typically naive and apply to many American schools.  If they find that a student applies at B and but attends another American school, then they send a bill hoping the student is afraid of running afoul of obscure American laws.  They use scare tactics to try to collect tuition and fees to which they are not entitled.  Fearful of being deported, many of the foreign students pay the bill.   Something like that will at least get their attention and a human will check the records carefully before they make another move.   The last thing a university wants is an investigation.  At the moment, some bored peon is glancing at your letters or day-dreaming during your phone calls.  You need to get them to sit up and pay attention, and such a letter will do that.  If they look at the record seriously, that should be the end of it.
If not, send the same letter to the local county attorney and/or the district attorney.
Let me repeat that I'm just guessing my way through this given the data at hand.

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text:
How do undergraduate theses affect master's application?
I am an undergraduate student and have a plan to apply to a master's program.
I am about to start to work on my graduation thesis for graduation at my university.
Question: How does my graduation thesis will affect applying to master's program?

This may depend on your situation.  What country and field?

@Kimball Europe, probably Germany, math.

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text:
How to find connections to go abroad as a visisting PhD student?
I'm PhD student and I want to go abroad as a visiting PhD student.
Is it recommended to contact professors directly if you want to collaborate as a visiting PhD student?  or it is better to get connection through your supervisor?
My supervisor doesn't have any connection for the places that I want to go!

This is far too broad and the answer is likely to be different for every subject and every country one might go to. It's also exactly the sort of thing your advisor is there to advise you about. Even if they don't have any direct contacts, their contacts may have useful contacts and they will know what the norms of your area are.

Please clarify where are the places you want to go to and the area you study.

I'm applying for universities in Germany( mainly Berlin) and the area of my study is quantum optics and quantum theory of condensed matter.

As a PhD student I did exactly that, contacting professors for exchange about two years ago, and that worked very well for me. (I ended up visiting a top UK university and the collaboration was, and still is, very productive.) My supervisor was involved in discussing the places I wanted to go, but I handled all contact. Some advice:

Study the professor's webpage (if they have one) to see if it says anything about collaborations. If it says on their webpage that they have no time, don't contact them.
Send the professor an email, give them a week or two to answer, then follow up with a second reminder-email if there is no reply.
Important things to do/mention:

Make sure the email is very short, but that it still describes precisely what you want to collaborate on. Professors are chronically short on time.
If you have a travel grant etc. that will fund your stay, it's important to say so. (They're much more likely to accept you if they don't have to spend any money. But I think most universities will waive term fees if you ask them.)
Add a sentence about your accomplishments so far, so they have some
impression that having you visit is going to be a net gain for them. Mention any papers you've co-authored, if you add a link make sure it's short (DOI, arXiv etc).
Try to keep the email self-contained, but linking to any papers, your CV or research webpage "for more information about me" is OK.
Also add a sentence describing how you think your proposed topic fits
with what they are doing, so they know you've actually checked out their group and read some of their papers etc.

In my experience, most people reply positively to such an email, so first send emails to the two or three places you want to visit the most. If none of those are successful, send to the next few places on your list. YMMV though.


text:
Etiquette: how to handle unwelcome invite to collaborate?
About a month ago I had a phone call with a research funder (RF) and an academic in my field (A), initiated by RF. I've been working publicly on research question X for some time, A has not. A is from a more prestigious institution than me.
During the call RF said "Richard [me] has been researching systematic approaches to X, using methods Y and Z". (This research is under way, and I have a funding bid in with RF for it, although we didn't mention that on the call. Methods Y and Z are original and I'm quite excited about them.)
A said they thought X was interesting, and they'd been thinking about another method to approach it - I think this won't work as well, though I didn't say that.
After the call, I said to RF I wished they hadn't been so explicit about Y and Z, since I was concerned that A would use them, and I would have preferred to keep them confidential. RF apologised, and said that they'd had bad experiences with A using other people's work.
I have since had a short email from A saying they've successfully begun working on systemic approaches to X, and asking if I'd like to collaborate.
Obviously, there's no patent on the idea of systematic approaches to X, and I don't even know if A wants to use methods Y and Z. However, I'm concerned that there's no acknowledgement that I'm already doing research on X, or of the call.
I also don't want to collaborate, since I already have a bid in, and even if that fails I feel dubious about A.
My goals are now:

Have A reflect on why they didn't acknowledge my work
Make it clear that any use of Y and Z will be unwelcome, and ideally dissuade them from using them (if they are)
Sound clear, professional and positive
Not antagonise A unnecessarily.

