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How can one's career as a reviewer be ended?
In this forum, I am reading this great question (What is required of a mathematics referee?) by a user with the name mathprofessor. There is an answer by a user with the name Buffy which starts with:

Sorry, but if that's all you do, then your reviewing career is likely to be short, ending the first time you approve a paper that is revealed to have an error.

I am wondering now: How exactly can somebody's career as a reviewer end after some paper they reviewed is revealed to have an error?
Sure, the editor who assigned the reviewer may not assign them ever again, but how exactly are other editors (maybe from different journals) notified not to take them as a reviewer ever again? Is there some way the editor who knows is allowed to reveal the reviewer's identity? Or some higher authority they can talk to? Or how does that work out in practice?
Let us assume the following:
If the answer is field-specific, let us assume we are talking about math.
Moreover, as in the other question, let us assume there is no fraud going on -- the author made a honest (but big) error in the paper, and the referee was too sloppy in their report and did not note the error.
Additional question: Are there known cases where reviewers had to end their reviewing career because they did not notice an error? Again, I am assuming no fraud is going on.
Edit: I want to say that the user with name Buffy edited the answer in question and made a much weaker claim. This solves my confusion. Thank you very much, Buffy!

Actually, my intention was just that the editor (and that journal generally) won't come back to you. There is no pillory and no tar bucket with feathers. You just sort of disappear. And the answer was specific to math and similar things as you note. It might be different for lit criticism, though I don't know that. On the other hand, it is possible that errors are missed even with due diligence. That is why  more than one reviewer is typically used. So a single error isn't necessarily review-career ending. But review in math is much more than copy editing.

The other question was about the actual requirements of the job of reviewing not about making a single error. The short "shock headline" quoted here doesn't capture what I actually said about the nature of the job. Please read it all before you jump to unwarranted conclusions.

Dear @Buffy, it's nice to hear from you and thank you for your explanation! I do, however, not understand what you mean with "please read it all". I read it all and I saw nothing more related to the "shock headline". That's why I asked.

@Buffy As pointed out in the comments to one of the answers below, your answer contains the phrase "your reviewing career is likely to be short, ending the first time you approve a paper that is revealed to have an error" (emphasis mine).  That does indeed imply that a "single error is necessarily review-career ending". If, as you say here, your intention was just that the editor and that journal won't come back to you, and that it isn't about a single error, you may want to consider altering that sentence.

@Buffy Also I would point out that when it comes to written communication, the intended meaning is not anywhere near as important as the meaning most likely to be interpreted by the reader. Clearly that answer was confusing enough to generate this question by the OP, and other answers and comments seem to concur.

Also, to emphasise how much of a nonsense it is to claim that one's reviewer career may end: plenty of journal articles in all areas contain minor/medium error. If the initial statement were true then this wouldn't be the case, clearly, and we would have run out of people doing journals reviews.

@gented: Well, Buffy's statement could mean that careers were over only for major errors. Indeed, I would hope that in other areas were errors could mean that lives/millions of money were lost, after such incidents, anonymity could be removed and bad reviewers punished.

@user109595 In all honesty nobody in this world puts money, development or lives at risk after one paper. Things take centuries before being accepted by the community :).

@gented: Of course you are right, but just for fun: Some of my professors suggested that they had their hard grading policy because "you will have a lot of examination-like situations in real life, where one small error will mean thousands of deaths";)

Well, not feeling obliged to review other people's papers anymore sounds like a nice deal so if you figure out an answer tell me.
Unfortunately, there won't be one.  Not only do I know plenty of mathematicians who have approved papers with errors in them but I've known a number of mathematicians who were well-respected in the community despite the fact that everyone figured there was something like a 1 in 8 chance that the main claim of any paper of theirs would turn out to be fatally wrong.  I can't say for certain that I've done it since obviously I would have flagged the error if I'd seen it and errors are so common that no one even mails the author for non-critical errors and a reviewer likely won't even be told if a fatal flaw in the proof is later found.
Hell, I've been halfway through extending people's published work only to email the author a question and find out that the proof is in shambles and they are struggling to find a patch.  So it's literally the exact opposite situation where the total absence of errors is what would be unusual.
Indeed, I don't know anyone who has reviewed more than one or two math papers who hasn't approved a paper with an error.  Studies suggest that something like 80% of published math papers contain some form of error (that's not a fatal error but still).  Sorry if I don't remember the source on that study but I'm sure if you google it you can find the relevant info.

Note that I think this is a compelling reason that mathematicians should completely abandon the blind peer review process in favor of something like a math social network with up and down votes.  Yes, still have two independent individuals read the paper and submit comments and demands for clarification but don't throw out all that the reviewers have learned by collapsing the judgement down to accept/reject.  The mathematician I was thinking of with the frequent errors still did good work but often pursued proofs that were particularly knotty and difficult to check.  The reviewers were well aware that certain parts of these proofs raised yellow flags but they couldn't specifically show there were any flaws and, since tenured professors aren't always willing to break things down to a tedious level or formality, I agree publication was the right call.   However, a math social network could have passed along the reviewer's sentiment that they still have some reservations about the argument in part X moreover, the initial review will matter less since the accumulation of comments and the ability to use all professional mathematical readers of the paper as a crowdsourced continuing review will do more to help us build a mathematical edifice we are sure is true.

Not a mathematician but wouldn't there be a huge difference between "an error" and "a fatal error"? Like if I hear "a paper you reviewed has an error" I would expect that to mean that the error makes the claim false and that there is now no clear way to fix it, not merely that the paper contains a false statement somewhere? I guess I'm suggesting "some form of error" seems like an awfully misleading metric.

Does mathematics typically do working papers before publication?

@user541686  Well, yes there is a difference between an error and fatal error but it's less clear cut than you might think.  For instance, does the proof P!=NP because "3-SAT isn't in P" contains a fatal error or non-fatal error?  It's totally unenlightening but since we know P!=NP iff 3-SAT isn't in P there is a sense in which if anyone ever proves P!=NP they've plugged the hole in this proof.
So in practical terms there is whether or not the theorem is true and then gaps in the proof of varying severity from trivial typo to requires decades/centuries of research to plug.

No, the answer is simply that @buffy is wrong.  In reality, editors work hard to find anyone willing to review a paper.  They will be hesitant to exclude anyone.  In most fields reviewers are anonymous, so only one publisher will know if a reviewer does a bad job.

But they won't come back to you for a second chance if you don't actually verify the mathematics to the best of your ability. And they assume that if you take on the task that you sort of agree that you have that ability. Copyediting can be done by others. It isn't the real job of the reviewer.

And please read the other post and my answer before you claim that "simply" I am wrong. The other post wasn't about making a single error, but about treating math reviewing as a copy editing task without really understanding the paper being reviewed. We really really want published math papers to be actually correct. The job of the reviewer is to assure that to the best of their ability.

You said "your reviewing career is likely to be short, ending the first time you approve a paper that is revealed to have an error" then below that you said "If you do an inadequate job for an editor, then you are likely done with that journal. Others won't know," The second statement is partly correct, and the first one contradicts the accurate part.

