text:
While doing PhD I did not consider the job prospects or requirements in my field. Will it be alright to ask my advisor for help with career path?
I made a huge mistake while doing my Ph.D. I did my Ph.D. on a topic that I was excited about but did not feel confident in. And lo behold, I got a Ph.D. in 5.5 years with skillset, which is not at par with the requirements of the openings in my area of research (computational modelling of the additive manufacturing process).
My research involved fairly simple methodology. I can publish many papers on my topic or research area in decent journals as there are several open ended questions, but that won't get me any tenure track position or industry job.
The majority of publications or grants in my research area is for experimental research. Computational research is not that hard to do and also does not get standalone grants. I should have carried out some experimental research during my Ph.D., but I was always hesitant to propose it to my bosses.
Now after graduating, I am realizing the slim prospects of landing a job with my skillset and CV. I want to do some experiments in my Postdoc position with my Ph.D. advisor. Also, I need some contacts for my next move. Will it be alright to ask my Ph.D. advisor (now postdoc advisor) for help with defining my career path?
Edit: The reason I am asking this because I am hesitant to blurt out my insecurities and my issues to my professor. I have good relationship with my advisor, I don't know if I should bother him with this.

@Wetenschaap my area of research is such that it is heavily dependent on experimentalists. So most of the experimentalists carry out their own modeling along with experiments. Their modeling methodology or rigor is not good, but still that suffices for the topic. I as a purely modeling person, am not essential. Noone needs a rigorous model if a simple model is enough to get one published. But, I cannot directly apply my experience to other topics as I am not technically sound for those domains.

I am not sure I understood the question correctly. You are asking if it is okay to ask your advisor about your career? But why wouldn't it be okay to ask? Or what am I not understanding?

Most advisors don't know how to get jobs outside of academia, it's kind of humorous how delusional many of them are.

Yes, and.
Yes, because one of the hats an advisor should wear is that of a mentor who focuses on your academic and professional development. I like Leonard Cassuto's take (in The Graduate School Mess) on how advisors should help students rather than trying to produce copies of themselves:

Advisers have to treat their students as their own people, not as family members, or worse, as potential mini-me's. Given today's job prospects, many promising scholars and teachers will choose not to pursue professorships. That decision may disappoint an adviser, but it's the adviser's job to fight such feelings. "Be suspicious," says English professor Leo Braudy, of advisers who "stop you from making your own mistakes and finding your own path." [...]

So there's an implicit assumption that advisors should help you with the next step after the dissertation. Yes, they write recommendations, but they should ideally be helping you figure out what that next step is. Hopefully they're also providing some kind of validation if you don't do what they expect.
So just ask. You might be surprised by the reply.
And? You can also look for mentors beyond your advisor. If your advisor is the kind that would treat you as a mini-me, having someone else helping you out would be huge. Even if your advisor is helping you, if they're a good mentor, they will acknowledge that you should be building connections with others. For instance, you can:

Identify people at your postdoc institution who you could talk to about their own career trajectory or the work they've done, to learn more about your options
Take advantage of digital conferences to meet people who do work you find interesting
Take a class or seminar with someone who could help you transition to experimental research

Yes.
The slightly longer answer is your advisor is there to, well, advise you in any part of the academic process/life. Honestly they should be talking to you anyway above career paths, to decide things like which projects to do (to maximize academic prospects), whether additional skills/training is needed (to be competitive applying for industry positions), whether you should be thinking about fellowships/grants (which need a lot of time to write, especially the first time).
Regarding you comment about you expertise not being needed. You got a PhD in your field. First, your supervisor probably had to convince people it was worthwhile (to get funding) and you had to convince people it was worthwhile (to get the PhD). So at least some people thought it was worthwhile and the results needed. Think of it this way, you say everyone uses a simple model, well now you are the person who can provide the better model for them to use.


text:
Should I put the raw data in the appendix of an investigation if it is available in the GitHub repository?
I am currently doing an investigation (IB Extended Essay if it is helpful) of how different architectural approaches affect website performance. To do so, I have written a program that repeatedly runs a series of tests on each of the three researched websites. I now have 3 tables (as CSV files) with 7 columns and over 100 rows (the tests were run 100 times) stored in a GitHub repo.
In the investigation itself, I am taking the average of these columns and go from there. What I am asking is, should I put the raw data in the appendix? On the one hand, it seems like a good practice to show the data, as it demonstrates where did the averages come from. On the other hand, those tables are massive, AND they can still be accessed in the repository. Should I put it or not?