Questions:

Is there a way to achieve this?
It would be useful to understand: is this normal behaviour from A? If the situations were reversed, I would acknowledge A's work and wouldn't use methods they were using. But perhaps I'm just naive?

This all seems quite bizarre to me; what was the purpose of the call with RF and A, and why did you take this call?

@BryanKrause because RF suggested the call, and they are a funder so I try to keep them happy. They wanted to introduce us, and for me to give feedback on a draft paper by A related to X. (In case it's relevant, RF are a philanthropic funder, not a government funder.) Why do you find it bizarre?

Mostly that it wasn't clear why a funder would be talking about your methodological details with a possible competitor without clearing it with you first. I know such things happen, but it shows they are either a bit clueless about etiquette themselves, or just don't care. I was trying to suss out whether they possibly think you incapable of doing this work and thought you'd have more success if collaborating with A and are trying to nudge in that direction. Their motives could be pure there, too (promoting mentor/mentee relationships), or impure (racism, sexism).

@BryanKrause thank you for the explanation. I hope it isn't that they think us incapable (RF invited us to submit the bid, and didn't mention collaborating with A then). I think it is just that the funder is inexperienced and keen to make connections between people in general.

This reads very much like a thinly coded version of “No thank you. By this email I am hereby recording the fact that this phone call with RF occurred and that methods Y, Z were discussed.” Now, you might think you have good reasons to want to have a record of those things. But it still comes across as a bit aggressive and mistrustful IMO, and also shows that your actual goals are a bit more than just being “clear, professional and positive”.
If you want to decline the collaboration politely and professionally and that’s it, I would send a much shorter reply saying something like “Thanks, I’m really flattered by your offer but feel like I have a bit too much on my plate right now to consider starting a new collaboration”, and leave it at that.
If you have other goals, like “marking your territory” in connection with methods Y and Z to discourage A from working on them, it would be best if you make that explicit in the question so that we can think what course of action is most appropriate. But I have to say, from my limited understanding of the situation, it sounds like now that A is aware of Y and Z, you have no way of stopping them from using those methods or submitting a bid for funding with RF that competes with yours, and you have no way of claiming any special ownership of the idea of using those methods. Maybe it sucks that that’s how it is, but I don’t see how having an email record that some phone conversation took place where some topic was vaguely discussed is really going to help you in any meaningful sense.

Thank you. My goals are as described in the paragraph starting "Ideally I'd like" - I'll edit the question to make it clearer! And yes, as it says there, these goals include trying to dissuade A from using my methods, if possible. I agree there's no formal way to stop this, but I was wondering if there was any other, less formal, way - e.g. by making it clear that any use of the methods mentioned on the call will be unwelcome.