The answer-fragment OP quoted is incorrect. Making a mistake while reviewing is not likely to lead to the end of your reviewing career. This comes from several angles (we neglect the possibility that the editors are hard-pressed to find reviewers):

In most fields you can't realistically be expected to verify everything in the paper yourself. For example if you receive a paper about a new discovery at the Large Hadron Collider, you can't be expected to build your own Large Hadron Collider, run the experiments yourself, and verify the discovery. It's simply not possible.
In most fields, there is some level of good faith assumed between the authors and the journal. The journal will not assume the author is actively attempting to deceive them (until proven otherwise). They will assume the author did perform the experiment. Therefore if you accept a paper that turns out to be a fraud, nobody is going to hold it against you.
Finally, only the journal that you review for is likely to know your identity. No other journal will know (unless you go public). It's possible editors will tell each other not to invite a certain reviewer, or perhaps if they are sharing the same reviewer pool, but there's no central repository of "bad reviewers" or anything like that.

In practice you'll only start receiving fewer reviewer invitations (i.e. reviewing career ended) if:

You retire or pass away.
You make it known that you're not reviewing anymore, e.g. with a notice on your website.
You become research inactive, e.g. by not publishing new papers for a while.

And none of those three options guarantees you won't.  Indeed, I doubt even hitting all three isn't enough to stop reviewer invitations.

That's why I wrote "fewer reviewer invitations" =)

Please. The other question wasn't about making an error. It was about taking a casual attitude toward the job. Reviewing in mathematics is not copy editing. If you take a casual attitude about the job then you won't be invited back to that journal. Same for the next journal who is unlucky enough to send you a paper. This question is not the same as the earlier one.

Shit.  Guess I just killed my stack exchange reviewer career since that was a clear mistake on my part :-)

@Buffy, don't blame us.  Blame the OP who characterized your post.  While I agree that you might get less invites from that journal if they realize you are taking it casually truth is that it would probably take a  long time before anyone noticed that even on the good papers u were slacking.
Indeed, Journals I review for go out of their way to instruct you to skim and if u favor reject just say 'not good enough' and stop wasting effort/time.  But if you are really unserious eventually they may ask less...but so what?!?!?  Pissing ppl off isn't good but you don't put reviews on a CV.

@PeterGerdes, bad papers are often easy to recognize. Really good ones also. It is the in between ones that are hard. Maybe they say something useful and maybe not, but the devil is in the mathematics. But if someone isn't willing to actually do the math then they shouldn't review math papers. It explains, sadly, the problems you mention in your answer here.

@Allure Buffy's answer is incorrect. And then you go on talking about "most fields" when Buffy's answer is to a question tagged mathematics.

@Buffy Does anyone actually do the calculations in the papers? I don't have an age long experience but for what I have seen (in different universities/countries) nobody does.

@gented, in math, more is involved that just what most people think of as "calculations". Proofs can be deep and subtle. The authors work to get them right (in the absence of fraud or incompetence) but mistakes can be made. But the job of the reviewer is to assure the editor and other mathematicians that there has been an independent verification. Otherwise nothing can be trusted and every reader then needs to reconstruct everything.

@sgf, yes, my answer and the original question is very restricted to mathematics and to very similar fields. I'm sure that almost nothing I said would apply to papers in literature, for example. But in some parts of philosophy, for example, the need is similarly critical. My daughter's epistemology dissertation made and proved certain unexpected and quite interesting claims. But her proofs needed verification almost as strong as a math paper.

So yes, @Allure, claiming that I'm "incorrect" because something I said about mathematics specifically doesn't apply to high energy physics or "most fields" probably requires a correction. In mathematics "good faith" abounds, but it isn't the same as proof.

@Buffy yes, of course, I know, I am just claiming that reviewers don't do that even in mathematics :).

@gented, then they aren't doing a proper job. This is giving me a giant sad.

OP did not mention "Buffy" or "Buffy's answer", and that may confuse people reading your answer. Edited. 2. Your examples from Physics are less applicable to math. There are no experiments to reproduce, plus, the assumption of good will does not mean the authors don't have some hole in their proof. Still, it can be extremely hard to locate such a hole.

@einpoklum: OP did indeed mention Buffy.


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Can a Ph.D student change his adviser, if he is supported by a Research Assistantship by the adviser upon admission (and possibly first year)?
According to my offer, I am admitted to the Ph.D program and funded by a Research Assistantship by Professor X. Nevertheless, I am interested in other research directions, and we are supposed to decide our adviser by the end of the first semester.
Is it appropriate to change adviser in my case, as I am funded by Professor X?

What country? What field?

It is usually possible, but plan for two things to happen:

[Almost certain] You will lose this RA-stipend. RAs are usually in the context of specific projects and under the supervision of specific advisors, so when you decide to work on an entirely different project with a different position (which is typically your right as a PhD student) you become ineligible to be funded in this way. You need to understand that most RAs come from projects, where a PI has promised to a funding agency or company that a certain project will be delivered within a time frame. If you then decide to work on something else, the PI needs to find another person to actually do the work that has been promised. Note that this does not necessarily mean that you won't have a stipend anymore, but it will likely need to be a different source (e.g., either a TA position or an RA sponsored
by your new advisor).
[Possible] There may be some fallout with the PI sponsoring the RA. I guess most people can accept that sometimes the first year shows that you are not an ideal fit and switching advisors is the best solution for everybody, but planning to switch all along when accepting the offer may understandably lead to some bad blood. In essence, you are trying to milk a year of funding out of a project you have no intention of actually contributing to long-term. Many people will find this highly disagreeable.

Thank you so much for your detailed response! I also asked some of my other friends, who told me that while I am working on this project based on Research Assistantship, my thesis does not necessarily have to be the same project. So, this actually helps me a lot as I would definitely like to gain experience in research while having an open opportunity for choosing a research interest that is more aligned with mine.

you become ineligible to be funded in this way — ...from the same grant.  Of course your new advisor is free to offer you a research assistantship from their grants instead.

By rights, you can (in most universities).
However, it will be super-awkward.
It seems like you did not enter the program through a scholarship but with a job (RA-ship) to fund your studies. This is an academic way of saying, "I give you a job. I also admit you in the program."
Therefore, you are free to choose any supervisor but you need to keep your job as your source of income (you eat, wear-cloths and sleep under roof, right?). Your current supervisor is your reporting officer for your job.
Best is to have an open-talk with your current supervisor. Usually, they are understanding and (though hard to believe) supportive.

How come this got minus-ed off? I am answering the best as I can.

Thank you so much for your response! It helped me a lot. It was not me who downvoted it; instead, I upvoted it, but due to my limited reputation, it is not shown in public unfortunately.

@NeverBe ... don't worry. All the best.

I give you a job. I also admit you in the program. — In sane departments, at least in the US, the department admits you to the program, not the PI. — (though hard to believe) — Why is it hard to believe??

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Early career drought and correlation with future performance
I've heard from not a few people that the first postdoc can be quite tough.  You've been kicked out of the nest and have to figure out for yourself what's worth working on, what's likely to turn into a real project, etc.  Many new postdocs struggle to publish or even submit anything in their first year.  Considering the high stakes of academic careers, it makes me wonder if that in and of itself is a sign to pause and figure out a different career path.  To put it as a question,

Is your paper output the first year of your first postdoc a good metric for future performance?

I imagine it is actually possible to answer this question rigorously with data, but I would be content with anecdotal responses from senior academics.

What field are you in?

A relatively competitive scientific field.

Biology? Medicine? High-energy physics? The de facto expectations for publications are wildly different for different fields, so the more information you can g I've the more helpful responses can be.

Understandably.  Unfortunately, for what I hope are obvious reasons, I prefer maintain an air of secrecy on this public forum.

