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How to have productive meetings with Ph.D supervisor
I am a Ph.D. student in theoretical computer science. I meet my research supervisor once a week for around 2 hours. I prepare some of my research and try to present in front of him. I always try to make a list of theorems and claims given in the paper to discuss with him in a certain flow but most of the time he starts asking questions and then we go in other directions (which is okay from a research point of view). Due to this, it sometimes takes 2 months to read a single paper.  I always try to follow my designed plan but it rarely works. Also, I don't feel satisfied most of the time because many times I am only able to discuss 50-60 percent of what I have planned. Please help.

I feel like this is something you should be discussing with your supervisor first and foremost.

Two hours weekly seems almost rich. I had more during my PhD, sure. But time seems not a constraint, but the topic choice.

If you are in the initial two years then it seems almost fine to me but if you are in the 3rd or 4th years of your PhD then I think it is not good as per my experience in the theoretical computer science.

Speaking from experience, both as a student and as a Phd supervisor in theoretical computer science. The meetings with your supervisor serve many purposes. To narrow the scope a little bit, let me only discuss the type of meetings you mention - where you read a research paper and discuss it to a high level of detail with your advisor.
In TCS (and maths, I would assume), the primary goals of having the student read a paper and present it to the supervisor are:

So that the student learns the contents of the paper, especially the main technical tools used and developed in the paper, to a degree where the student can recognize a setting where these tools can be applied, and apply the tools in relevant settings. Because this is research the tools will have to be modified at least slightly every time they are applied. Hence, in order for the endeavor (reading the paper) to be any useful at all the student needs to achieve a very deep understanding of the paper she is reading.
So that the student learns to read, understand, and present (and eventually write) technical proofs. This is a big one - it is incredibly important that whenever you feel that you understand a proof, that you are able to present it at various levels of detail. On one end you should be able to give a “big picture” view of what the Lemma statement actually means, what it gives you, why it should be true, and why this is a non-trivial statement. It is equally important that when probed, you are able to re-create to full detail a presentation of the proof. By full detail I really mean full detail - are you saying “let x be an element of S” you better have proved that S is non-empty first. Are you invoking Lemma 3.5? You have to point to precisely which objects you are applying Lemma 3.5 to, why these objects satisfy the premise of Lemma 3.5, and which objects this invocation of Lemma 3.5 generates for you to use further in the proof.

The level of understanding that I describe above is really the only level that will be useful for you in your research. It also takes a lot of work to get there, this goes way beyond the level of understanding you need to get A’s in your classes. For this reason it is perfectly normal to take 2 months to read a 10 page paper. This is also a great cause of misunderstandings and frustration between students and advisors (the student thinks “I already know this to a level where I would ace an exam on this paper”, while the advisor thinks “the student has no idea what is going on”).
I can not speak for your advisor, but in such discussions with students I often ask follow up questions in order for the student to herself come to the realization that she needs to understand this or that part of the proof better.
Also, professors are not gods. In fact, for me, the vast majority of follow up questions that I ask is because I am struggling with understanding what it is the student is talking about, and I’m trying desperately to figure out whether I missed something obvious, or whether the student is talking nonsense. Doing this (for 2 hours) is mentally exhausting to the point of the infeasible. For this reason the conversation will often naturally after an hour or so shift to lighter topics.
I can’t actually know whether any of the above applies to you, but I do find that the above is a pretty common problem. Let me end with some pieces of advice (much of which has already been said in other answers).

Talk to your supervisor about this. This might well not bring about the change you are looking for, but you will better understand each other’s motivations, frustrations, etc.
If you are worried about your productivity, show initiative. Ask your supervisor about what are the next natural papers to read, with or without discussing these papers with her. Then read them, to the best of your abilities. Ask your supervisor for research questions, and think about them. Talk to your fellow students, and initiate research projects with them. Remember that in the last year or two of your Phd. you should be able to complete a research project from A to Z without any help from your supervisor at all. This involves obtaining the relevant background, asking feasible and interesting research questions and answering them. The best way of getting there is to try to do this as much as possible from day 1 of your Phd studies, and then using your supervisor to help you with your weakenesses. As an example, when I was a student I had no problems with solving problems, but had no idea how to find relevant research questions, and so I would lean on my supervisor and collaborators for this to a large degree. For you there might be another aspect of research that you will need extra support for, and that is what supervisors are for!

Interesting, we've reached opposite conclusions about what the problem is, but I agree with your answer too!  Without being in the meetings it's hard to know which of several plausible scenarios is happening.

Very true, which is why “talk to your advisor about this” is really the most actionable piece of advice.

I would add a third bullet to the list of reasons advisors have their students read papers — To get them used to poking at assumptions in search of both bugs and new results. Why does the paper make this assumption? Does the result still hold under a weaker assumption? Is there another faster algorithm we can plug in here? Does this still work if we add a dimension, or change the coefficient ring, or change the metric?  What if that constant parameter isn't a constant? How does this result relate to that other superficially-unrelated paper that uses similar-smelling tricks?

" the primary goals of having the student read a paper and present it to the supervisor are [...]": it's far from clear to me that the supervisor wants this to be the focus of the meetings, especially if he constantly diverts them from it. It sounds like this could be an assumption made by the OP that the supervisor has failed to explicitly contradict.

@arboviral absolutely, although the reasons for the diversions could be what JeffE outlines in his comment. Talking to advisor is really the only cure here.

Your advisor doesn't need to understand all the details of the paper, so long as you understand them.  The point of meeting with your advisor isn't to go point-by-point through the paper, it's for your advisor to help you out if you're confused or stuck, to give you suggestions of research directions to go in, and to supplement the material in the paper with related information.  Your advisor listening to you explain the details of something that you already understand is a waste of both of your time.
The only thing you've said in your question that seems like it might be a problem to me is "it takes 2 months some time to read a single paper."  You should discuss this with your advisor, but I'd suggest that you do more to condense the point of the paper so that you focus your discussion on the key points and what your advisor wants to discuss, and then you move on to the next paper rather than spending week after week on something you already understand.

Disclaimer: this is based on my own experience of both sides of this but in life sciences, not computer sciences. And individual supervision styles vary; there is no single "right" way to do this (although some ways are right and some are just wrong).
I am not completely sure that what you're currently getting is unproductive; you might just have a different idea of the 'product' than your supervisor. The function of a doctorate is to equip you to function as an independent researcher. If you have technical/theoretical questions and have not been able to answer them yourself, then you can by all means bring them to the meeting - but your supervisor may feel (and this is an entirely valid perspective) that these meetings are not for answering a long list of preprepared specific questions which could be dealt with via email (or that he might expect you to be able to resolve independently). It sounds like he sees your plan as a springboard to get into fairly open-ended discussion of the area of research. This is a great opportunity, and you seem to partially recognise this, as indicated by your quote below.

he start asking question and then we went to other directions (which
  is okay from research point of view )

As a supervisor myself I would prefer to bounce ideas around with a student than go through a paper item by item (unless there was a really good reason for it). There is however a balance - in the early stages you want to make sure a student has a firm understanding of the basics, in the middle stages you want them to start developing big ideas, and by the end you want to make sure they'll submit on time :)

Meet with your supervisor and discuss your concerns with him. Tell him that you are not sure whether your current style of meeting is productive enough. Try to find a solution together. The goal of your discussion is not that you just spend an hour or two with him. Your discussions should advance your research and help you, but that is not happening right now. So it is your own responsibility to address this issue with him. All in all, this looks like something that can be solved quite easily after a short discussion with your supervisor.

Please don't confuse advisory meetings with Journal Club.
If you don't belong to a Journal Club, I suggest you start one.  In Journal Club, the members take turns presenting.  When it's your turn to present, you can "make a list of theorems and claims given in the paper" and present them to the club "in a certain flow."  In Journal Club, you can expect to be allowed to finish what you've prepared.
For your work with your advisor, the initial stage is about finding a topic.  Some advisors propose a specific topic.  At the other extreme, the student proposes it.  There are lots of collaborative ways in between of finding a topic.  The advisor should provide guidance, though, especially in the sense of avoiding getting stuck in a cul-de-sac (a topic that's not going to go anywhere).
Try this: when you bring in a paper as material for discussion, and your advisor starts asking you somewhat tangential questions, write those down (or record them), and spend the next few days working on one or more of those questions.  In your next meeting, report on that work.  Remember, the PhD is about doing original work, not just retracing someone else's steps.
As you get more into it, you will probably start to ask yourself some of that type of open-ended questions, and then you can show up to a meeting with your advisor to report on what you asked yourself, and where that took you.
(Fast forward after some time working in this way)
If you become concerned about the amount of time that has passed without your having settled on at least a preliminary area of inquiry, you can express your concern to your advisor, e.g. "I'm concerned because I don't have a research topic defined yet."  Then give your advisor some time to think about your concern -- maybe one to four weeks.  Hopefully he will have some ideas for how to get things moving toward a topic definition in a more efficient way.