Here is an almost-useless general evaluation of your situation: either methods Y and Z are difficult to apply to X, or they are easy.
Y and Z are difficult
If Y and Z are difficult to apply to X, then you are in little danger of being scooped by anyone. Even if someone has had the idea, they will have dismissed it by now, either completely out-of-hand or after initial experimentation. By persisting in Y and Z you have developed comparative expertise which has left you with unique insights into X.
In that case, a rising tide raises all boats. Collaborating with someone who has complementary expertise will increase your own skillset, and the freedom to specialize will let your team outcompete other groups working on X.
As an example: while working on my own research, I found that another group (which wasn't even on my radar!) had published about their software development which very closely paralleled mine. Thankfully I was spared the agony of decision because they reached out to me, after learning of my work from a professional contact.
Our subsequent collaboration has resulted in both myself and them each saving months of work -- I have learned a great deal about good software development practices, while they have benefited from my theoretical and practical insights, and we've both made new friends that have opened much wider potential networks to us both.
They've benefited, and so have I; it feels very silly to even try to think about which of us has benefited more.
Y and Z are easy
On the other hand, if Y and Z are easy to apply to X, then you're in mortal danger of being scooped at any moment. It's only a matter of time before someone else has the idea and publishes.
In that case, a race to the finish is what you must win. You simply have to publish first. If Y and Z are really that easy to apply to X, you should be able to publish quickly! Even if it's just a preprint to mark your priority.
As an example: There was a bit of theory in my field that I worked out months ago, in a few days. I still haven't published it, and every time I check my Google Scholar alerts I fully anticipate that someone else will have gotten there first.
But while I wait, I am furiously putting together my manuscript. I've already finished writing everything but the results, and I anticipate only two or three weeks' more work to finish those. Once I'm done I'll run it past my supervisor, and then we'll get it out.
Interestingly, I've examined my feelings about what will happen if I'm scooped, and they aren't actually too bad! One does get used to the sting (or leaves academia, which frankly is a rational and wise choice these days). In part it's precisely because this idea was so quick and simple to write up that I'm confident I will have more ideas like this.
Indeed, I have two or three topics that I want to pivot to after I've finished this one -- or, if I'm scooped, after it's finished with me. Interestingly it's precisely the collaboration I mentioned earlier that's given me the time and headspace to plan my next steps and give me confidence. So if I'm scooped -- au revoir! It's on to my next gig.
But what about A and their email?
Interestingly, your best response to this situation depends very little on A and their internal state. Either you'll decide that collaborating is best (my first suggestion), and send a short and simple email stating your choice and asking for next steps -- or you'll decide that collaborating is a choice you "currently don't have room for due to the various priorities already present, despite what an honor it is to be offered the collaboration opportunity!"
In either case you don't need to spend time and energy worrying about what A is thinking and why. That's time and energy you're not putting into research. And indeed, telling A that "even though PR mentioned methods Y and Z to you, I'd really rather work on them myself" -- in any wording -- is simply drawing unnecessary attention. (After all, if A is a nice person, you run the risk of needlessly offending them; if A is a nasty person, you've just drawn more attention to an area ripe for exploitation!)

I think this is really good advice, thanks!

Y and Z are fairly easy, so I should crack on and do a preprint asap. Follow-up question: am I missing a trick by not doing the same to others? Currently, I wouldn't pick up an idea or method that I knew someone else was working on first - it would feel rude. But is this just How Academia Works, and no-one else considers it rude?

But having an idea is the easiest part of doing research. You have to implement the idea, validate it, and build a network of peers who would use it and cite you (and who would review your papers, read your students' theses, speak at conferences you organise ... ). Also, I presume you will hear most ideas at conference talks where speakers will already have done some legwork preparing to publish those ideas, meaning you might work to "take" that idea only to have waste all that work when they publish ahead of you. Maybe your area of academia works differently -- it couldn't work in mine.

I agree that having an idea is the easiest part. I'd note that implementing and networking is easier for more senior academics - they have RAs and existing networks. Does that mean it's ok for to implement an idea that one heard about by chance from a third party, as in this situation? That still doesn't feel right to me - but perhaps much of the 'work' of academia is in acquiring seniority, therefore anything not illegal is fair game, and I need to be a realist about this and just focus on acquiring my own seniority!

However, I'm concerned that there's no acknowledgement that I'm already doing research on X, or of the call.

I think this is an uncharitable reading of A's emails. I agree with Bryan that it is odd for the funder to discuss methodologies in such a way, and I believe you if you say A has been known for stealing methodologies, but this sounds like an offer to work together because you have been working on the same problem, even if it wasn't as explicit as maybe you'd have liked.

Ideally I'd like A not to use Y and Z (if they are).

You can't really ask for this - I would consider accepting the collaboration so you can continue using Y and Z and they use Y' and Z' or method E.
Personally, I find your email a bit confusing, how can a work be "fairly advanced" if you've not heard back about the funding? Maybe this is field differences. The hints toward "I think you were using [their method]!" also come off a bit patronizing.
You two seem to beating around the bush with each other. You are either going to have to accept the collaboration, which you can establish ownership over Y and Z, or ask them not to work on your approach, which may not be successful depending on A's personality.
I would lean toward accepting the collaboration, and then you can ask them to leave you Y and Z as colleagues, rather than enemies.