A typical project in my field takes about 1.5 to 2 years... The idea that you can get something published in your first year is just unrealistic, esp. if you are new to the field.

If you're not productive early, it's doubtful you will be competitive for higher end jobs in academia.  It's a tournament system and the odds are against you, just numerically.  Doesn't mean you are a bad person or a dummy.  But yes, maybe getting out of academia and into the general economy or government is wise.
It's important for young researchers to pick projects that are high likelihood of success.  Or "areas" with potential for several papers. I once told a grad student in my group "how will you publish that when it doesn't work", who was being pushed to do a dumb set of experiments by my advisor.  And I meant it.  (Some things can/can't publish negative results.)  Probably shouldn't do dumb experiments...but at least if you can publish some "data point" paper(s) afterwards it's not a total loss.
Don't just be a non-thinking "subordinate".  Have your own opinions.  There are always more possible things to do than time to do them.  Give your time to what deserves it. If you are incapable of having good opinions about what projects are worthwhile...you are NOT a budding PI.
Yes, you should be a paper-cranking machine as a postdoc.  If you can't do it now, how will you do it when you are tenure track at an R1 school?  This isn't grad school and you should hit the deckplates running.  And avoid multi-year laser building projects like the plague.  Let some other sap do those.
Look at these two questions of yours:  Should I quit a project where I can't see how to contribute? and How to tactfully "decommit" from projects?  I would think the answer to these early questions would be obvious now, in the context of this later one.  You need to focus and churn out first author papers.
P.s. I'm sure the "reassurance crowd" will down vote this.  But you need to hear the cynical view.

I appreciate your cynical response, actually-- it's clear that if I wanted to be a tenure-track professor then I would need to be working myself to the ground busting out tons of papers.  Good thing I don't.

Is [the first] paper output [during] the first year of your first postdoc a good metric for future performance?

In my opinion: No. (Although I agree that "it is actually possible to answer this question rigorously with data," that's rather time consuming.) Opinion-based questions are off-topic here, but in the context of the following back story, I think I can provide a reasoned answer.

You've been kicked out of the nest and have to figure out for yourself what's worth working on, what's likely to turn into a real project, etc.

I disagree with the above rationale: Once "[y]ou've been kicked out of the nest," you have research that can be published (possibly with some additional work). So, the first paper published after leaving needn't require "[you] to figure out for yourself what's worth working on, what's likely to turn into a real project, etc.," you can publish research that was largely conducted before leaving.

Research from the PhD actually turned out to be part of the problem for me-- it required an additional year of work to submit it and kept me from getting new collaborations off the ground.  Other people I know of really didn't have much else they could publish from their theses and spent their first postdoc year trying to figure out what to do next.  Do you think it's possible to recover from even these situations?

@artificial_moonlet What's the question? Recovering from being "kept...from...new collaborations"? Or recovering from "spen[ding a] first postdoc year trying to figure out what to do"?

There are at least two ways to treat a first postdoc or the first year of any academic job post degree.
The first is to use it to work over the backlog of problems that you saved in your "work backlog" notebook. You have one of those, right? If you are still as student, reading this, I suggest you get started on one immediately. If you saved descriptions of work that you had to put on hold during your dissertation work along with hints, and if you reviewed and updated the backlog periodically, you can probably get quite a few publications started or even into the pipeline by the end of your first year. You don't really want to be starting with a clean slate.
The second way to approach the first year is to get yourself attached to other researchers in your field for collaborative work. If the institution has a large enough faculty, most of them can be local. You may not be "first author" on everything (anything), but you can get out there, but also establish relationships that will last and boost your productivity. If you are in a small place, or isolated by subfield, you can, perhaps, use conferences to meet people and try to set up communities of interest, or join those that already exist.
In general, though, it is good to be working on a variety of things of different difficulty. Some of them might result in early publications, but aren't earth shattering. Others, you can work on for wider impact, though the going may be much slower.
And when you go for the next job, that backlog of work in progress is your friend.

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Is it necessary to get a masters degree for industry jobs in Machine Learning or AI?
I’m about to enter my ultimate year of a physics BSc at a top university in the UK, and have done a computational physics  internship with a research group at the university and am currently doing an internship at Harvard that requires strong machine learning skills. I was hoping this would be enough qualification to justify being able to get an entry level job in ML or AI and use that to one day lead myself into a job working with DeepMind, OpenAI, IBM Watson - places like these. I also have some fantasies about working in game design randomly, although I think that needs less a graduate degree and more a portfolio of coded games perhaps.
However, with those ML and AI jobs I was citing, does it behoove me to get a graduate degree if I want to one day get hired by them? I personally am quite drained from exam stresses and don’t think academia suits me as much as I used to think it does, but if it’s necessary for my goals in industry it might be worth considering.

It depends, I think, on what sort of job you want. For people in the trenches, even at IBM/Watson, an undergraduate degree is probably enough to get hired. You would likely be a team member building things at the direction of a manager. Creativity would be in the "how to do this" rather than in the "what do we need to build" area.
However, at the level of doing research at IBM, and I assume others, the requirements look a lot like they would for an academic position. Lots of the people there have doctorates, actually. I don't know that a PhD is necessary to get hired, but the more education you have, the better your chances.
I know people at both these sorts of levels at IBM and at Oracle.
It used to be that at IBM the trench types could get a doctorate paid for at the company, but that option has disappeared for a while now. They might be a bit flexible about giving you some time-slack to do it, depending on the manager, but funding is unlikely.
At smaller companies and especially at startups it is probably much more flexible, but also risky. I also know people doing interesting things at such small software shops who have a more basic formal education though they are good at learning on their own and staying at the forefront.

You're asking in the wrong forum - the place to find the answers to these questions are with the employers themselves.
To work at DeepMind see their website. They don't have formal degree requirements but they will perform an aptitude test. As long as you know how to do your stuff, you're fine.
To work at OpenAI, again see their website. Like DeepMind they don't have formal degree requirements but they do require published papers or 2+ years of ML experience.
And the same goes for IBM and whatever employer you're interested in.
Good luck.


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Are contributions to the American Political Science Review labeled "Letter" peer reviewed?
I suspect that in general, they are not, but perhaps someone who knows better could clarify.
However, I am looking specifically at the American Political Science Review, where contributions labeled "Letter" are much longer than is typical in other journals. Are these "Letters" peer reviewed?

Ask them if you can't find it in their online materials. If the correct answer is "sometimes" then answers here might be misleading.

Yes, they are peer-reviewed.
See also their author instructions:

The American Political Science Review (APSR) publishes letters, or research notes. [...] Although letters are reviewed like manuscripts [my own emphasis], they are shorter, more focused, demonstrate a novel perspective on existing research, and encourage scholarly debate [...].


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How useful is the GRE Exam?
How useful is the GRE for the academic career/research/daily academic tasks?
It's not required in my country but I'm wondering about the intrinsic value of its study material.

Answers in comments and related discussions moved to chat. Please read this FAQ before posting another comment.

The GRE's effectively only good for one thing - getting admitted to graduate school. You will need it if the program requires it as part of your application package. Most US graduate programs do require it. If you study elsewhere then there's a good chance you don't need the GRE.
About whether it's useful study material, note that the GRE is an exam, not study material. You can use the GRE as a benchmark to see whether you're mastering the study material, but not as the study material itself. As for whether it's useful, knowing more things is usually never worse than knowing fewer things. However, will knowing more about undergraduate-level e.g. physics or mathematics help you in your career/research/daily tasks? If you teach physics or mathematics, then presumably so (although at that point you probably don't need the GRE because you are already intimately familiar with the material), or maybe if you work in science communication, provide private tutoring, etc. In most careers though, it will be irrelevant, and you can ignore the GRE.