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How to answer questions *honestly* about some professors from Visit Days students?
We are having Visit Days soon, and we (current grads) are expected to have one-on-one conversations with visiting students with research interests closest to ours. One typical question we get, "How is Prof. X? What is it like working with them?".
As a current grad, I can see the names of the visiting students along with the professors who are their top choices for advisor, and several students have listed two professors I've tried to work with in the past (they had been my top choices when I joined this university).
These professors are great researchers, but, in my opinion, not good at all as advisors. I am not going into details because that'll end up being a rant, which isn't the point here. But my view is strongly shared by all my group peers who had, at some point, tried to work with these professors (due to their fame as researchers).
Because nobody had warned me before  I started working with these professors, I ended up wasting two years in grad school, in my opinion, a very, very high price to pay. I would like to be very honest with the visiting students. At the same time, my field is quite close-knit, with all top professors collaborating with those at other places. If these visiting students end up not joining us, I'd not want them to remember me as the person who bad-mouthed these famous researchers.
How can I honestly answer questions about these professors without coming across as bitter (which I admittedly still am)? If I just state the facts, well, even those are going to be coloured by my viewpoint, and will therefore be biased.

By "honest," do you mean "no holds barred," or are you willing to distill the information down to key points based on the facts?

Related - https://academia.stackexchange.com/questions/82887/how-honest-should-one-be-with-their-students-when-talking-about-the-realities-of/82931#82931 - and my answer there is relevant to your own experience.

Provide the information needed but do it with positive remarks.  Avoid negative statements and anything that would be embarrassing if quoted in public.  Example:

Prof. X has an ambitious research program.  This group attracts students who come in with extensive prior research experience.

Prof. Y is much sought after as an invited speaker.  Due to his/her conference travel commitments, s/he tends to attract students with a high degree of self-sufficiency.

Prof. Z is a relatively recent arrival in the department.  S/he provides a solid training in lab techniques and a strong suit is guiding students in defining their research question.

While I like @Pete R. Clark's thought process, I am still nervous about being too honest. I think your answer is exactly what I'd be most comfortable saying. I also really like your first line about saying things the way I'd say if I know my words could be made public. I'll therefore accept this answer. (In fact one of the professors I didn't like working with definitely fell in category 2. that you describe).

@convexityftw - It's so hard to predict when someone is going to repeat something you've said to the person you'd least expect. // In music school there were some big name professors who spent a few days in residence (on campus) every month or two. Their students would be completely on their own between campus stints. That worked for some students but I really benefited from weekly lessons with my teacher (not such a big name, but a wonderful teacher).

I like this a lot because it is not actually saying bad things, but it should still get the point across to a reasonably self-reflective student.

From experience, this doesn't work. Think of the following question: "What can you tell me about Prof. X?" - you can't contrast him to Prof's Y and Z. Also, disagree avoiding negative statements entirely.

@einpoklum The answer to "What can you tell me about Prof. X?" is exactly the one quoted above. What's wrong with that? If people want to dig deeper you can, but nobody can force you to spell it out for them.

@xLeitix the problem is that it doesn't work as a warning without the contrast, and providing a warning seems to be the ultimate goal here.

“Avoid negative statements” — I disagree, I believe this is very counter-productive advice. Unfortunately I therefore have to downvote. Avoiding negative statements, where appropriate, is deceptive and exacerbates the problem that OP wants to solve. Be charitable, but don’t sugar-coat.

@JacobRaihle This is completely untrue. If you ask me about X, Y, and Z, and I give you the provided soundbites for all three you should take away that X is ambitious (==expects a lot, more than the others), Y is absent a lot, and Z is not very established. If I give you a brief rundown like this, what I choose to talk about should in itself give you all the info that you need.

@xLeitix Yes, that was the point. The contrast with other professors makes it clear, but it only works if you bring up other professors to contrast against (as such, I would recommend doing just that whether or not you are asked to).

@JacobRaihle, don't these answers implicitly contrast Profs. X/Y/Z against a "typical" professor in the department?

You're doing prospective students a grave disservice if you avoid negative remarks, when that is unanimously how people feel about this professor. OP himself said he wasted two years with this person. Why should he frame things in a way which undersells how terrible that was?

I wish I could downvote this answer 100 times. This is terrible advice. You're basically screwing over the prospective student by pussyfooting around your actual feelings.

First of all you should decide whether you want to convey any negative information, factual or otherwise, about these faculty members.  You are certainly not obligated to discuss the issue at all.  You could for instance contrive not to be present for this part of the Visit Day, or you could show up and say "I'm sorry, but I don't have anything to contribute in response to that question.  Maybe you should ask someone else."
In my opinion though, absenting some very clear and serious negative consequences for you, you should provide feedback on your experience, because as you say,

Because nobody had warned me before I started working with these professors, I ended up wasting two years in grad school, in my opinion, a very, very high price to pay.

You go on to write

I would like to be very honest with the visiting students. At the same time, my field is quite close-knit, with all top professors collaborating with those at other places. If these visiting students end up not joining us, I'd not want them to remember me as the person who bad-mouthed these famous researchers.

Telling the truth about your own experiences is not "bad-mouthing" anyone.

How can I honestly answer questions about these professors without coming across as bitter (which I admittedly still am)? If I just state the facts, well, even those are going to be coloured by my viewpoint, and will therefore be biased.

I suggest that you plan out what you will say, or could say, in advance.  Indeed you should concentrate on factual information.  You should also remind them that this is just your own experience, and that others' experiences might be different.  This should encourage the visitors to seek out information from others, which is good.
I also don't think "bias" is the right word.  Your answer to the question "What's it like to work with Professor X?" is inherently about your feelings on the matter.  If you had a negative experience, then that's the correct answer to the question as far as you can provide.  It doesn't mean that others will have the same experience -- and again, you can emphasize that in your response -- but it is your take on the situation.
What is the alternative?  Dishonestly describe your experiences and thereby lure further students into bad experiences?  That's not helpful to anyone.

I like this answer, and would emphasize "concentrate on factual information." Your experience is a fact, even if your perception of it is colored. "I started working with Dr. Einstein my first two years here, but didn't have a good relationship with him and produced relatively nothing. I've been more productive since then with Dr. Fermi." - in a statement like this, you aren't saying Dr. Einstein is a bad advisor, you are only stating your experience. Good advisor relationships are usually about fit - it shouldn't offend anyone to share that you didn't fit.

This profile is actually pretty common in academia, and those professors typically know that they're not good advisors because they're not interested in being advisors.
Keeping that in mind, your statement can be informative and accurate while not being derogatory:

Prof. X is a great researcher, with many publications in top-tier journals. They have a very busy schedule, and cannot dedicate much time to advising. They can only supervise highly motivated and autonomous students who aren't expecting to see them more than once every 6 months.

It gets your point across.
It makes it clear for the students if their profile would fit.
Prof. X will be thankful for you not to send students in need of much supervision.

How can I honestly answer questions about these professors without coming across as bitter (which I admittedly still am)?

By explaining what happened to you, and perhaps to other people, and sticking to the facts - rather than providing your conclusion about those Professors' character. (And note that the way events made you feel is also a fact.) Let the person asking you reach their own conclusions.
Also, by qualifying your answer with a mention of other people who have had better experience with these Professors, whom the person asking you the question might also consult.
However ... be advised that not embellishing and not being ultra-positive will often be perceived as disloyal bad-mouthing, by certain people. Honesty has its price and no good deed goes unpunished - in many institutions.

Thanks for such a thoughtful response. Yes, as someone who is just starting out in my field (and also being originally from a country where "respecting one's seniors/elders" is a thing), I can't bring myself to criticize anyone senior without feeling terribly guilty  - even if I, with full honesty, believe in that criticism.

@convexityftw: I say go for it anyway. You should feel more guilty about giving visitors a less-than-honest impression. I know I do.

There is a fine line where you can be factual and yet not bitter or come over an badmouthing/backstabbing.
A key aspect is to be clear whose experience you are talking about, rather than asserting a generality that is always true for all people.

"People like him for his clarity of thought, but for me, he was a hard professor to work for.
"I found that I was left more on my own resources than I would have liked. It might have been just right for someone else though. It depends how you prefer your teaching"
"For some students who need to feel nurtured, its less good a choice. For others who need to feel pushed, its an excellent choice".
"It depends what you want in a professor. If you want X then you might prefer prof X. If you want Y then prof Y might be a good choice".

No professor or personality trait  is universally good/right or bad/wrong for everyone.
So instead of judging and opinioning your professors, try instead to describe what kind of person would be a good fit or poor fit, and let them decide which fits them.

Rather than give advice about specific faculty, try to give advice on how to choose an advisor.  Then it's up to the prospective student to make their own
valuation of how much it matters.
For instance, if you want to advise against a certain professor because they don't spend much time with their students, you can say: “When choosing an advisor, you should ask yourself: ‘will I do better with an advisor that expects to see me once a week?  Or once a month?  Or once every six months?’”
These (and others) are questions that prospective students don't know to think about.  You're giving them advice that's valuable not just for avoiding a specific professor, but types of professors.  It can be helpful even if the prospective student lands somewhere else.
The prospective may feel you've already adequately answered the question, simply by the fact that you didn't say, “Prof. X is amazing! You should definitely work with them.”  But if they demands to know which of these Prof. X belongs to, you can say “I found Prof. X was a six-month person with me, and I'm more of the once-a-month person, so I ended up working with someone else.  But you should talk to some of his current students to get more information.”