Thank you. I'm definitely not keen to accept the collaboration - partly because it benefits A far more than me, and partly because I don't think their email is a good basis for a collaboration. Thanks for the feedback on tone, that's useful.

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text:
How to say please erase\cutoff my lower gre score information from my application
Want to admit an abc university. GRE is not a requirement for them originally, BUT since i have taken it, my score is REALLY lower than what they can consider. This is an academic program and in case of having a GRE test, UNFORTUNATLY, their policy is that it cannot be too low. 12% is not acceptable. Need help to write a letter about erase/cutoff gre information from my submitted application and  give me admission on.
If have any query please ask,thanks in advanced.

Why can't you simply not submit the scores? Or have they already been sent?

Here's an answer assuming you have already sent them your scores.  If not, then you don't need to do anything.
There may well not be any mechanism set up for removing information from a submitted application, but it can't hurt to ask.  You should be able to find contact information for graduate admissions somewhere on the website (for example, here is where you'd find it for the Berkeley EECS department).  You can send a short e-mail saying something like "I applied to [name of program] this fall and accidentally submitted GRE scores that do not properly reflect my background and accomplishments.  I understand from [web page] that GRE scores are not required, so please remove them from my file.  Thank you!"
They might not actually do it: just because they don't require GRE scores, it doesn't follow that they must ignore them if you submit them and then change your mind.  But I don't think asking them to remove the scores will hurt your chances of admission.
I'm puzzled by the whole idea of having a strict cut-off for an optional test score.  It makes me think that either the department is doing something weird or they aren't communicating clearly.  In any case, though, submitting a very low score when it's optional looks weird and could hurt your application, so asking to remove the score from your application seems sensible.


text:
Can I call an assistant professor "Professor"?
My former teacher, who had done her PhD in a top-10 university in the UK in 2009, is an assistant professor in my former school.
On the day when I visited my former school, I saw her at the school canteen unexpectedly. I smiled and nodded to her before I said "Good afternoon, Professor Aiko." We were talking for a few minutes before she went back to her office. When I was sitting on a subway train on my way home, however, I was wondering
if it was impolite for me to call her that.
Can I call an assistant professor a professor, and say "Hello Prof. Nickname"?

The practice depends on the country and to a certain extent, on the custom of a particular institution.  In the United States, someone who holds the doctorate us usually called "doctor" even if they also hold the rank of professor.  No matter, what you did is OK.

@BobBrown: Even within the US, this varies from place to place, and at some places (perhaps more often at major universities) "Professor" is preferred to "Doctor" when both apply.  See also my answer here and its comments.

"In the United States, someone who holds the doctorate us usually called "doctor" even if they also hold the rank of professor."  That is very subtle and institution-dependent.  Paul Halmos has a really nice passage about it in his autobiography.  At some schools "professor" is more honorific because there are lots of other people around with doctorates.  In fact I feel that way, and even though I agree that what you describe is the standard practice at my school (we're in the same region, after all), I prefer students to call me "Professor Clark" or "Pete" and many of them do figure this out.

If I call Professor Clark, Prof.Pete? Is it impolite or weird?

@kitty: Neither, but it's not as cute as you think.  If you did it more than once or twice, I would ask you as nicely as I could to please just call me Pete.

I am sorry, Pete. I came up with that question and want to make sure if it is correct.

Related question: http://academia.stackexchange.com/questions/31954/how-an-assistant-professor-is-called-in-north-america

@kitty: I'm not scolding you.  I'm just saying that people use that appellation from time to time and seem to think I'll find it highly amusing.  It doesn't bother me; it just doesn't highly amuse me.

I would say "Prof Pete" (or "Prof Aiko") is generally both weird and a bit impolite, certainly less polite than "Prof Clark".  Would you call your physician "Dr Katherine"?  (maybe, but I wouldn't)  Calling someone "prof [first name]" is unusual, and when it happens to me, I assume the student mistakenly thinks Kimball is my last name.

At my place, we simply refer to them as "Sir" or "Mam". Eliminates a lot of the confusion, as even if they're the Dean or a professor or assistant professor or anyone older than us, we never have a doubt on what to call them.

Just don't call me late for dinner.

This reminds me a lot the recurring gag in The Office where the characters have different views on the job titles "assistant regional manager" and "assistant TO the regional manager".