We should distinguish between the different GREs.
The general GRE has three components:

Math. If you are in physics, math, or engineering, you should get a perfect or near-perfect score. These are middle-school math questions; you should be able to ace this test with minimal preparation. In non-STEM fields, your ability to do math is unlikely to be considered relevant. So for most applicants, extensive studying for the math section is not needed and will not be helpful after admission. (I cannot speak to the "soft sciences").
Verbal. These are difficult questions about reading comprehension, logical thinking, and English vocabulary. All of these are nice things to have, but can be difficult for non-native speakers. Further, it is difficult to study for this test; memorizing long lists of vocabulary is tedious, time-consuming, and will have a small impact. Learning to read carefully and think critically is helpful, but the GRE is a dubious measure of this.
Writing. This is the only one I really think is valuable -- being a strong writer really helps your day-to-day life in academia, and the GRE's methodology seems reasonable (write an essay on a given topic and have it scored).

There are also subject GREs in physics, math, and other subjects. These are specifically designed for those applying to graduate school in the respective subjects. The physics one allocates 1.7 minutes per question on average. Obviously this is very different from research, where you can spend months working on one problem. Still, this does have some loose connection with your familiarity with certain basic concepts.
TL;DR: the general GRE has limited usefulness after you get into grad school and is difficult to study for, so I do not recommend spending time on it. Possible exception for the writing section. Studying for the subject GRE is not a bad way to review certain basic concepts that you may have forgotten, but success on the subject GRE is only loosely correlated with success in research; they are fundamentally different endeavors.

Just to corroborate the claim about the Math section being on middle-school-level math, it's true.  I mean, for anyone who hasn't taken the GRE, I'm sure it sounds like an exaggeration, but it's literally middle-school-level.

Thanks for corroboration. I've always been deeply unsettled that the verbal GRE is harder than the SAT, but the math is easier -- of course all students should improve their reading and writing skills in college, but it's apparently okay that most know less math after graduation than they did going in...

"If you are in a STEM field, you should get a perfect or near-perfect score."  This is wrong.  If you are in physics, math, or engineering, it would be correct.  But STEM also includes biological and social sciences, where many PhD students struggle with math.  However, they do have to do some simple math in their research, so the Math GRE might serve some filtering purpose for these programs.  Overall it's a pretty poor quality test, though.

@AnonymousPhysicist - thanks for the correction, I always forget that STEM is broader than just physical science, math, and computers. Updated my answer.

@cag51 I've heard tons of physicists say that, but it's just not true -- the average scores of math and verbal are comparable. Physicists just forget how much math they have learned relative to other STEM fields.

I agree the average scores are comparable, but not sure what part of my answer you disagree with. It's true that some STEM fields use little/no math and so might not ace the math section of the GRE; I had already updated my answer to reflect Anonymous Physicist's valid point.

Any exam is really only useful for whatever organizations look at scores on that exam, so the GRE is itself mostly just good for getting into graduate school. Of course, it could in principle also be used to judge for yourself whether you have the competency necessary for graduate school.
That said, there is some evidence to suggest that success on the GRE is a poor indicator of success in graduate school, and many graduate schools are dropping it as a requirement. What that means is that the GRE may not be particularly useful as a metric, for yourself or others, regarding your ability to handle graduate school in your chosen field.

"Any exam is really only useful for whatever organizations look at scores" A good exam will help the student learn.  The GRE is not a good exam.

tl;dr-  If you're planning to go to grad school for one of the fields that has a subject-specific GRE, then the review materials for that subject-specific GRE might be helpful to you.  However, the standard-GRE is more like an aptitude test (sorta like an IQ test); it's unlikely to be worth reviewing unless you're just curious how you'd do to boost your confidence.

Two types of GRE: The standard GRE and subject-specific GRE's.
There are two main types of GRE:

The standard GRE.If someone takes any GRE, they likely take this one.  It's mostly meant to be an aptitude test.

Subject-specific GRE exams.These exams focus on specific subjects, usually for students who want to get a graduate degree in that subject.  For example, the Math-GRE is for prospective Math graduate students.

In the United States, prospective graduate students are commonly required to take the standard GRE.  Some departments additionally recommend/require a subject-test.
It's worth stressing the huge difference between these.
For example, there's an "Quantitative Reasoning" section on the standard-GRE that most people just call the "Math section", but the most advanced math is stuff that most students should know long before graduating high-school.  Any student going into a mathematical field should find the study materials to be utterly trivial, or else they're probably in trouble.
By sharp contrast, the subject-GRE for Math is designed to test Math majors on what they should've learned in college.  From the official website:

Mathematics Test
Overview

The test consists of approximately 66 multiple-choice questions drawn from courses commonly offered at the undergraduate level.

Approximately 50 percent of the questions involve calculus and its applications — subject matter that is assumed to be common to the backgrounds of almost all mathematics majors.

About 25 percent of the questions in the test are in elementary algebra, linear algebra, abstract algebra, and number theory. The remaining questions deal with other areas of mathematics currently studied by undergraduates in many institutions.

Unlike the standard-GRE, someone who wants to get a PhD in Physics or Engineering could do poorly on this Math test while still being adequately prepared for their PhD program.

Study materials for the standard-GRE probably not useful.
There're three parts to the standard-GRE:

Verbal ReasoningIf I recall correctly, it's mostly a lot of vocabulary questions.  They call it "reasoning", but I think the logical aspects of the questions are pretty trivial if you know what the words mean.  But, many of the words they choose aren't commonly encountered in regular or even academic texts.

Analytical ReasoningThis is the "Math section" of the standard-GRE.  The math in it's really basic; you probably learned the basic math in early elementary school (Ages 5-7 in the US), while the most advanced math is more middle-school-level (Ages 12-14 in the US).

Analytical WritingThis is the "essay section" of the standard-GRE.  I think the goal's basically to show that you can write a short essay on some topic.  Its grading seems more subjective than the prior two sections'.

Study materials for these likely aren't too helpful.  Because:

The verbal reasoning (vocabulary) section can be studied by memorizing lots of vocabulary for words that many people don't know specifically because they're rarely (if ever) used.  Your time could be better spent by studying just about anything else; I'd put this knowledge as being about on-par with Dungeons and Dragons (D&D) trivia.

The analytical reasoning (math) section is just basic math stuff.  I think most people should be able to ace it if time weren't a factor.  If a student were to find this math study-worthy, then they may not be right for graduate-level studies.

The analytical writing (essay) section has test-takers write a short essay.  If any part of the standard-GRE is worth studying for, it might be this one, just because it's practice in basic communication.  However, I'd suggest that if you want to practice this material, you might want to try writing some good questions/answers on StackExchange instead.

If there's a subject-test for your major, its study materials could be useful.
At current, there seem to be 6 subject-specific GRE's:

Biology;

Chemistry;

Literature in English;

Mathematics;

Physics;

Psychology.