This is a great answer! I already accepted another one, but I'll keep this in mind when actually talking to the visiting students. Thank you!

@convexityftw: Thanks.  It's a technique realtors use when they want to steer people away from neighborhoods (which is forbidden by their ethical code). They can't say: you don't want to buy a house here because the schools are bad.  They can say: you want to look at the school system before choosing a location to buy in.

...except the immediate followup will surely be "Which is professor X?" and you're back in the same issue but now you've put yourself on the spot and you cannot easily use other answers given here to handle it.

@Stilez: Good point.  I added something to the answer indicating how one might handle that.

I assume the purpose of this event is to provide useful information for
incoming students. Presumably, you have been asked to participate
because someone thinks you can provide some worthwhile advice.
It would be surprising if you were chosen to participate with no
knowledge that you took a somewhat indirect route in your own career.
I would say your obligations are to share information you think will
be helpful and relevant. Perhaps your primary message might be about
what eventually worked well for you and what contributed to your success.
You might also acknowledge that personalities of advisers and students
come into play. Some students need different kinds of technical and
emotional support than others. So you can urge students to consider these factors
in choosing an adviser.
One objective way to measure the success of various advisers would be
to look into the number of successful interactions with students and
the quality of the resulting work. You can encourage prospective
students to look at the output from each professor under consideration and judge for
themselves. You might also suggest the importance of an initial
discussion between prospective adviser and student where mutual expectations
are frankly discussed.
I think it would be OK to say that some of your own interactions with
advisers in the department have been unsatisfactory, and to point out
how in retrospect these mismatches might have been avoided.
You should try to focus on the needs of the particular individual students you
are trying to help. To be most effective, you should decide in advance
what specific personal misadventures it would be useful to mention and which would be best to avoid. You have an obligation to give information you think will be helpful, not an obligation to give your life history.
Finally, on the chance that any of your unsatisfactory interactions
with advisers resulted from actual abuse, I believe you have an obligation to
report that to the department in advance of any discussions with
prospective students.

Shift the conversation.  Rather than answer the question about what it's like to work with Professor X, who you don't like, ask about their interests and talk about Professor Y, who would be great for that.

An astute visitor is going to get a very clear message from "I'd rather not talk about that, let's discuss Professor Z...". That may or may not be a good thing but should be pointed out.

@Nij So rather than than say "I'd rather not talk about that", just talk about what you want. Don't call attention to the fact you didn't answer the original question.

I'd consider this as very rude to the visitor if they have a good reason to ask about Prof. X.

I think the folks who said you should be tactful but direct in telling prospective students about the potential pitfalls of working with some folks are on point. I'll add another potential thing to say:

Professor Y is an excellent researcher and very well-respected. In my experience, she didn't have a lot of time to supervise me as a student. That said, I felt like I got much better guidance from Professor Z.

Or something along those lines. Be more or less direct according to your judgment. Let's hope there's something positive about some professor you can say!!
I am sympathetic to the fact that your field is close-knit and that you don't want to jeopardize your future relationships. I'd urge you to balance that with your instinct that prospective students deserve to know what to expect. You can state the facts without bad-mouthing people. You'll have to assume that your interlocutors are mature enough to make a sound judgment about your message. From what you said, it sounded to me like you weren't sure you could assume this. I'd urge you to give this a second thought.

Do not assess the professors how good advisors/reseachers they are, you are not entitled to do so. You can only assess how their way to advise fits to your needs.
You can mention the topics the professors are intersted in, their results, their typical schedule etc. Let students decide, whether it fits their preferences or not.
If you want to share your expirience with working with the professors, describe what you had expected and why it didn't fit to your needs. You and the group you are in is too small sample to extrapolate conclusions. Who says the asking student's needs doesn't fit with the professor's way to advise?

I never said anything about making a generic statement like "Prof. X is a bad advisor". I specifically asked how to describe my negative experience being advised by Prof. X, if a visiting student happened to ask about that professor (which I know is going to happen, because several visiting students have listed said professor as their first advisor of choice).

@convexityftw I have understood your third paragraph stating exactly that. These professors are great researchers, but, in my opinion, not good at all as advisors. sounds to me as These professors are bad advisors.

Talk about your own experience and about what didn't work. You don't need to say that it was the professor's fault, but telling what happened to you may make students think what can happen too them.
For example, "Since I wasn't able to work 120 hours a week, I didn't meet Prof X expectations and the project needed to be abandoned". Probably you can find better examples.

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Is it okay to work on a problem which is incremental as your first Ph.D problem?
I am a Ph.D. student in theoretical computer science. I have recently come across one problem on which somebody has already done work, but in that work I figured out one problem which may be small (I don’t how significant it is). I asked my colleagues about this, and some of them suggested me to pick a new problem for your first Ph.D. problem. I am in confusion what to do.
My question is: Is it okay to work on a problem which is incremental as your first Ph.D problem? Incremental in my context simply means designing a faster algorithm.

What did your advisor say?

Isn't it the job of your advisor to give you advice on this kind of thing?

The general answer to the question contained in the last two sentences is "yes -- obviously so". The specific answer for your actual situation (which is the only answer that matters) is a firm "maybe". I don't see how you expect to get a useful answer from random strangers who know none of the relevant details.

Yes!
Your goal for your first problem is just to publish something. It doesn’t have to be significant. It doesn’t have to be in a top conference. It doesn’t have to be related to your eventual thesis topic. It doesn’t even have to be in the same subfield as anything else you publish in the future. Just publish something.
This is just getting you used to the process of writing and revising and submitting and being frustrated by bad reviews and rerevising and seeing the results in print, so that none of that stuff is a barrier later.  This is inoculation against the inevitable future Impostor Syndrome telling you that you can’t do this, because you already did this.

I know a couple of people who encourage (or even require) their new PhD students to work, usually in their first 6 or so months, on small problems with the intent of publishing their work, even if just on arXiv.

@101010111100 Yup, I’m one of those.

To add to JeffE's answer: Yes, and it is encouraged for inexperienced researchers.
Check Eamonn Keogh's awesome slides on how to do research:
http://www.cs.ucr.edu/~eamonn/Keogh_SIGKDD09_tutorial.pdf
In particular, read from page 20: "Finding research problem":

Some people have suggested that this method can lead to  incremental,
boring, low-risk papers...

Perhaps, but there are 104 papers in
SIGKDD this year, they are  not all going to be groundbreaking.
Sometimes ideas that seem incremental at first blush may turn out  tobe very exciting as you explore the problem.
An early career person might eventually go on to do high risk  research, after they have a “cushion” of two or three lower-risk  SIGKDD papers.

Data mining is not my field, but I heard that KDD is the top-tier conference there.

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Incompetent Advisor
I've come to the conclusion that my advisor is incompetent (he does not have a good understanding of the fundamentals and doesn't know how to judge or generate research ideas). I mainly chose to work with him because he works in the research area I'm interested in. Having interacted with him for a couple of months now, I feel very confident that he doesn't deserve to be here and didn't earn his name on most of his publications. He was recently hired and I would be surprised if he got tenured.
Having said that, I actually think I'm strong enough to conduct research independently. However, I'm very worried of what could happen down the road. I want to get a faculty position and you get hired based on on many factors: the recommendations you receive and the reputation of your advisor are perhaps one of the most important. Isn't it just a disaster to have such an advisor, even if you have a good publication record?

This reads a bit like a rant.  For the final question, are you basically asking if it's a bad thing to have a bad advisor?

I am wondering if it's a deal breaker or something you can deal with?

I'd suggest thinking out the question a bit further, then work it into something a bit more explicitly concrete.  For example, if you'd like to ask about the long-term consequences of having an advisor who doesn't understand fundamentals of the field, how to form projects, etc., then that'd be one question.  Another might be seeking actionable advice on how to accomplish some specific objective given a common situation.  A trick to the latter is that, on SE, we can only give advice on how to accomplish a goal that you specify; we generally don't suggest default goals in open-ended scenarios.

The reputation of the advisor is of much less importance than the usefulness of the guidance.

Is your position that your advisor should give you all the ideas and you just carry them out? Or, do you think you should come up with ideas and s/he provides feedback and guidance?

Isn't it just a disaster to have such an advisor, even if you have a
  good publication record?

Yes it is.
However, this fact is too obvious to state. Therefore, I think you intended to ask

How should I proceed?