What would you gain by including the data? This might depend on the medium in which the paper is published.

"Supplementary material and raw data is available from ..."?

There is no need to put the data into the paper itself if it is accessible and you point to its location. For a printed paper it is mostly useless, of course, and if it is online, then it is only a click or two away. No one is likely to complain about the minimal added effort.
But, like any other web resources, your reference to it should include a date (last referenced). Then if it is later changed for any reason, the reader will have a better sense of what is going on.

source: Stack Exchange

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

sort: votes


text:
What's the formal name of 'search committee' in a cover letter for postdoc application?
When writing a cover letter for my postdoc application, I have a question about how to write the recipent's name at the beginning of the letter. It's not a specfic person, but a committee. But I don't know the formal name of the committe (it is not provided in the info page). Can I just call it "Postdoctoral Search Committee"?
Thanks in advance!

Can I just call it "Postdoctoral Search Committee"?

Yes, that's fine and normal in your situation.
If a specific person is named in the advertisement, use their name.

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
E-mailing a paper under review to a prospective PhD advisor; a co-author wants all co-authors to be CC-ed. Is this OK?
So I am stuck in a very weird situation. I am a prospective PhD student, and I emailed a supervisor that works in a field of research very close to mine, and is very successful.
He replied stating that he is interested to have me in his team, and requested my papers. One of my papers is under review.
I asked my co-author which is my advisor for a permission, and she said it is okay to send the papers as long as I cc all co-authors in the email.
I feel like this is not a nice way of emailing a distinguished professor, especially that I do not understand the point of ccing the co-authors. I might offend the professor, which I do not want to happen.
I appreciate the advice.

I asked my co-author which is my advisor for a permission

Here a better move would have been that of asking all your coauthors for permission.
I'd now:

Inform all your coauthors, cc'ing your advisor, asking if they are OK with that.
Inform your advisor that you would not feel comfortable in cc'ing the coauthors in the discussion with the prospective supervisor.
Write to the prospective supervisor without further copying your coauthors. At most, if your current advisor insists with that, use a blind cc.

So you are saying to Email my other co-author, and cc my advisor and ask if the other co-author is okay with it? but not cc them in the mail reply to the prospective prof?

@sandra Yes, I'm suggesting to email all your other coauthors, cc-ing your advisor. If there is just one more coauthor, email them with your advisor in cc. You can also say that you previously discussed this with your advisor.

@sandra I've made an edit with one more step.

This feels paranoid to me.

@AnonymousPhysicist Better feel paranoid than sorry...

@Massimo why sorry? as a co-author of a scientific paper that it is meant to be published, why sharing it with one confident person (i.e. professor) would need an authorisation from the co-authors when it is under review?

@sandra Although I find the whole idea of asking for permission strage, I suggest that you send an independent email to the new professor related only to this paper where you can CC all your co-authors and you start it with; "According to the request of Prof. XYZ, ....." The new prof will understand that this additional step isn't coming from u and u sound more professional. So, u satisfy everyone!

@Younes Because not all authors are comfortable in sharing papers under review and some can get quite angry about that.

@MassimoOrtolano So I am thinking of sending two emails (based on you and Oleg's response). One email at first in reply to the Prof, stating that I am doing this because my advisor wants me to do so (even tho she said to write it in a way like she doesn't know I am CCing her, I really don't know why she's doing this, but I cannot make myself look bad). and then write another reply to the prof's email with the papers and CCs. Would this be better?