If you're preparing to enter graduate studies in one of these areas, or else you're just interested in what undergrads in those areas often study, then it could be productive to review the study materials for them.
For example, if you're interested in getting a PhD in Physics, then you might want to look over the Physics-GRE to review what you may've covered in undergrad and may see again in grad school.
However, even though Physics is a math-heavy subject, you don't necessarily need to worry about the content on the Mathematics-GRE, which would be more of something for a prospective Math graduate student to review.

There is a very common complaint about the GRE made by physicists and mathematicians: "the math part is so easy it's worthless, while the verbal part is so artificially hard it's worthless". This would be convincing, except that the exact opposite complaint is made by humanities people: to them it's the verbal that's trivial and the math that's artificially hard. So it seems to me that difficulty is actually reasonably calibrated.

@knzhou I get what you're saying, though my point about the vocabulary section isn't that it's hard (I got top scores across all sections), but that the information you might study to prepare for it's fairly worthless.

@knzhou I do admit, though, I struggle to understand how people might find the math section hard.  I mean, the vocabulary, I get -- if someone hasn't made the effort to memorize a bunch of words that they'll barely ever see/use, then they can't really answer questions based on those words.  But the math section is common material that everyone had to do in grade school and relies on very basic reasoning skills.  So, I mean.. how do people graduate high school if they can't do the math that the math classes required?

I mean, for a lot of fields it's possible to go through four years of undergrad without ever seeing as much as a + sign. Which isn't a bad thing -- math is just irrelevant. It might be the equivalent of being tested on whatever foreign language you learned in high school if you haven't seen it since.

The GRE is useless as anything but a filter for applications.  For instance, the ability to do middle school level mathematics in a 1 minute time frame does not reflect on the individual's ability to do higher level mathematics research and produce innovative things, as long as they have a background.

Welcome to Academia.SE. Many existing answers have already raised these points; please avoid posting duplicate answers (particularly "low-effort" answers). Once you have enough reputation, you will be able to upvote.


text:
I sent an angry e-mail to my interviewers about a conflict at my home institution. Could this affect my application?
I applied to a foreign university. I was interviewed and now I am waiting for the result.
I had also applied to another research opportunity abroad, which is organized by my current department head. I was very hopeful that I would be selected for this opportunity because I am the first-ranking student and my English is very good. I spoke respectfully with the head professor about it on several occasions, but it seemed like he was making excuses and was not fairly considering me.
I recently found out that my classmate was selected for the opportunity abroad. He had performed much worse than me on classes we had taken together, and his English is very weak. I lost control and told the head of the department where there is a research opportunity that I would report this obvious injustice to the leading mathematicians at the university that had interviewed me recently. I did indeed e-mail my interviewers.
Now that I have calmed down, I realize that I should not have emailed my interviewers in this manner. Could it affect the outcome of my application?
Appendix: Thank you for your suggestions and advice. In fact, I have realized that I should always remain academically professional. I also sent a follow-up email to my interviewer and expressed my regret at my previous email.
Appendix 2: Now that I am more calm, I realize that my act was childish. I was not the employer to decide whom to hire. I emailed the head professor and and the one at the institution where there is a research opportunity expressing my regret. But now I feel like I need to try even much more than before to become successful. Good luck specially to me

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I am going to just be honest in this response.
Why would the researchers at the British university you applied to care about what professors do at another university?
If I received an email from an applicant to my university about a matter at another program, I would think it was strange. Why would I care?
"Leading mathematicians" at a university unaffiliated with the research program you were not accepted for likely do not have time to become involved in petty politics and fights that are irrelevant to them.
Now, as for how it will affect your application, your email might likely mean nothing in the end. The interviewers will likely blow it off or do very little about it. This plays in your favor. Least said, soonest mended.
This being said, sending an email like you did could give an indication to the interviewers that you are whiny and immature.
I would consider sending a follow up email to the interviewers saying that you acted in haste and have realized that it is obviously not their job to referee such disagreements. More often than not, the interviewers would think it odd that you had initially emailed them, but will also move on with their day as normal if you recanted what you said and just moved on. At least for me, I do not have time to psychoanalyse every applicant I come across for maturity.

"Now, as for how it will affect your application, your email might likely mean nothing in the end": well, it certainly means that @Guest1 is not able to handle well conflicts and stressful situations, so, yes, it can certainly affect their application in a negative way.

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I do not have time to psychoanalyse every applicant I come across for maturity.  No, but when they do it for you, by sending a wildly inappropriate email, it's really hard to ignore.  OP has shot themselves in the foot.  It will be a hard lesson.

I had some troubles following your question, but if I understood correctly then I would assume that:

The professor interviewing you is highly confused right now. They seem to have literally nothing to do with your university, the program, you (other than having interviewed you recently), and the person that you accused of being unjust - and yet they are drawn into a conflict that they have no stakes in nor responsibility for.
You may indeed have lowered your chances of getting accepted considerably. In the best case your email would be seen as odd. In the worst case it would be seen as grossly unprofessional, painting you as a trouble maker who will randomly lash out whenever something happens that you consider unjust. I have seen students like that, and I know of no professor / admission committee that wants to bother with this kind of drama.

However, now that I have calmed down I have realized that I should not have let even injustices affect me and it was unnecessary to email my interviewer.

I think your reflection should go deeper than that. It is true that part of being a professional is also being able to absorb smaller perceived unjustices like that (empathy and an ability to accept that grades aren't everything helps here), but I also can't help but wonder what you were trying to achieve with this email in the first place. To me (and note that I am only going by your short recap) this sounds rather vindictive, serving no other purpose than to get back at the person not recommending you. If that is indeed the case, you should take a good hard look at your actions in this case and learn from that for the future.

@Guest1 For further reflection the professor might have been evasive because his real reasons for not choosing you is your character. If you behaved similarly in the past or gave him reason to think you would, it's possible he considered you unfit or did not want to recommend someone that could reflect bad on him when it turns out at the other university that the person feels entitled and handles rejection badly. I'm not saying this is the case, but for the future, consider that grades and what you perceive to be valid criteria are not necessarily (all) the criteria someone else applies.

@Guest1 You might consider that your effort to impact their reputations was also likely entirely ineffective, whether or not you were treated unfairly. Your interviewers, who barely know you, aren't going to change their opinions about your department head (if they even had opinions about him in the first place) because you think you should have been selected for an opportunity you didn't receive. They might, however, change their opinions about you.

@FrankHopkins your comment sounds harsh but seems to be correct with 99% probability.

Firstly, thanks for being brave enough to make this post and seek advice.  The responses you will get are going to be critical of your behaviour, so let me pre-empt this by saying that the fact that you are now seeking advice is a good thing.  With great respect, everything you describe in your post is way out-of-line, and yes, quite obviously your email is going to severely harm your application.
Even before we get to the email, losing control at your Department Head over his selection of another student for a research opportunity is not an appropriate response to that circumstance.  This selection may seem like an "obvious injustice" to you, but there are many possible reasons it could have been made, notwithstanding your superior grades and English language skills.  A Department Head is an experienced academic, and they generally have sound judgment on these matters, so it would have been far better to find out the reasons for the selection of the other student.  It would also have been far better to seek feedback on your own short-comings, and how to improve your chances for later opportunities.
If there was indeed some unfairness in the selection process for that application (and you do not specify what the nature of that unfairness might be) then there are ways to raise this in a professional manner.  There may have been some opportunity to complain or seek a review of the decision under university rules, but even if there was not, "losing control" at your Department Head, and threatening (and then carrying out) a campaign of defamation, is not the appropriate response.
As to your email, this is also totally out-of-line, and it reflects terribly on you.  The university selection panel you have written to has no role scrutinising the decisions of your Department Head, so what this email demonstrates to them is: (1) you are prone to lash-out and defame others when you do not get what you want; (2) you only see your own assessment of the "injustice" of a decision, and are not adept at seeing the matter from the point-of-view of others; (3) when you have a grievance, you take a "scorched Earth" approach rather than raising your grievance in a professional manner and with regard to appropriate procedures; and (4) you expect unrelated bodies to weigh into your grievance.