In your case, you should proceed with extreme caution because you might end up with not finishing your PhD. Ignoring your supervisor and going your own way is not a good idea.
You might want to change your supervisor. This is precisely where you should proceed with extreme caution. Claiming that one of the professors lacks knowledge about the basics of the topic is a serious accusation directed both to the hiring committee, and to the professor. You need rock solid evidence to back your claim up. Else, you might be in trouble with the law, also.
It occurs to me as if you are very overconfident. Some statements in your question do not add up:
If you are strong enough and have a good publication record, even in the beginning of your PhD, then how come you are not in MIT, Harvard, Standford, or some other crème de la crème institute? If you are in one of them, then how come one of the professors is not competent?
Let's say, you are actually at a very prestigious university, and your advisor is really not competent compared to you (which is nearly impossible). Then why do you waste your time ranting about your advisor rather than writing your upcoming paper?
As a result, jumping to conclusions usually hurts. My humble advice would be to taking a step back and trying to change your mind about the situation.

You can change your supervisor without getting into the question of whether he is competent or lacks basic knowledge, and risking the corresponding political blowback.  Just say you would prefer to work with somebody else.

@NateEldredge Exactly. Therefore, OP must be very careful not to "spill the beans" when talking to committee. Continuing to work on the same topic might also raise some suspicions.

I can not judge your advisor; he may be completely incompetent. If you know that's the case, change your advisor as soon as you can.
However, I always thought that my own advisors were incompetent, and now I know that was not true. The reason is rather simple: they don't spend as much time with your project as you do. If they understand the details of your project more than you do, that means you're not working hard enough.
If that's the case, my solution is to think of your advisor as a knowledgeable person that you can get an outside perspective from, and not as a person who would know how to solve your problems. Also, the more you go to them and ask their perspective, the more they learn about your progress on the problem, and the more they can help.
Another thing in my experience was that I didn't trust my advisors' opinion on a lot of cases because they didn't explain their reasoning very well. I ended up regretting ignoring their opinions when I saw years later that they were right and the problems were solved the same way they told me.
Of course all of this is my personal experience and may not apply to you, so make a judgment for yourself if any of this applies.


text:
What should I do while in an undergraduate engineering course to keep a proof of the math knowledge I gain by self-study?
I'm an undergraduate electronics and communication engineering student (sophomore) at an Indian university. I joined this engineering course because I found the areas of quantum computing/information and quantum engineering quite interesting, and I felt an EE background would help me later on to pursue higher studies in these areas.
Lately, although I still have great interest in those areas (quantum computing/information/engineering), I am finding myself very much interested in certain topics in mathematics and mathematical physics. Namely, mathematical foundations of quantum mechanics and quantum information (which involves learning a lot of extra math topics like functional analysis), differential geometry and topology (and their application in theoretical physics), statistical learning (I'm finding the application of statistics in machine learning quite interesting and have been reading quite a few books related to that) and discrete mathematics (graph theory and combinatorics).
The natural thing to do in such a case would be pursue a minor in mathematics. But, unfortunately, our university does not offer any minor degrees or dual major degrees. So, it's not possible for me to formally take extra classes in mathematics. Upon pondering a bit I realize that I might want to pursue my higher studies in some interdisciplinary area which involves knowing things from electronics engineering as well as from the rigorous mathematical physics and statistical learning (machine learning/data science/AI). I'm not sure if such an interdisciplinary area of study even exists at the graduate level (?). But I'm really enjoying learning the new things in mathematics and I don't want my spending time on learning these things go in vain.
So, in short, what would be the correct way to keep proof that I'm actually learning these extra things (so that I can show that I actually know these extra subjects/topics while applying for grad school) ? Should I participate in some research projects in these areas? (But then again professors don't seem to accept people who haven't taken formal courses into their research projects). If it were computer science, I could have taken online courses on sites like EdX and Coursera, for certificates. But for mathematics, no such site exists which gives out certificates based on completion of certain courses.

Similar q here : https://academia.stackexchange.com/q/103948/72855

@SolarMike The thing is that I don't want to study mathematics "just as a hobby" (unlike what the OP of the question you linked, wants). I wan't to learn things properly so that I can take up advanced math courses in grad school.

"[U]nfortunately, our university does not offer any minor degrees or dual major degrees. So, it's not possible for me to formally take extra classes in mathematics."  It's not possible at your university to take anything outside of your major or minor?

@MichaelSeifert Exactly. At least not "formally". I've tried asking some professors to allow me to audit math classes but they said that would not be possible. They were willing to suggest me textbooks to read on my own, though (basically back to square one).

related https://academia.stackexchange.com/questions/93680/how-can-i-make-self-studied-course-in-undergraduate-official-when-applying-to-gr

I feel sufficiently compelled to answer this as a recent math and physics major who completed his degree requirement.
In my undergraduate class, I was taking various combination of 4 math and physics units each semester -- 4 unit is the heaviest load one can take in a semester.
At the top end they were partial differential equations, real analysis, Abstract Algebra, Topology and geometry, mathematical physics, Advanced topics in Quantum mechanics and atomic physics such as quantum mechanics operators, measurement theory, spin and orbital momentum, LS coupling, jj coupling, helium atom, fine structure, hyperfine interaction, atoms in magnetic fields, electron spin resonance, transition probabilities, astrophysics and condensed matter physics, dynamical systems, applied and computational modelling of physical systems.
On top of these, I took various quantitative units in economics and did very well even in absence of the prerequisites.
, denotes a limiters of the different subjects/ units/ course/ modules
This is a 3 years standard bachelor but I completed it in 4 years. If you are prepared for the sheer amount of hard work, extreme burn out and a lower than average GPA, do it. Mine dipped slightly below a 3.0/4.0 but I had strong references and computational skills.

The natural thing to do in such a case would be pursue a minor in mathematics. But, unfortunately, our university does not offer any minor degrees or dual major degrees. So, it's not possible for me to formally take extra classes in mathematics.

Everything on your transcript is just ceremonial. What is more important is you knowing the subjects and actually being able to demonstrate it on a technical test/ chalkboard when called.
I'm speaking this as someone who has recently started collaborate on a research project with a professor while looking around for industrial opportunities.
If you're looking to work alongside research members, academics or professors, you may be asked to provide some insight as to what you have already covered in your time; in this case, you are free to draw upon what you have taken in your undergraduate curriculum and free time.
People effectively wants to know what you know, not what you have taken.
In my limited experiences, professors are actually impressed with students who challenge themselves by taking advanced units, even if they consider you foolhardy.

Upon pondering a bit I realize that I might want to pursue my higher studies in some interdisciplinary area which involves knowing things from electronics engineering as well as from the rigorous mathematical physics and statistical learning (machine learning/data science/AI). I'm not sure if such an interdisciplinary area of study even exists at the graduate level (?).

While I am equally unfamiliar with such combination in academia, you may circumvent the lack of such opportunities in universities through independent study.
Most research these days are cross functional across seemingly unrelated fields so much is dependent on the candidates to independently learn.
In my short experiences with looking for opportunities in areas of data analysis and machine learning, the common litmus test is a request for candidates to undergo a technical test much like how developers are subject to technical tests despite their year of experiences.
In STEM, hardly anyone will give you the luxury of knowing something just because something came up on your transcript.

But I'm really enjoying learning the new things in mathematics and I don't want my spending time on learning these things go in vain.

If this is not a contradiction then there is insufficient data.

+1 This is a very good answer which shows the various aspects. "If you are prepared for the sheer amount of hard work, extreme burn out and a lower than average GPA, do it."....this is an enlightening point of view. Thanks.

I'm really enjoying learning the new things in mathematics and I don't
  want my spending time on learning these things go in vain.

If you're enjoying it, it's not in vain. Also, mathematics is used in pretty much all areas of science, so no knowledge in maths will be useless, that I can promise you. For example, as an undergraduate student in mathematics I thought learning algebra and group theory was just a waste of time for me, that I just needed to pass (it was an obligatory course) and forget. However, now I'm doing a PhD in statistics and stochastic analysis, and I stumbled upon groups many, many times. You never know.

If it were computer science, I could have taken online courses on
  sites like EdX and Coursera, for certificates. But for mathematics, no
  such site exists which gives out certificates based on completion of
  certain courses.

There are in fact multiple online courses in mathematical subjects, especially statistics and machine learning. For example, Imperial College London offers a specialisation in Mathematics for Machine Learning (https://www.coursera.org/specializations/mathematics-machine-learning). Just browse for "mathematics" or a specific subject that interests you. Moreover, many lecturers put their notes and exercises online, it's an excellent way to learn. Just search for what is most interesting to you. You can also get a relevant textbook and do some self-study. Options are countless?
How to you prove you've done it? You don't need certificates, really! If you decide to apply for some academic programme or a job, what matters are your skills and knowledge, not certificates. I personally sometimes feel that I remember most from courses I didn't pursue certificates in. Why? Because I focus on what actually is relevant or difficult for me, not on solving many exercises that just give me "easy points".
Just pick a subject and a source, and start learning. You can even contact a lecturer for some advice (just e-mail them), they probably would be happy that someone finds their notes interesting. Whatever you do, good luck!

Another idea is to use MOOCs. Places like edx.org and coursera.org offer advanced coursework that might suit your needs (even if you already studied the materials and just breeze through for the certificate). You can either pay the fees to get the real certificates which you can include in your resume / applications, or you can do what I do, which is to take the course for free (audit) then screenshot your final progress report showing that you did the assignments and passed the tests, which should be nearly as good. Keeping a copy of the syllabus will also help show the relevance of the materials.
P.S. edx.org is a little easier on free users since you get a final grade on all coursework at the end, where-as coursera.org doesn't let you take some of the tests and doesn't show a final grade the same way.