To those who might be slightly offended by such address (i.e. 'Prof Firstname') please do keep in mind that many exchange students, or students who have not been in the host country long enough and belong to different ethnicity might be having a hard time figuring out first name from last name. Also there are cultures where addressing someone by their first name (especially a teacher, mentor, 'guru') is taboo, as it is considered disrespectful. Overall, in today's time and day, if you wish to be addressed a certain way, consider it your own responsibility state it clearly & without ambiguity.

In the US I would use "Doctor" or "Professor" depending on which title sounded better with their last name.

Yes you can.
The "Assistant Professor" still teaches. The word Assistant is there to denote the rank within the academic system. Some have taught longer and are more accomplished and are rewarded accordingly.
Actually, calling the person "Assistant Professor Jones" would be very awkward and cumbersome. It should be avoided.

Yes, you can call any kind of professor a professor, and you should.  Addressing someone as "assistant professor" or "associate professor" would be...well, it's simply not done, so I can't say if it would be rude or just weird.
It is similar to military protocol, actually: e.g. if someone is a rear or vice admiral, you call them admiral.  In contrast to the above example, I'm sure some knowledgeable party could be specific about what bad thing could happen to you if you screw that up!

similarly you wouldn't call a special endowed professor "Otis E. Randall University Professor" in an informal conversation or email. I feel that "assistant" is a similar modifier.

But in the UK, at least historically, there are not assistant and associate professors but rather lecturers and readers.

"Rear Admiral (lower half) Associate Professor Grace Hooper". I would go for just verbosely weird.

@Davidmh: Hopefully you'd at least spell her last name properly...

@StrongBad: indeed, all across the UK, professors are experiencing a devaluation of the "Professor" title. I assume without proof that there's at least a little resistance therefore to calling newly-minted associate professors by the title (and not just from full professors) on the basis that it's the end of civilisation. One should check Debrett's if it really matters, or a particular university's own internal guidelines :-)

Weird, and also might sound a bit sarcastic to be honest.

@SteveJessop In the UK, it's much less common to address professors as "professor", regardless of whether they're in a department where only the most senior academics have "professor" in their job title or one where nearly all the academic staff does. When I was a visiting lecturer in the US, I was addressed as "professor" any time a student talked to me, even though I didn't have the title; in contrast, I hardly ever hear the word used as a term of address in the UK. So I doubt UK academics are losing much sleep about this. :-)

@DavidRicherby: well, I meant "calling" in the contexts where a title is used: long-form citations, speaker lists, invitations to Buck Palace tea parties, that sort of thing. Hence my mentioning Debrett's. I'm just reasoning that if all academics were completely unfussed about this then the easy fix would be not to give anyone any academic titles at all (or to make everyone a Professor, like discordian Popes). This has not happened, therefore some academics somewhere must be minimally fussed about it.

Yes, you can call an assistant or associate professor "Professor." That's completely normal practice. The only time it might be inappropriate is if you are writing them in a formal context. "Prof. Smith" is always OK, but saying "Mary Smith, Professor of Unusual Studies" isn't really appropriate if Smith is an assistant or associate professor.

The difference is between a salutation and a role.

This is not an answer but an anecdote about my current university. For whatever reason, someone decided that the faculty with Ph.D.'s should be addressed as Dr., whereas those with only a masters degree should be called Professor. There are some Ph.D.'s on the faculty who are offended if you call them Professor, despite the fact that they hold the rank of Professor. To me, this is much ado about nothing. I always caution my own students to be aware of our peculiar situation. However, I tell them to call me Mr., Professor, or Dr., whichever they feel most comfortable with.
(I had experience with two graduate schools in the US. In one the facuty were all addressed as Dr., in the other, all were addressed as Professor. Local norms and customs are hard to figure out!)

"Whereas those with only a masters degree should be called Professor" - weirdest one I ever heard.

Interesting. Which country is this? It sounds like Mediterranean influence.

@henning - This is the US. You wold have to know the institution to appreciate how bizarre this situation is.