+1. I once had an applicant for a permanent (industry R&D) position who sent a resume along with a 20-page philosophical manuscript with his "thoughts on the concept of being employed" (with axioms and proofs and figures). I didn't even open his resume -- the fact that he thought it was appropriate to send such ramblings when applying for a job told me everything I needed to know about his professional judgment. Imagine how much more damage OP's e-mail will do.

@cag51: A part of me can't help but actually be a bit impressed (and curious) about that.  He sounds like a hoot.

Throwing accusations around without proof of wrongdoing will not make you any friends, not at your university and neither where you applied. First, let's address the accusations and why you should have kept them to yourself:

You didn't attend the interview of the chosen student. He/she might have shown desirable traits beyond academic prowess
Maybe the student had relevant experience that you were not aware of
Most people are a poor judge of their own ability

Even in the case where you, objectively, were the better student, it still is not proof of any wrongdoing and learning to take defeat graciously reflects much better on you than throwing a tantrum.
Finally, this email you sent will definitely affect the way you are seen by the interviewer. At best, it will be seen as childish/petty, but it could also reflect a troublemaker personality. I suggest you immediately retract what you said in this email unless you have proof, along the lines of 'I now recognize I was too hasty in throwing such accusations, and I'm sorry for involving you in this matter'.

@Guest1 Apart from any other consideration, in mathematics there is a high standard when using the word "proof". I doubt that you have anything which could be considered a proof in any rigorous sense. Using the word "proof" in a weaker sense is not a good strategy when trying to apply for something in mathematics.

@Guest1 See, the thing is, it's not about who's right. You might be right, or you might not. It's about maturity and graciousness. What could you possibly gain from sending that email? Vindication? Revenge? Either way think about what that tells the interviewer. All he knows is you're able to do the work (probably?), and also don't take rejection well. He doesn't know you, he probably isn't personally familiar with the professor whose reputation you've tried to tarnish. You've shown that if he tells you 'No' that you will whine about it to his colleagues and try to destroy his reputation.

I think even sending a retraction e-mail would require a huge amount of finesse... If you can't send a good one, it may be better to just be silent and hope the incident fades from memory as quickly as possible instead of spreading into legend with your name attached (either way, I suspect this bridge is thoroughly burnt).

It seems you are missing a few key points here.
The most important one is that people sent to this "research opportunity abroad" are ambassadors of your current department.
Don't shoot the messenger: You have shown that you are entitled, vindictive and hot-headed. Taking this into account, it seems that your head professor chose wisely by not picking you as an ambassador.
A motivated student with basic English skills can become fluent abroad in a few months.
Your behavior surely affected negatively the outcome of your application, and will continue to do so if you don't work on your social skills. Good luck!

I really want every single student to become as successful as they deserve. However, a student who even does not know the basic grammar about the verb “to be” and who has never read any textbook being used to lecture notes must not be preferred to me, I mean when such a student is chosen why am I not chosen then? My personality? No, because I tend to help the classmates and even the professors if ever.

@Guest1 Your personality might perfectly be the reason, as the action you took was quite unprofessional, vindictive and maybe even irrational

I know the reason why I was not chosen, it was not about my personality. @Lamak

@Guest1: So... what's the reason?

@Guest1: First, I'm really sorry that you didn't get the position you desired. Still, I have to say that your whole behavior and comments here make it clear why you wouldn't have been chosen. The sooner you realize your personality or lack of social skills really might have played a role in the rejection, the sooner you'll be able to move on and have better chances for the next opportunity. The way you present it, it doesn't seem that you learned anything from this failure.

@EricDuminil because the majority of the comments imply that there is something wrong about my personality, I will think about it. Thanks for your suggestion.

@Guest1 as someone who once attended college in the UK (a long time agao, admittedly) but who still has friends and family living there, I can assure you that the British (academia) generally dislike and distrust anyone who raises a "fuss" over perceived injustices. It seems to me that the tone of the email was likely to be aggressive, another red flag. Instead, your academic record, letter of recommendation and letter of statement should stand alone and convince the reader(s) of your merits and academic achievements.

I'm sorry to add insult to injury, but @Guest1, just reading your (edited) question  suggests that you are impulsive, hot-headed, fiery and, most concerning of all, entitled.
Please do a little self-introspection and analysis, and more importantly, ask those people nearest to you: family, friends, peers, and professors an honest assessment of your character.
Get that precious feedback, assure them that you will not be offended, hurt or be upset, and while they are talking, listen, do not interrupt them.
If the feedback is generally positive, then chalk the email up to inexperience and a moment of poor judgement. It will still serve as an invaluable lesson in humility.
If the feedback is mixed or shockingly bad, it will be easier to comprehend the self-inflicted damage that email has probably committed. We don't know what words were used in the email nor its tone, but if I had received an email from an “unknown” applicant who accused a professor of bias and another candidate of being unqualified, I would certainly think twice before considering that person's application.
However, in your post you mentioned that the professors to whom you forwarded the email, had actually interviewed you

I would report this obvious injustice to the leading mathematicians at the university that had interviewed me recently.

Perhaps you performed well in your interviews, perhaps you left a positive impression, in which case these mathematicians will probably overlook your (spiteful?)  heated email, and seeing you have since apologised, that too should also play in your favour. A person who is humble enough to apologise when they have realised their mistake is, in my books, commendable, unless the  email was clearly written by someone in the throes of a conniption fit, only you know the answer to that.

I never knew I might be entitled. Circumstances may have caused me to look entitled. I never wanted to act impulsively. All of a sudden, I was faced by so many rejections from all of the scientific institutions to which I had applied, except for one to which I am grateful for it gave me the opportunity to introduce who I am in an interview. The fact that I was rejected by all of the other ones even without being interviewed gave me a very bad feeling. So I started to expect my mathematics department head to support me academically. I was completely wrong, and I learned my lesson.

I will try to fix these faulty traits in me, so I think this lesson has helped me not to become fiery and act impulsively any more. I may have looked entitled, so I will review myself so that I do not look entitled any more

@Guest1 I would ask your former professors for guidance. Good luck with everything.

I think that most of the answers give you pertinent advice. You applied for a research program. In the future, you will probably apply for post-doc, permanent positions if you decide to stay in academia, otherwise you will still have to apply. The majority of the applications will fail, which is normal and there can be some disappointment. In order to be not too much affected, here are some advice.

First, we have to keep in mind that there is no total ordering of the candidates. It is surely not so often that there is a candidate who is better than all the others in all the possible aspects which are required for a position. It is also hard to say "A is better than B" otherwise the role of the commissions would be easy.
Second, as pointed out in other answers, there is a big part of unknown: about the profile of other candidates for examples and also how their interview went. Somehow surprisingly, there is also a part of unknown about your interview. The member of commissions are usually not emotional hence you do not know exactly how an answer to a question was received.
Third, we have to consider that we only need one application which works and that when one failed, we did not lose any thing because we had nothing before (having the position was not a debt).