Don't completely take your eye off the ball on the EE degree.  That is a very portable degree with applications from microelectronics to building construction to power.  Even if you like some subfields better (or neighboring fields), getting that EE degree gives you a lot of option value.  Make sure you don't mess it up.
EE is actually a rather mathematical topic.  Within EE, try to emphasize areas that are at least mathematical or connected to your neighbor fields.  Examples are spectral analysis or computer circuitry.
Specific authors/books are failing me now, but I have come across some rather advanced math books that were written by EE profs.  Maybe those are good to read.  Ones is something like Irresistible Integrals (there are two books like it, can't recall which was from the EE prof).  Another is the Leanord Lewin text on polylogs.
Don't immediately try to jump to the fanciest, most advanced area.  For example, functional analysis is certainly not required for the standard junior year quantum course in physics (which is probably already more advanced than you are getting in EE courses).  And you actually get a lot of benefit learning things the simple way first.  Look at how physics does classical E&M three times!  Freshman year, junior year and then teh Jackson in grad.


text:
Is looking up the source of tests and using those to practice considered cheating?
The question (Is studying past exams I found online cheating?) was sort of relevant but did not answer my question, so please do not mark this question as a duplicate:
Onto my dilemma:
I recently had a raw score 20 points higher than my classmates and was suspected of cheating. I scored almost perfect while others only got around 60-75. I actually found the test beforehand (coincidentally) because my teacher passes back old tests and quizzes (and his sources are obvious). I sought online materials because the textbook and the practice problems are utterly inadequate for relatively difficult exams. I know it gives me an advantage, but couldn't everyone just do what I did? Don't I have the right to study things that are openly accessible on the web and use that to my advantage? It's not like I hacked a school server to access materials.. I literally just found it by using some google search 'hacks' like verbatim, quotes, filetype, etc. I ended up not getting a score for that test, but did the teacher really have to do that? I didn't even copy the test word-for-word. I knew how to do most of it and just used it to make sure that I knew what I was doing. I am currently under a lot of backlash due to this incident and am trying to justify my standing. What are your thoughts and what prevents me from using those sources?
Clarification: it was not even the teacher's own test.

It's the teacher's fault for using an easily-found source of questions. So no, not cheating.

that's what I thought too... thanks for the input

No, that is not cheating as the comments point out. You have invested time looking for material to practise and come across some. However, if you had to “hack” a system to get the test that is a different case.... :)
The “cheating” or , at least poor practice is from the teacher just taking and using verbatim a test from somewhere - editing, changing questions, changing numbers is often done to make a new or suitable version.
Using a test from somewhere else may be ok, but all the questions need to be checked : vocabulary, level etc before use and adjusted as necessary.


text:
How to write a personal statement for a "PhD orientation program" (in mathematics)?
I'm about to apply for a short "visiting and orientation program" at a large prestigious university where I may be interested in applying for graduate school.

This program lasts a couple of weeks and consists of

several courses that present the research done by every research group in the math department;
meetings with the faculty members and current students.

For the admission, I'm required to submit a statement of purpose.
Now, the scope of statements of purpose written for graduate admission is quite clear: they need to show research potential and experience in an area of interest.
However, I'm confused about what makes a good candidate for a PhD "visiting and orientation program".

That is, what kind of information, qualification, and motivations may admission committees be looking for in a candidate for such a program?

Can you say what country this is in? I've never heard of such a program in the US.

I speculate as I do not know the faculty and their philosophy.
To my own experiences (PhD 20 years ago, and had some DBA students on my own before I went back to industry), I would suggest you differentiate between research potential and experience against "visiting and orientation". For an orientation program, ...

I would expect people to be open to all directions of learning, in our own as well as in different areas.
The ability to network,
ability for out-of-the box thinking,
ability for telling ideas but also listening.

Think about onion rings around the exploration of your topics.
How do you show those abilities? Examples from your life?


text:
Is it discrimination to hold someone from a minority or underprivileged background to the same academic standard as regular students?
Suppose a graduate student is found to be noticeably or even significantly behind in overall academic and research competence. For example, they may have significantly weaker language and comprehension skills and technical skills such as using a computer or navigating the web. They may also be lacking other peripheral skills which are often important for graduate students. This may be indirectly related to being from a minority and/or underprivileged background where such exposure and opportunities to learn can be limited.
If he/she are held to the same standards as his/her peers when comparing their relative performance, would this be considered to be discrimination if his/her situation was known? On one hand, same treatment would be fair to his/her peers and avoids human judgement. On the other hand, one could argue that it is unreasonable to expect the same amount of performance when they are missing necessary skills and experience.
There was a comment that 'held to the same standards' was too vague. As a result I want to provide some hypothetical situations in which it is necessary to compare the performance of a student with his/her peers.
Suppose an advisor has limited funding for RA and travel opportunities. They want to provide them to students with the best performance either as a means of rewarding them or to provide a better return on investment. This would mean the graduate student in question would have little chance of obtaining it. Is this discrimination or an unfair bias?
Suppose again the average graduation time for a program is 5 years. However, due to the slow progress of the student (compared to their peers) they may be held for 6 or 7 years before being deemed ready to graduate. Is this a discriminatory practice?

Maybe the question should be, do you have an opportunity to assist them to help themselves improve. Is there a way you can help them mitigate their (and others) limitations without changing your grading of their work? E.g., maybe encourage them to join a study group or refer them to a language course.

What does "held to the same standards" mean, in graduate school (e.g., I'm thinking of mathematics). Is this about "grading"? Is there any reason to "compare" individuals? Do you have some obligation to "fail" a certain fraction? The context is very unclear.

@paulgarrett I've made some additions

I don't think you've asked the question you actually want to ask, because "Suppose a graduate student is ... significantly behind in overall academic and research competence. ... This could plausibly be due to being a minority" is the textbook definition of a racist comment. I presume you didn't mean to imply that students' ethnicity determines or affects their language comprehension or academic ability. So why don't you take the time to rewrite your question to ask what you actually meant?

@TomChurch I am asking the question I mean to ask. I've changed the sentence to be more specific but the point remains. No, I am not implying being a minority affects prevents one from learning at the same rate. Being from a minority background can however affect their language comprehension ability as English can be a third or even fourth language.

@Co3O4: This is one of those cases where people really really care that you don't appear to mix up correlation and causation: it's not that the ethnicity itself affects language comprehension ability in general. Rather, it's that the language you grow up with at home/school affects your ability to comprehend other particular languages differently (i.e. you'll understand more similar ones to your native language more easily than more foreign ones). It's an obvious fact, but many people will completely flip out when you don't word it carefully.

I'm voting to close this question as off-topic because it's too broad and more about political theory, ethics, and/or legal philosophy than academia.

Using different standards can have two negative side-effects: it can turn some of the "underprivileged" into slobs (why should I work more if I will pass just because of my status?) and it can turn some of the majority group into racists (how come they got a better grade despite performing worse than me?)

@Co3O4: Though I agree with your intention more than Tom Church's interpretation, to avoid this ambiguity, it might be better to say that it is indirectly related to them being a minority (i.e. their race doesn't directly cause their lack of comprehension; but their race can be a cause for social disadvantages which in turn can cause a lack of comprehension)

Although I voted to close as unclear what you're asking, I do encourage you to edit your question to make it clearer.  Are you asking about ethics or law?  (Hint: you are permitted to ask more than one question at this site.)  If you're asking about law, it's important to specify the country.  The US law about this is clear and has been written about here to some extent; but I would love to see more information written up here for other countries.

I think you have to consider the whole.  If I were to be judged on my web-using skills, for instance, I'd be well at the bottom of the class, but that really has nothing to do with my ability to translate science into usable programs.  Or FTM to copy-edit everyone else's papers.

FWIW, this is the exact reason why countries like India have Reservations to make "discrimination" apparent. Everything goes downhill from there. IMHO - one "should" hold everyone to the same intellectual standard - not knowing tools/techniques are trivial and lack of exposure to it shouldn't be the reason to consider one as "intellectually inferior". That's my rule of thumb in situations like this.

Meta post about on-topicness of this question

Its discriminatory to hold anyone to a different standard. It doesnt matter how handicapped they are.  If a minority cannot succeed on merit alone then it in fact validates racism as scientifically based.  Quotas that supposedly serve the minority do more harm, by discriminating against the majority, by pushing people into situations they are ill-prepared for, and by affirming that merit is not sufficient for their success and so are not fundamentally equally capable.

This should be two separate questions. Is it discriminatory to hold minority students to different academic standards or to give them extra help? Absolutely.  Is it discriminatory to hold someone from an underprivileged background to a different academic standard? The better thing to do would be to try to arrange extra help to help them overcome deficits arising from their previous educational environment.