In Hungarian, we address only full professors as "professor". [Professzor úr! /Professzor asszony!]
"Mister/Ms teacher" would be the universal addressing for educators. [Tanár úr! / Tanárnő!]
(The exclamation mark goes with addressing in writing in Hungarian.)
"Mister Assistant Professor" would be awkward.

My impression is that, when someone is a professor and holds a doctorate, it's appropriate to use the "higher" of the two titles when addressing him or her.  Which title that is depends on the institution.  At some institutions, the people with doctorates are a proper subset of the professors; there "doctor" is the higher title.  At other institutions, all the professors and some other people as well have doctorates; there "professor" is the higher title.
Of course, to follow this advice, you have to know who has a doctorate, and you have to know people's ranks, and you have to know what sort of institution is involved. In the absence of that knowledge, just use a title that seems appropriate.  As Chris said, some people can be offended if you guess wrong, but I expect that those people are not very numerous.  And, as far as I'm concerned, their being offended is their problem, not yours.

I am a visiting professor and this is not my primary role. I have asked the human resources department at the university how I should be addressed. They suggested that the verbal title professor is appropriate. However, when written, I should state that I am a visiting professor ie Professor Nickname, Primary role details, Visiting professor, University details. Actually I always invite people to use my first name anyway!

Yes, being a Professor is a profession, the Assistant, Associate, or Full Professor just denotes rank.
At my school students also address lecturers as Professor in recognition of their role (and a sign of respect) which is perfectly fine and appropriate.
I'm in the US, and a professor (with rank of Associate).
The best thing is to just ask the person in question, some of my colleagues are rather informal, my cultural background is more formal. Consequently, different people will feel differently - you can't go wrong if you ask.

Yes, You can.
Hello Professor Nickname and Hello Assistant Professor Nickname: Simply compare these two and you will see that the first one seems more polite and normal. (However, culture of calling people and it's etiquette may vary in different countries and universities.)
However, I think that Hello Doctor Nickname or Hello Mrs./Mr. Nickname are good choices if you are in doubt about the politeness/correctness of using a specific title.

PS: This may be too pessimistic (and not so true) but I afraid, using Hello Assistant Professor Nickname may cause the person to feel that the student wants to remind that professor her level of profession (something like: you are an assistant professor not a professor) and this may cause her to be annoyed.

Another quirk: Here at a large Austrian university, my official German job title is "Universitätsassistent (postdoc)", which directly translates to "University Assistant (postdoc)". The official translation, however, is "Assistant Professor". And yet I don't have the rank of an Austrian Professor (neither "ordinary" nor "extraordinary"), and so German speakers would in fact be wrong to address me as "Professor so-and-so".
This is of course not only confusing to me. Since I also have a somewhat foreign name, students address me in all kinds of ways. I just got use to it as a fact of life.

I would just go to the sports analogy.  You have head coaches (professors) and assistant coaches (assistant professors).  I can't imagine calling any assistant coach who has coached me "assistant coach".  Just saying it is a bit demeaning and basically reminding them that they are just an assistant.  I think at best if used you would seem a bit naive and at worst a jerk.

In Finland, in most fields, anyone would be immensely confused by any titles beside their names, usually their first name or a nickname, outside some extraordinarily official circumstances. Just to give further indication of how country-dependent this really is.

In our country, Prof holds a higher value when you are in the academe.
We have many PhDs but only few becomes a full Professor. And nobody calls you a Prof until you become a Full Professor. You are not even considered a Prof if you are an associate or an assistant Prof. Come to think of it, You can earn your PhD by completing a program (4-5yrs) but to become a full Professor, you need decades and decades (minimum # of researh, min # of Publications in ISI journal, Min Number of Community Work, Min # of teaching experience, Min Number of presentationa, etc). Its very difficult to become a Full Professor that it holds more value than any position in the academe.

What country might that be?

In Australia the convention seems to be the opposite of that described in most of these answers --- it is usual here to reserve the title of "Professor" only to someone who is a fully professor.  It is certainly not offensive to call someone "Professor" if they are at a lower level, but it might feel unearned to the recipient.

I assume the last column pertains to writing only (while this question seems to be mostly about speaking face-to-face). Or do you really say "G'day, Assoc Prof Ben" in Australia? :)

Yeah, it's only writing - in person you'd just directly say, "G'day ya ugly bastard!"

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