A co-authored paper is automatically a piece of intellectual property collectively owned, and if there is no explicit arrangement otherwise, it is to be handled by unanimous decisions/consensus. It is not yours to do as you please with it, plain and simple.
Your supervisor relaxed this by saying to you that you just have to inform the co-authors while actually sending the paper out. I strongly disagree.
You do have to take your coauthors' permission/consensus to send the paper out (and if you don't like that, start writing solo papers).
So the advise already received is sound: communicate with the co-authors, obtain by e-mail their agreement to send the paper out, send the paper out without cc-ing them.

So if you were the prospective advisor,  would you be offended? The co-authors are cool with it as long as I CC them.

@sandra I would have found it weird that you are cc-ing anybody while sending me your papers, because I would expect that any kind of permission etc as I have mentioned in my answer would have been obtained prior to e-mailing me your papers. My automatic thought would be to e-mail you back asking you why you are cc-ing other people. And why are your co-authors want to be cc-ed? Now that they know and are ok with the act? This is the weird part. Their name is on the paper, it is not like you are presenting it as your work alone.

If I were the prospective advisor, I would be suspicious of a prospective student that shared work in progress without the explicit agreement of all coauthors (not just the advisor).  Also, it's not my paper, so what right do I have to be offended by its authors' desire to be kept in the loop?

@JeffE Let's accept the OP's fear and anxiety about "offending in any way imaginable the prospective supervisor", however exaggerated/unfounded it may be.

This is wrong because the intellectual property is owned by the university, not the authors, in most cases.  This is a question of ethics/culture, not law.

@AnonymousPhysicist Who said anything about "law"? I certainly didn't. The concept of collective ownership and related notions in the post exist independent of any legal incarnation.

"Intellectual property" is a strictly legal concept.

@AnonymousPhysicist Both words are part of the common vocabulary of English, so no, "Intellectual property" means a product of my mind that is mine... in parallel of course with its legal meaning.

I think you are claiming that intellectual property is a moral right.  That is wrong.  It is only a legal right.

@AnonymousPhysicist This is wrong because the intellectual property is owned by the university, not the authors, in most cases — In every university I've ever been part of, university policy explicitly acknowledges that authors, both students and faculty, retain all intellectual property rights (or as they are called in this context, copyright) to their papers.  So in my experience, even in the strictest legal sense, the first sentence of the answer is correct.  (I am not a lawyer.)

@JeffE Universities definitely retain patent rights, which are the (potentially) valuable rights.  Are you sure about copyright?

Patents are not papers.  Yes, I am sure about copyright. Here are my university's regulations; see "Section 4: Copyrights".  Also, many/most journals ask authors to transfer copyright to their papers to the publisher; if authors didn't retain copyright to their papers, they wouldn't be able to legally sign those forms.

I generally agree with Massimo Ortolano, but does it not work out easier?

Write the actual email to the important prospective advisor with a response to everything else. Mention that the paper under review will come with a separate email.
Write an email to the same advisor, CC'ing all the authors of the paper under review, as requested. This email states:

Dear Prof. XXXX,
you were interested in my research. Here is my latest work, which is still under review.
I CC all the coauthors. If you have questions on it, you are welcome to ask me, but you might want to address the person who did the contribution you are interested in (per author statement -- you _have_ author statement, don't you?).
Nada, nada.

It might come over as a bit of a weird flex, but I would not see it as offensive.
The benefit of my approach is that you do not overthink it. You are slashing your strange case into two very regular approaches: an email to a prospective supervisor and a mail, sharing a paper of yours.

As discussed in the comments here, the prospective advisor should not be angry with this approach. But your coauthors of the paper under review might. So, that's what for is asking them separately, as suggested by the other answer.

My advisor insisted that I reply to the email and CC them. That is what I think would cause the problem. I don't know why but she insists that this is the safe way even though the professor is highly respected.

Yes, it's fine to CC your coauthors when sharing a draft of your paper.  It just informs your coauthors that someone was interested in your work.

Have you done this before? Didn't the prof get offended?

You're not taking into account that the OP communications with the prospective advisor do not have the only goal of sharing a paper, but also to find a position and there can be additional information, discussion etc. that need not to be seen by the coauthors.

@MassimoOrtolano Exactly, that is what I am concerned about.