You are asking two separate and completely unrelated questions. The first, which you posed in the title, concerns the meaning of the English word "discrimination". The answer to that question is very simple: no, treating all students according to uniform standards and policies without consideration of their membership in various ethnic or racial groups is not discrimination; rather, it is precisely the absence of discrimination. That says nothing about whether it is a good or a bad (or moral/immoral, ethical/unethical etc) policy, it simply answers the question of whether it fits the meaning of a particular word in the English language.
Your second question was about how graduate students from minority and/or underprivileged backgrounds "should" be treated, which I interpret as asking about whether the policy of applying uniform standards to all students alluded to above is a good or a bad thing to have. This is a special case of a large set of questions associated with the terms affirmative action and reverse discrimination. It is a controversial topic that has been and still remains the subject of a large amount of debate as well as litigation, and if you care to learn more about it, there's a large body of discourse on such questions that you can find referenced in the Wikipedia articles linked above or with a google search. It is a sufficiently complex topic that I feel I can't meaningfully comment on it in a short post, and in any case enough has been said about it by people who have given the subject much more thought than I have to make anything I can think of saying about it laughably simplistic and uninteresting.
To clarify, this answer expresses no opinion about what policies should be in place for treating graduate students from underprivileged backgrounds.

You are asking two separate and completely unrelated questions. -- Agreed (and which is why I voted to close this question as unclear). I like your take on it, though (the question even makes a little more sense now). +1

I like this alot, but I disagree with your definition of discrimination. If the standards you hold all students to are discriminatory in nature, then holding them to that standard is discrimination. Imagine a standard that all tests would be held on Fridays at sundown (a conflict between the standard and the Jewish faith). In Wales, forcing Welsh students to take tests in English, is a big one. A uniform policy might not allow animals into the classroom, but that would be discriminatory against individuals that need service animals.

@StrongBad you have a point, and maybe I was being a bit simplistic, but in my defense, I did not actually attempt to give a general definition of discrimination, I only opined that the specific things OP was asking about did not meet the definition. I agree that in principle, with enough bad faith even uniform policies could be devised that were in fact discriminatory in nature, and your examples do a good job of illustrating that, but I find them rather extreme and unrealistic, except perhaps the one involving Wales. I stand by my assessment that what OP asked about is not discrimination.

@StrongBad This is way too broad a definition of discrimination for practical purposes. What if some religion is against the idea of taking a test at all? What if the native langages of all students are different? What if I claim my goldfish provides me with emotional support? Should we make a test in 35 langages held on 6 different days with all animals allowed? Then it will be discriminatory to the one who needs to take the test at night, because their doctor said daylight negatively affects their performance. This cannot work as a society model.

@Zozor: There’s a big difference between your extreme examples and StrongBad’s reasonable ones.  As you say, it’s unfeasible to meet extreme and arbitrary requirements; but that’s no argument against aiming to accommodate reasonable and well-founded ones.

@MadJack: The question isn't particularly unclear though. OP has simply conflated two separate things. Closing the question and not answering it isn't going to particularly help OP with seeing the two separate sides of the question. If anything, OP's conflation of the two helps with understanding the cause of OP's confusion; which actually helps with providing an answer (which, as Dan did, merely refers OP to existing discourse on a broad topic, while still answering OP's question as best as possible)

@StrongBad: Your example is highly contextual; it relies on the notion that exams are mandatory and inevitably essential (by design) to pass a class, and somehow also implicitly forbids justified absences (e.g. illness, emergency, religion)??? Loosening any of the constraints you've added to the example drastically alters the problematic and supposedly discriminatory nature of the example. E.g. inviting all your friends to a lunch party for your birthday, which just happens to be during ramadan. Is that discriminatory towards your muslim friends? This is very subjective.

I think that is an unfair judgement. It is possible to ask the question of whether or not something should be done regarding to the policy of assessing or comparing graduate students with avoiding discrimination as a primary objective as in this case (though perhaps I was not sufficiently explicit in framing it). Thus I want to know if it can be somehow argued to be a discriminatory practice. This has nothing to do with whether or not it is moral or 'good/bad' to do so. There can be other ways to make it equitable for the underprivileged without damaging the integrity of the policy.

@Co3O4: Your question, and your latest comment here, highly depends on what you understand to be the definition of "discrimination". If you use a context-free dictionary definition (= to discern a difference), then holding minority students to different standards is the literal definition of discrimination. If, however, you are using a contextual definition (= to unfairly disadvantage a particular subset of people), then holding minority students to different standards is an attempt to counter societal discrimination. You need to disambiguate what you mean with "discrimination".

@Co3O4: As an easier example, the issue with the definition of "discrimination" that I'm trying to point out is similar to the semantical juxtaposition of being diagnosed as HIV-positive (i.e. testing positive for the disease) not being a positive (i.e. good, beneficial) state of health. A word can have different meanings in different contexts; and sometimes these two contexts cause a seemingly contradictory meaning.

Furthermore, should not be another type of discrimination robbing a more capable student(s) of their place in a course to "help" less capable students? Why making tests or entry interview then? As long as they tick the right boxes....

@PLL: I don't agree that my exemples are so extreme. It's fairly common to have classes with 20+ different native languages in international universities, and crazy religious requirements are commonplace too. My point is, at some point society needs to step in and say: OK, that's the rule, now you have to comply with it no matter what you think or what you are. Otherwise it just becomes crazy. Also, how do you draw the line between a reasonable and an "extreme" requirement? The goldfish guy will tell you that bringing his quiet and risk-free goldfish to the test center is nowhere near extreme.

@Zozor Have you had people say they are religiously against tests, and that their goldfish provides emotional support?

Zozor, for what it's worth, @StrongBad's example is not a theoretical situation only.  Workplace policies against head coverings of any sort are superficially non-discriminative, but in actual practice they can be and are used in places to discriminate against Sikh men and Muslim women (among others).

@AytAyt it wouldn't surprise me if a sect of Pastafarians were against tests and gained emotional support from goldfish.

https://www.economist.com/blogs/gulliver/2018/02/no-birds-allowed This happens all the time. For religious reasons it’s even easier to find, just google any cult with 10000+ followers and half of them will give you a good reason not to take an exam on a specified day or without a specific attire.

"The answer to that question is very simple: no, treating all students according to uniform standards and policies without consideration of their membership in various ethnic or racial groups is not discrimination; rather, it is precisely the absence of discrimination." This is incorrect. This can be a textbook case of indirect discrimination, and in some areas, it is prohibited by law. For instance, if you required everyone to attend a Christmas party where pork and beef was served, then you'd be discriminating against Hindus, Muslims, and Jews.

It would be discrimination to not hold them to the same standard. It would not necessarily be fair on the underprivileged students,but where do you draw the line? Who's to say a "privileged" student has a benefit in a specific subject? If a privileged student is studying criminology to they get leniency on their grading for not having experienced as much crime? Who's to say their background hasn't helped them in other ways?
If you start grading based on a student's background you start to diminish the integrity of the course. "You only passed cause you're from a poor family".

Graduate school (excluding law school and medical school), for example in mathematics, is not much about grades, at all. The feedback loop is much more complicated, and much more individualized, in any case. People have wildly varying backgrounds, but/and can/do succeed in grad school. The successes need not be pre-scripted, and need not be identical. Mostly, no one "fails", etc.

It is not discriminatory to expect that graduates of your program attain a certain standard of excellence, as determined by the (uniform) graduation requirements established by the program. It would be derilection of duty, however, to bring in a student substantially below your department’s expectations for incoming students without offering some mechanism or plan whereby the student can “catch up” with her peers. Note that this doesn’t mean you are obligated to move heaven and earth to do so—the student also bears significant responsibility for meeting the program requirements just like everybody else.

Big +1 for catch-up and not lowering standards.

I agree with @Mołot that catch-up is probably a much better mechanism than changing standards. The partial responsibility of department/advisor but also the student is a good point. This is the most relevant answer in the context of the question (i.e. graduate school).

The only fair way is to assess abilities is to do the same way for everyone. This does not imply that you can't offer additional resources to students from underprivileged backgrounds (e.g., additional, Spanish-speaking tutors for Hispanic students) but in the end, you will have to apply the same standard when measuring ability or a diploma becomes meaningless: Did this student applying for X get an A because she was good, or because he was Hispanic?

It is not clear to me that the good version of this question is about "grading". It's about grad school, where smart people do not form a homogeneous population in any case, in terms of their quirks, background, specific talents, and so on. Grades are not good indicators, in my experience. Maybe you could usefully re-phrase your answer to not needlessly refer to "grades"? I hesitate to edit...

Fair point. I meant "grading" not in the sense of giving a grade on a scale from 0 to 100, but more in the sense of "ranking" or "assessing". I edited the post.