It seems that it is the fact that you were affected that led you to write the email. Next time, it would be better to ask for example the aspects of your curriculum that you could improve instead of putting into question the choice of the commission.

I was rejected by almost all the institutions I had applied to without clear reasons which made me feel very bad. I know that interview is part of an application but I was not even interviewed before being rejected. I could not tolerate these rejections and so I acted very unwisely. But I am sorry and I will never do such a mistake again.

To be more clear, I expected to be either admitted, or rejected with a clear reason. If my applications had been rejected with clear reasons I might have even sent them a gratitude email for their assessing my applications equally. However, I now know that instead I should only work on my social skills and improve my scientific profile

@Guest1 As a general hint in that regard: You will likely receive more rejections than acceptance answers from job applications in your life, depending on how broad your application pattern is and what area you apply for. Typically this gets a bit better when you grow more experienced as you become specialized and apply to positions fitting your specialisation such that the candidate pool shrinks, but still, rejections are common. And in particular, in 99% of all cases you will not get any particular reason. Often there is no clear reason and if there is it is much safer legally for [cont]

@Guest1 an employer to not specify that reason in a rejection, as that might open them up to get sued. Whether they would win or not does not matter, if they don't provide  a reason that's a sure way to not provide any grounds for any legal case to build on. You can counter that general tendency by applying very specifically to jobs that fit perfectly for you, but especially at the beginning of any career that's not easy to do.


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Presenting a survey/review paper at a conference
I have noticed that senior members of the community often present survey-like work at conferences, especially if they are giving a plenary lecture or have an extended time slot in a mini-symposium.
I am currently working on a survey/review paper, but a senior mentor advised me that it is not good to present such work at this stage in my career.  (I'm currently a postdoc, only about a year since I got my Ph.D.)
Why is this the case, and when would it be appropriate to present such work?

Please specify your academic domain, because practices vary widely.

There are several reasons for this point of view:

when looking for a survey/review paper in a journal or talk at a conference, the first thing I do – is looking at the name of the researcher, how good (and how many) are his works in this field (and subfield of the overview talk).
to give a good survey talk, you both have to have a "big-picture" vision, as well as exposure to various details in many methods. It is hard to achieve both at the early stages of your career. And, most importantly, your potential audience has a tendency to think that it is unlikely.
giving review talk is, in my opinion, harder than a novel research one. The structure is different, and you cannot focus on the novel idea that is your baby and you are presenting. I would say, you need better presentation and slides' organization skills to prepare a similar quality survey talk.
presenting survey talks and publishing review papers is not perceived as good for your academic career. While it counts as a publication (and is no doubt useful for the research community), it is no equal in terms of the impact on your CV. Surveys can rarely define somebody's career and they play less of a role during application for a tenure-track position.

Is it fair? No. Can a young researcher give an excellent, inspiring, and even novel overview talk? Sure. Can that boost your research reputation? Sure. Still, unlikely in general.
I can totally see why the preparation of the survey paper itself is very useful:

by preparing a review paper you learn the subject matter, past and recent progress in the best possible way
you create a quality publication for others to enjoy
you learn the skill of writing a survey paper itself (which is different from a regular paper in a journal)

However, in my opinion, the benefits of actually presenting such a paper at a conference are limited for an early-career researcher.


text:
Struggling to present results from long papers in short time slots
Most of my work thus far comprises two rather long and detailed papers that rely on a common underlying framework. (I know this is not great for a young academic, but it is what it is right now.)  This framework is new and often misunderstood, so I find it is important to devote ample time to explaining it when I present my work.  Unfortunately, with time slots at conferences being rather short (~20 minutes), I often don't have time to present what I think are the really cool results from this framework.  I have been trying out various approaches and formats for presenting this work under time constraints and don't yet feel confident about it.
One thing I haven't tried is the following: glossing over the details of the framework and focusing on the cool results instead.  My concern with this approach is that I may not be taken seriously; there seems to be an unspoken norm in my field that young academics ought to present painful details in order to prove how smart they are.  However, I struggle myself to follow details, and if the main purpose of presenting my work is to entice people to read it on their own time, then I think that highlighting the cool stuff would be more effective in achieving this goal.
My question: is this approach (minimize time for details of framework; maximize time for cool results) worth trying out at my next conference, or would I risk hurting my budding reputation?
P.S. It may be helpful to know that my work, and the framework in particular, has a large mathematical component.

"there seems to be an unspoken norm in my field that young academics ought to present painful details in order to prove how smart they are." More likely young academics do not know how to give an effective presentation.  Or perhaps most academics regardless of age.

What is your goal?  I think there are two good ways to do presentations.  One is aimed to inform the audience, and the other is aimed to impress the audience.

Can't it be both?

You might be interested: https://academia.stackexchange.com/questions/121427/does-giving-an-easily-understood-talk-make-the-audience-think-you-did-something

there seems to be an unspoken norm in my field that young academics ought to present painful details in order to prove how smart they are — There is an unspoken norm among young academics that there is such a norm, when in fact, there is no such norm. The best way to impress your audience is to inform your audience. Nobody (but you) cares how smart you are.

@AnonymousPhysicist Only one of those two ways is actually good.

@JeffE I'm not so sure.  Ideally informing is the right thing to do, but the success rate is very low.  In my experience, impressing your audience has a higher success rate.

there seems to be an unspoken norm in my field […]. – Let me pile up on the other attacks on this: At least 80% of conference talks (mostly irrespective of the speaker’s experience) are a waste of time because so many people blindly following alleged unspoken norms that are detrimental like listing irrelevant details, showing every result, table-of-contents slides, talking extensively about the history of their work, etc. It’s a self-sustaining idiocy. Before you follow what appears a norm for talks, ask yourself whether there is any point to it and how you felt about others to that norm.

I 100% agree that this unspoken norm is stupid-- at the same time, I've received a lot of raised eyebrows for challenging it.  I would argue that we young folk are picking it up from somewhere, i.e., enough of the old folk do this or subliminally reinforce doing it that we continue the trend.

"Impressing" has the danger of sounding empty, or valueless. Another way to express it would be "interest-ing" the audience. Hooking them. Get them interested enough that they take the initiative to dive into the details. If some of the hook also involves them being informed, that's good, but no one can expect the information in a project to be meaningfully condensed into a 20 minute presentation.

You might consider this anecdote (I understand these two scientists each already had a major reputation by this time ... but perhaps the "lesson" transfers to your situation)

May I ask what field this is? Also if people question your method, they wouldnt like your 'cool results'. Also whos framework is it? Yours? Your supervisors?

While we're questioning slavish adherence to norms: if the results are already out there in published journal papers, and their justification relies on a lot of fiddly details that are best presented in writing, why does OP feel obliged to present the work at conferences at all?

I idly wonder if the way this norm gets transmitted is that there are one or two vociferous regular audience members at conferences in the field who demand a lot of painful technical detail, probably to the detriment of the rest of the audience.  Certainly there's a (very senior) chap in my field who has that reputation, and I must confess I've been known to pander to him when preparing a talk where I knew he was likely to be in the audience.