@MassimoOrtolano There is no need to include the additional information in the email, but surely it's not a secret that sandra is a prospective PhD student.

It can just be "Dear Prof. X, Here is the manuscript you requested."

@AnonymousPhysicist There is certainly the possibility of sending two separate emails, one with the additional information and one with the paper, but the other coauthor may not like anyway to have the paper shared when under review. In my experience, while some authors are quite open, some others really don't like to share their draft papers and can get quite mad about that. Since we don't know the authors involved, as I said, better be safe than sorry. Or do you really want to put the OP at risk?

@MassimoOrtolano Damn, saw this comment just after posting my answer, suggesting exactly this.

@MassimoOrtolano Ethical scientists do not keep secrets.


text:
When is it okay to update other search committees?
I'm on the academic job market this season for a position in a STEM field. I've had one on-campus interview and may receive an offer from this school within the next week or so. I've also had Skype interviews with a few other schools, but haven't received any on-campus invites from them. (The Skype interviews occurred about 3 weeks ago.)
At this point, should I let these schools know that I've had an on-campus interview? Or is it safe to assume that I've been rejected by them if I haven't received a campus invite already?

An interview is not a job offer.  Don't say anything until you have, and have accepted, an offer.

Correction: If you have an offer—a formal, written offer—from A but would prefer an offer from B, you should tell B about your offer from A. Who knows, they might match it.

Without saying anything about other interviews or offers, it is reasonable to call up a search committee chair at a place that skype interviewed you and ask them what the current state of the search is.  You're likely to get an answer like "We're meeting tomorrow to pick a short list for on-campus interviews" or "We've invited several candidates for on-campus interviews and you weren't selected."  If you don't ask you probably won't get any information.

Don't make assumptions. Nearly everywhere will let you know when you are no longer under consideration. You may or may not be high on their list. You could be high and they are just dithering. But they would rather make it definite, just to avoid fruitless communication.
But it is probably a mistake to tell them you've had an interview, as it may confuse them about your interest. Wait until you have an acceptable offer before you notify them.
Trying to "nudge" them in your favor could work either way, if it has any effect at all. It is a risky thing to do. Nudging might be worthwhile if you are juggling multiple offers.

Just a bit more info in there: They usually let you know if you are in the shortlist, then not selected. Otherwise, very few universities let you know anything ("only the short-listed candidates will be contacted" is usually on the text of the job posting)

It's often the case that shortlisted candidates will be held in reserve in case the top candidates don't do well in interviews or turn down offers- they can then invite lower ranked candidates to campus to interview.   Thus you might not hear anything until a candidate is made an offer and accepts the offer.

Never.

Interviews are nothing, they don't really mean anything more than "you made the short list". Still a long way from hired...
You should only communicate the other committees when you have something concrete, like a written offer. Otherwise, you would be just wasting people's time. Why would a committee member care if you went to interview somewhere else?
@guest "auction" only works when you have more demand than supply. If you are a one of a kind rockstar of an academic, then sure, that would work. Otherwise, plenty of supply, very low demand...

A general advice in any job search (academia or civilian world or NFL) is to let the other parties know when things have become competitive. It doesn't guarantee you get something done with the other parties.  But it will often move things along.  Especially if you are a good candidate and are likely to come off the market.
Be gracious about it (just wanted to let you know that I am moving down the path with X...would love to interview with you, T.)  But don't hide your light under a bushel.  At the end of the day, both sides are seeking to create an auction.  Make sure you do the small things you can to make an auction for you.
Edit:  Just looked at Buffy's comment.  Yes, an offer is much more powerful and deserving of a nudge.  I would still consider if you can do the nudge (gently) with less than an offer.  In particular, if you think things will move fast with the other party and you won't have a lot of time to shop an offer.  Judgment call, but my gut feel is power for the people.