Is it discrimination? No, as it is it's not discrimination. You're treating all the students equally, without discriminating between them, so it's rather the exact opposite.
However, unlike what some might think, "Am I treating everyone on an exactly equal footing?" is not the gold standard of ethical actions. For example, we can all agree that providing special bathrooms for people with reduced mobility and giving them priority access to these bathrooms is good, right? Well, that's discrimination, too! But good discrimination... (Which may be an oxymoron depending on your definition of "discrimination".)
You can't just say "it's not discriminatory" and be done with it. That's intellectual laziness and dishonesty. "Is it discrimination?" is perhaps one of the questions you should ask yourself, but certainly not the only one.
One problem is that the word discrimination is so negatively charged that people are reluctant to use it for situations where discrimination can be good, and try to contort words into meaning their opposite. But in the end it's not "discrimination" that matters, it's "are my actions moral?". But of course, it's much harder to answer, and many people take the shortcut. We're all different, and pretending that moral actions can only result from pretending that everyone is exactly the same is at best naive.

The answer is very well written and your point about intellectual laziness is very true, but unfortunately you’re also misusing the word “discrimination”, which according to the dictionary refers to unjustly treating different groups of people differently. So hiring a smart person over a stupid person is not “discrimination of stupid people”; providing accessible bathrooms is also not discrimination; in general, there is no such thing as “good discrimination” - that would be an oxymoron - but there is such a thing as “good examples of treating people of different groups differently”.

... So, as I said I think the core of your argument is valid, but your answer needs to be rephrased. For example, you can say “treating all people equally is not the gold standard of ethical actions”, etc.

@DanRomik I looked at two dictionaries, they said "treatment or consideration of, or making a distinction in favor of or against, a person or thing based on the group, class, or category to which that person or thing belongs rather than on individual merit" and "prejudiced or prejudicial outlook, action, or treatment" (where prejudiced is "resulting from or having a prejudice or bias for or especially against"). Yes, as I said the word is so negatively charged that it's usually understood as unjust discrimination. But really, the word says nothing about justice...

I think I found the one you used: Oxford dictionary? "The unjust or prejudicial treatment of different categories of people, especially on the grounds of race, age, or sex." It does say unjust or prejudicial (and prejudicial isn't always against, it can be for). Anyway I'm not a native English speaker so perhaps the nuances are lost on me (although in French "discrimination" has the same very negative connotation, even though formally it's not necessarily negative). I've edited my answer a bit.

interesting. I was referring to Merriam-Webster, which has a definition almost identical to OED.

@DanRomik Uh... I don't see the word unjust there... (That was in fact the second dictionary I used, which is why I was surprised! I wouldn't have gone to check otherwise...)

you’re right, sorry. I also checked a couple of dictionaries. The word “unjust” is specifically used in the dictionary definition given by my iPhone and google (“the unjust or prejudicial treatment of different categories of people or things, especially on the grounds of race, age, or sex.”) Also, to my understanding, “prejudicial” also encapsulates an element of injustice.

@DanRomik Frankly, I'd have to say that the iPhone's definition is not accurate in this case. Certainly, unjust discrimination is a type of discrimination (and not an uncommon one,) but not all discrimination is of that type. At best, that's a secondary definition of the word (as, in some contexts, unfairness could be implied.) "To discriminate" just means to make a choice or discern a difference between some set of things, though, without regard to whether the reasons are good or bad.

"You can't just say "it's not discriminatory" and be done with it." I disagree. Not every policy must be evaluated based on morality, not is it supposed to correct social inequality. Graduate school is quite different from basic education (K-12) in terms of purpose; it is also not a charity. Questioning the motives of the question as "dishonest" and "naive" from various assumptions is not conducive to a good answer.

@Co3O4 And yet you've just exposed your true motives: determining whether it fits the technical criterion of being "discrimination" if you follow some policy to the letter, rather than trying to know how to act morally. Graduate school is not a charity? So what? Does it give you a license to act unethically? Also, I wrote "at best naive". I had initially written "at best naive, at worst an active attempt to actually undermine people from a given background", but I thought at the time it was best to not assume bad intentions. I stand corrected.

I disagree with the other answers. While on the surface, holding all students to the same standards sounds like the definition of fairness, if those standards are in fact discriminatory, then holding students to them is discrimination.
The simplest example I can think of is in Wales, students are allowed to take exams in either English or Welsh. Holding all students to a standard of taking exams in English (or Welsh) would clearly be discrimination against a group. One could argue that not allowing students to take exams in Spanish is also discrimination, and to an extent it is, but not all discrimination is illegal and not all groups are protected.
Another example would be to force students to take exams on Friday evenings. This would conflict with the Jewish Sabbath and cause issues for some students. Discrimination can also occur if the standard does not allow accommodations for individuals with disabilities.

Your examples are quite different. Moving an exam from Friday evening to accommodate for Shabbat will not influence the integrity of the course. Allowing to take an exam in Welsh will not influence the integrity of the course, unless it's a course on English language or literature. Where do we draw the line between a discriminatory standard and a required skill?

@svavil defining discrimination in general terms isn't hard, and strongbad gave the most considerate answer, but indeed the line-drawing is the difficult part. The further we get from the 'simple' world of ideal principles toward the complex and realistic world in which those are applied in practice, the more difficult and contested the answer becomes. Therefore I voted to close the question as too broad and off-topic. (In fact, it's also opinion-based.)

What you're describing is not discrimination, as Dan Romik says it is the exact opposite. Making accommodations for people based on their individual needs is, in fact, discrimination. The problem is that the word discrimination is negatively connoted, so people are reluctant to use it for such situations and try to contort words into meaning their opposite. For example, we can all agree that providing special bathrooms for people with reduced mobility and giving them priority access is good, right? Well, that's discrimination, too! But good discrimination...

What I'm trying to say is, "is it discrimination?" is a poor criterion. "Is it moral?", " Is it ethical?", "Is it legal?" etc are much better criteria. Focusing on one word, even a negatively charged one like "discrimination", is counter-productive. Otherwise you get, for example, people arguing that "they're not racist" because they're targeting a religious group instead of a "race" (← meaningless word), as if proving they're not "racist" solves everything. Similarly, proving "it's not discriminatory" doesn't solve everything. Sometimes it's even the opposite.

If I based my definition of academic standards on a curriculum taught in a school that only a minority attends, the majority would certainly claim that they are being discriminated against, despite only being held to the same standard.

@NajibIdrissi providing accessible access bathrooms is not discrimination, but making bathrooms non-accessible (or failing to make them accessible is). Giving priority access to any any group is discrimination. Rules that discriminate, whether intentionally or not, is discrimination even if those rules are applied equally to everyone.

@StrongBad You completely missed my point. We can argue all day whether providing only non-accessible bathrooms is worthy of the name "discrimination" or not. I say it doesn't matter what name you give to it (although I still think that the word "discrimination" does not fit, cf. a dictionary). What matters is that it's bad.

@NajibIdrissi note that I said that certain policies are the absence of discrimination, not its opposite - a distinction that I feel is important because of some of the valid points StrongBad raised (and which I already had in mind while I was writing my answer). But largely I agree with your side of the discussion more than with StrongBad’s position (I especially liked your last comment pointing out that which word we use to label a thing is less important than whether the thing in question is good or bad).

"...If those standards are in fact discriminatory, then holding students to them is discrimination" is an interesting argument; part of the reason why I asked this question in the first place is to see if it was possible for some interpretation beyond the dictionary one. I disagree with @henning that the question is too broad because it is applied specifically to graduate school competence. While I am inclined to agree that a particular standard for those with disabilities can be discriminatory, regular graduate students should have at least partial responsibility for their own competence.

This is by far the best answer. The source of OP's confusion (assuming they're not just trying to be bigoted) is that "academic standards" can actually encode discriminatory attitudes or conditions that systemically disadvantage certain groups of people rather than simply being "objectively academic".

If you are assessing the students on the correct criteria then it is not discrimiation. However, often we judge people on a proxy for what we really care about.
So, for example, if I set an essay on the the structure/function relationship of the genome, I am trying to assess a students understanding of a particular section of biology. If I then give a poor mark to a student whose first language is not English because the quality of English is poor, this is discriminatory, because some groups of people have better/worst English, but this is not supposed to be the skill being assessed. However, if instead of biology, the programme was English, then it would not be discriminatory to assess the quality of English.
Similarly, I might want to assess how hard someone works by how often they are in the office between 9am and 5pm (yes, I know this is a terrible way to assess effort). But if someone is from a culture with a siesta, they might work 9am-1pm and again 3pm-7pm. They are working just as hard, but my criterion only works well for people of one culture.

The question about how to deal with resource allocation is more nuanced, and for me would be a question not of reward, but of who would benefit most.  So a student who doesn't yet have research to present probably would not benefit from travel to conferences as much as one who did. But for RA help, i would generally look at two student and go: this student is going to complete their project without extra help, where as this one is never going to finish without support. Thus the RA help would go to the one who needed it so that both students could get over the line.


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Statement of purpose: how to give motivations for applying to a certain graduate school without stating the obvious or gratuitous flattery?
In a statement of purpose (for graduate admission, in mathematics), how can one address the question of "why do you want to attend this university?"  without making it sound like I'm stating the obvious or giving out gratuitous flattery?
In paticular, for reference's sake, I'd be interested in reading some sample statements where this issue is addressed smoothly.