Attempting to fit the material of your paper into a talk is a common mistake: even for shorter papers, there is typically simply too much to include all of the significant details.
Instead, I recommend thinking of your talk as an advertisement for your paper. Your goal is to present enough of the key interesting material to be able to convince somebody that it is worth actually reading your paper.
Once you accept this as your goal, the length of the talk does not actually matter. As an exercise, you might even try making just a single slide for giving a two minute talk (as one might in a "lightning talks" session).
What, then, should you put into whatever time you have available? Think of the story of your work, as opposed to the content.  Your abstract may help you here.  As a starting point, I would suggest this as a general framework suitable for most talks:

Set up the problem, explaining why somebody should care about what you are doing.
Sketch the approach that you are taking, explaining why it is reasonable.
Point out some critical insights that were necessary to make the approach work.
Show your key results and explain why they are significant.
Come all the way back to the set up and explain the progress that has been made on the problem.

Depending on the details of your work, there may be some differences, but this may at least help you get started sketching things out.

Insights are more useful than details.

nice! also it's a good idea, at the end of the talk, to speak about further studies on the subject or perspectives, I think.

My concern with this approach is that I may not be taken seriously; there seems to be an unspoken norm in my field that young academics ought to present painful details in order to prove how smart they are.

There are all kinds of norms that are wrong, and this is one of them.  Painful details are just painful and nobody can follow them during the talk, anyway.
Without knowing your work, it's hard to give specific guidance but the goal of your talk should be to convince your audience that your work is interesting.  Proofs are usually boring. Your framework might be interesting. Your "cool results" are certainly interesting to you so you need to make sure that your audience even understands why the area they come from is interesting. But everything needs to be at the level of explaining the big picture and roughly how the system works. Don't be afraid of saying things that aren't quite true, if the precise statement is just too long and hard to follow. For a trivial example, it's OK to pretend that all prime numbers are odd, as long as you mention that this isn't quite true, and as long as 2 being prime doesn't mess up your whole argument. Keep things mostly about intuition rather than about fiddly technical details.

The other answers here are excellent.  I will just add that students and young academics "trying to prove how smart they are" by bombarding audiences with rapid and overwhelming technical detail actually has the opposite effect --- it tells the audience that they are not smart enough to understand audience context and present material in a clear and digestable form.  This is usually a sign of low intelligence, not high intelligence.


text:
Changing affiliations and conference registration
Say the deadline to register for a conference is now, but the conference doesn't actually run until 3 months from now.  During that time, I will have changed institutions.  When I register, should I use my current or future affiliation?
There have been several questions here about how to deal with changing affiliations on papers, but I think the nature of my question is different, since there isn't a paper or publication at stake, per se.

There are no hard and fast rules here, and the conference organizers almost certainly do not care.
For most circumstances, the only thing that matters is this: which one do you want people to think of you as being from at the conference?
Most of the time, this will be your new institution.  If you know you're going to be there when you register, why not just give that affiliation?
Otherwise, you may end up doing what I've often seen people with recent changes do, taking a pen and modifying their affiliation on the spot.

I would say, it is not a big deal which affiliation you use for this purpose.
One case when it might matter is if you are reimbursed for your trip through one of the institutions. Then, using the right affiliation might help in a smoother accounting process.
Also, if you are presenting some research at the conference, you probably want to have the affiliation of the institution where this research was majorly performed. This is reflected in your slides and conference proceedings (if present). These affiliations can be handled separately from the one you use for the registration: slides and paper abstract you usually prepare yourself.
If you think that having the new affiliation printed on your badge is important, that might be a reason to use the new one. That's what I would go for.

And, it is not unusual that the conference could print a new badge for you on the spot (usually big conferences accept walk-in registration).


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Is it necessary to have a background in philosophy in order to get a position in logic in philosophy departments?
What the title asks.
Apparently there are some professors in departments of philosophy working on logic or semantics (e.g. William Starr or Nino Cocchiarella [retired]). Does one need to know the "real philosophy" to get such kinds of positions in departments of philosophy? Or does one only need to know logic/semantics (and not, say, treatises of Plato)? And does one have to have a PhD in philosophy, or does a PhD in math or linguistic suffice?

While it doesn't strictly require a degree in the field, knowing how to write papers/books/etc. in the fashion expected is a non-trivial skill which will vary widely, and is something you are directly or indirectly trained in during a Ph.D.  How a philosopher writes and presents a work is usually much different from how a mathematician writes one.  And not knowing how to write and format things according to the field's standards is an easy way to get labeled a crank.

The correct, if not very useful, answer to the title question is no, not absolutely necessary. But philosophy departments aren't likely to advertise very often for mathematicians or computer scientists grounded in computability (an important topic in epistemology).
Like any other modern academic field, philosophy has specialization, and some departments are very specialized. So, with certain skills, but not a broad knowledge of the foundations of philosophy you would find a few positions open, but I suspect they would be rare.
Being specialized is both a blessing and a curse. The curse comes because you might not be suitable to teach the courses that need teaching, but the blessing is that you know how to go deep into some important topics.
If you have a degree already in math, philosophy might present an option if the right position came along. But it would probably be a mistake to try to build a career on the assumption that it would be easy to do so.
Also, of course, if you just love it, there is no real reason why a mathematician or linguist can't enter into collaborative relationships with philosophers on topics of common interest. Such relationships can be highly productive.


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Does a minor obtained in a graduate school matter?
Some universities require that each graduate student have a minor. I wonder whether it is helpful in the long run? For example, if one has PhD in mathematics with a minor in philosophy, would it be helpful to obtain a position in logic in a department of philosophy? [Probably related to this question.]

I would guess that very few universities require a minor for a PhD.  It does not make sense to have a minor for a degree which is focused on in-depth study of a narrow subject.

@AnonymousPhysicist Berkeley CS requires a minor (or at least it did when I got my PhD).

I had a minor for my math Ph.D., but it was in a closely related math area. I think this was actually required where I was at. I don't recall what the formal requirements were, but I think you simply filled out a form listing supporting graduate work in the field, and half of your "level 2 qualifying exam" was over your specified minor field, with the approval being (I think) a judgment call based on sufficient supporting evidence for that minor (courses, performance on the "level 2 qualifying exam" material, etc.). I've nearly forgotten about it, and I don't think I ever mentioned it on a CV.

I plan on doing one (not required at my university) because it'll make my mainstream research better, not to get expertise in two fields.

As you kind of alluded to in your example, the answer to this question depends a lot on what kind of "long run" you are planning to pursue.
First, in a career where your minor subject is irrelevant, then no, your minor likely will not matter. Sounds obvious, but this is likely the case for many people.
Further, in a career where your minor subject becomes your main focus, such as a mathematician transitioning to a position in philosophy, then you will likely need to demonstrate your qualifications with more than just your PhD minor. Your minor may be noticed when looking for your first academic appointment, but in the long run, it will be much less helpful than publications in philosophy, recommendations from fellow academics in philosophy, coursework in philosophy subjects etc.
There are a few situations where the minor could be helpful, such as if you are applying for an entry-level job in some interdisciplinary field. However, there are many more situations where the minor is either irrelevant or insufficient to prove your qualifications.

Based on my own experience (i.e., n = 1), a graduate minor during my PhD helped me a lot. In my case, I earned a PhD in an environmental field and earned a minor in applied math. The minor helped me demonstrate quantitative skills. I have also seen other people who earn either a minor or master's degree during the course of their PhD in statistics and this help them a great deal.
More broadly, a graduate minor can be helpful if it compliments your primary field of study. For example, a PhD with a major in wildlife ecology with a minor in biology would likely not be beneficial, but a PhD with a major in wildlife ecology with a minor in sociology might be helpful if one wants to do human dimensions research.