This could be a good opportunity to mention particular faculty there you might want to work with, if there are any such. (But don't go overboard, or say anything that's not true.) In any case, in my experience, these sections generally don't affect decisions -- with the one big exception that if you say you want to come to study geometry, and the committee knows that all 3 geometers in the department are retiring, they might not admit you for your own sake. (Another reason not to say anything that's not true!)

Riku, this is a key question.  They want to know if you are applying to them because you were told that it's a good idea, which means you may not apply yourself to the studies, or if you are eager for what they have to give you.  So tell them why it has to be them, and not some second rate establishment out in nowhereville.
Something along these lines will not go amiss: "I will benefit from the unique situation that MIT offers.  In particular I look forward attending the lectures of Dr X, and also the opportunites to enjoy the cross fertilization of ideas with students of other disciplines, such as  ... and ..."  Try to find 4 or 5 reasons that are about why this university, and this university only, is the one that will inspire you to achieve more than any other.  It's OK for one of them to be a social reason, if it's one that the reader will identify with, such as "I want to join the chess club" or "New Orleans has the best sea food restaurants in the world".
Obviously at the interview they will ask you justify what you put in this section, so make sure you can do that.
You will come across this question again and again in your life.  I have been in the interviewer's seat and I ask it for the same reason.  If you answer this well, I am more likely to hire you than the person who says "yours is the best place".
Finally a warning - if I get a good answer to a question, I google the wording to see if its genuine or plagiarised.  So don't copy answers off the 'net.
Best of luck with your endeavours.

Stating some courses they offer is a great way to show them that you have done your research before your application. If that course is unique, then that might add extra value. For example, suppose you want to apply to the University of Michigan, with a specific interest in electromagnetics. Then mention some courses such as the 'EECS 526: Plasmonics' is a course you look forward to taking. In this way, you can demonstrate the committee that you really want to attend this school.

It is not a trick question. There is some reason you're applying to this school: what is it?

If this is a top school in your field, you should not pretend you're unaware of this. Instead, say something like "It should be clear why someone with my background would be drawn to MIT. Some of the most interesting research in mathematics is happening at MIT, in particular [blah]. I am also excited by the high caliber of the other students."
If the true reason is location, I would again be honest; they are going to notice that you are local and infer your real reason anyway. For example "Since I am married with children, remaining in Seattle is non-negotiable. I am fortunate that U. Washington has...[other reasons / good qualities here]."
You can mention specific professors, but bear in mind that the professor you list may well read your application. As others have said, being too specific (I want to work with Dr. X) can cause problems if you are dishonest.
Most universities have some program (e.g., interdisciplinary studies, community outreach, etc.) -- mentioning this is maybe a good idea, but again be honest; simple statements ("I also read that Nebraska has a collaborative with Nebraska State; this seems like a good idea") are more endearing than over the top statements ("I am extremely passionate about inter-university relationships; networking with my peers at Nebraska State will present a superlative opportunity for my professional growth.")
Finally, there is no need to go overboard on this section. A short paragraph where you state some fairly obvious reasons is fine -- it is your potential to complete a good PhD that really matters; here they just want to see that you have put some thought into this.

One last comment. Don't write anything you wouldn't feel comfortable saying out loud in a one-on-one conversation. Too many of these essays have cringy, boring stories about the author's childhood, or dreams, or identity, etc. You are a professional making a professional decision to apply to this university: here you should state your professional reasons why you are doing so.

If you have to ask this question, the answer may be that you don't need to address this question. Obviously, if there are specific faculty you believe you want to work with then you can mention that and why you want to work with them. But if you can replace the university name in what you write with a different university and it is still true then I'm not really sure you need to write anything about the university at all.
Instead I would focus on what experiences you've had that make you think you are interested in pursuing math research and anything unique about your educational history that schools may not know just by looking at your transcript.
As someone who recently went through the application process for math PhD programs, I did not mention specific reasons why I wanted to attend a specific program in my statements.


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How should one proceed when they receive no job offers after a considerable amount of applications?
I'm getting way ahead of myself, but being nervous on the job market I asked an advisor what happens should a candidate receive zero job offers. To which the reply was, "That never happens."
I'm sure that some people have had this experience before. I'm in the social sciences in a discipline that is very competitive with fewer than normal options outside of academia. I still have a ways to go time wise for job expectations, but I am curious about what options others may have gone for in situations where they either received no offers or none that were more appealing than something else that wasn't planned.
My assumption is that people will shoot for adjunct positions or similar options should nothing else come along, and try again in following years. Can anyone speak to being in this kind of position, or knowing someone who has gone through it?
Of course I expect and hope not to be in this position, but I am planning for everything. Others have told me that they apply for upwards of 70 positions in a year, which to me is insane (I don't know how assured I could be in the quality of that many applications). I have probably applied for 20-25 positions thus far, so I don't know if I should be approaching the process differently. And in the worst case situation, where to go from there?
Edit: Thanks all for your sensitive and helpful comments.

This is a very wide and open question, but the first thing to do is to get advice from somebody else. I would not trust somebody who claims that "this never happens" to know the first thing about the academic job market.

Simply as a matter of numbers, most PhDs do not end up in an academic career, or even in a career that is related to their degree.  Take this as an opportunity to think about what you should do with your life.

Is a postdoc an option in your field? That would be the standard alternative in my field (computer science).

"Others have told me that they apply for upwards of 70 positions in a year" Just in the last 2 or 3 days I made a comment here about applying for over 100 positions during 5 separate hiring years between 1993 and 2001, and I know many others did similarly. This may depend on the field, but my 1990s experience in math is you apply to tenure-track positions from November to around March, then in late March to early April (unless things look pretty good) you start applying for visiting positions, and then as the summer drags on, what would have been deal-breakers begin being considered . . .

It certainly does happen. And when it does happen, people tend to leave academia for a job in industry, commercial sector, retail, etc.
Unfortunately, the current culture of academia still tends to focus on success stories and turns a blind eye to unlucky candidates, almost treating them as they never existed. Your supervisor's response falls is this sad mainstream paradigm.

It certainly does happen.  I have a friend who, in the 70's, took 7 one-year adjunct positions consecutively before he got a tenure-track job.  That means he kept U-Haul in business during that time.  (That's 8 moves in 7.1 years.)
Also, in the late 80's, the US had a large influx of Chinese grad students (when China was trying to repair the damage the Cultural Revolution did to their education system.)  Half of them didn't get jobs the first year out.  Many of them were offered one-year "assistant lecturer" positions at their Ph.D. schools, to tide them over and give them another year to apply for jobs.
So that's two things that can happen.  The other non-ideal situation is that you paint houses to feed yourself until you can find the academic job you want.  Not ideal, but it can be cathartic. There's nothing wrong with any kind of honest work.  Just keep applying and keep your attitude up.  Be like Dory:  Just keep swimming, just keep swimming....

I am also in the social sciences, and I do know people who didn't end up with a tenure-track job upon completion. At this stage, you are not totally out of luck for a tenure-track job (mine came through later than this), but you should be keeping your eye out for suitable alternatives. Talking with your cohort peers might reveal if there is still movement on the primary market at this stage, or if everyone is working the secondary markets now.
Suitable alternatives (secondary market) would include: visiting assistant professor jobs, lecturer/adjunct jobs, postdocs (including in your current institution at centers etc.), government or thinktank research jobs.... Sometimes these are posted in the same places as TT jobs, but they can also be on other websites (especially gov't and thinktank websites) or found through networking. You also might have the option of stretching your PhD an additional year and redoing the search next year.
At this stage, I would send an update to all committee members and ask to meet with each to discuss strategy. At the meeting you should ask them to reach out to their networks for you and especially ask them to help you network for things like post-docs.

As a follow-up, I think 20-25 applications is pretty light. I really focused my applications and I did around 40.

Some humble (and maybe too obvious to state) suggestions from personal experiences.
Tailor your CV and cover letter according to the position requirements
This is usually underrated. But helps a lot. In the last decade, the interest to the academic jobs increased dramatically. Thus, some job advertisements receive abundant number of applications. As a result, some really good candidates get eliminated in the first stage due to their lack of presentation.
Lower your standards
Yes, it might not seem too attractive to apply for a position in a low-tier university. But you have to start somewhere. At the end of the day, your work speaks for itself, not your institution. If you are a good scientist, you will conduct quality research wherever you work. My favorite professor used to tell me that "a pen and a bunch of paper is enough to be a good mathematician." It is not the same thing for social sciences, but the core message, I believe, applies to every field.
On the other hand, you may adopt a mission for yourself: improving the institution from low-tier to higher tiers.
Networking is important
Academia mostly works with references. Therefore, no matter how good you are, it might be the case that people who have strong references get ahead of you. So, try to attend some events, and get to know some people. They are way more approachable than most people think. And believe me, most of them really appreciate ambition. If they have no openings available, they will surely lead you to some good possibilities.
I wish you the best of luck while going through these tough times.

a pen and a bunch of paper is enough to be a good mathematician in the 21 century? .. Not so sure.

Why not? Mathematical facts do not change by time, I think.

I am constantly reading in papers and references. I think they'd be needed quite as well.