text:
Is it a bad idea to ask my erstwhile PI to say in a recommendation letter he "forgot" to acknowledge me in a prior work?
Three years ago, I was an undergrad majoring in Biochemistry in a major US university, and did significant research work in preparation for my thesis.
I am currently polishing a personal statement for PhD applications. To help illustrate a point, I started looking into the publication list of my erstwhile advisor for ideas, for the first time in a year. It turns out he published an article on Nature last year, that credited several fellow undergrads in my lab as co-authors, but not myself. I was never notified of the publication, nor mentioned in the acknowledgement section. The article relied on a database that I helped to compile, and mentioned one of the conclusions I made in my senior thesis. Clearly, it's too late to ask for any revisions to that paper.
Even if these are not sufficient grounds for including me in the author list, I wonder if I am justified in asking that professor to say in his recommendation letter he "forgot" to add me as a co-author, or include me in the acknowledgement section? I had asked him to prepare a recommendation letter months in advance, but it will be at least another week before he is expected to send any.
As for my personal relationship with the professor - his recommendation for me is probably not the most emphatic, but we have generally been on good terms up to this point. Will simply raising this question damage our relationship, or even his recommendations?

What do you hope to gain by having the prof mention that they 'forgot' to include you?

Do you mean "emphatic" or "empathetic" in your last paragraph? Do you mean that you are not particularly close, but that you are at least on good terms?

what is "PI" acronym? to me the acronym expands to "private investigator" but "private investigator" does not really fit the sentence so i ask for clarification.

Principal Investigator.  It's the grant holder, and is used more generally in academic science for the person who runs the lab (i.e. your boss).

The biggest issue to me is that he used a conclusion from your thesis without citing it! That is plagiarism if you are not a co-author. He should have cited your thesis. I don't care how obscure it would be to find. Theses are always citable.

TIL that "erstwhile" is a word

@user347489 Yes, one that is largely affectation in this context. "Former" would be overwhelmingly preferred in academic contexts.

Asking them directly to acknowledge "forgetting" you is a battle that you cannot win, I am afraid. However, if you approach this strategically, you can still probably get a letter that bears the same message as being acknowledged on the paper would.
From your description it seems safe to assume that your authorship was omitted accidentally. It is a sad but not entirely unusual reality that contributions of undergraduate students who helped with a large project over time can get forgotten, not out of malice but simply because nobody keeps track of who did what. Reminding the supervisor of your contributions (be as specific as you can) that ultimately led to a high-impact publication should do no harm then. If this was an honest mistake, I can imagine they will want to make it up to you.
On the other hand, failing to acknowledge contributions of co-authors is a serious academic misconduct. Admitting it openly and in writing could possibly harm your supervisor's credibility and I don't expect that this is a risk they would be willing to take just to increase your chances to get a position. If you want them to acknowledge something specific in the letter, you need to ask for something they are likely to agree to.
Consider the impact of being properly listed as a co-author of the said Nature publication. People assessing your application have a good idea how preparing such large publications work and that the success of it depends primarily on the first author / supervisor developing the original ideas and orchestrating the work. Undergraduate students often do rather the mechanical labor. From this perspective, being listed as a co-author doesn't say more than: "I have an experience from a successful lab and I can do the mechanical labor good enough."
The first part of that message is on your CV already. You can ask your supervisor to testify the other part in the recommendation letter.

"authorship was omitted accidentally" Compiling data does not earn authorship.

It is up to the authors and the customs in the field to decide which contributions earn you a place in the author list, sure. However, if a person contributes, they should be acknowledged. Since neither that happened and the OP states the work relies on their contribution, such an acknowledgement was clearly omitted.

I realized today that the professor probably made contributing to that database a lab assignment for more junior students, around the time I left college. So technically, the contributor list could be swamped by students who were only marginally involved.

Does "coming from a successful lab as an undergrad but having no history of publications while there" send the wrong message to PhD admissions committees though?

I am not familiar with PhD admissions in the US and in your field. From my experience (EU, computer science), having a publication before starting a PhD is certainly an advantage but not a requirement. Moreover, publications where you are not the main author tend not to be valued too high.

@AnonymousPhysicist That heavily depends on the field in question! In the life sciences, compiling data is often half the paper.

You should ask the professor to describe your contribution to the database and the relationship between the database and the publication.
No matter what the reason is that you are not an author on the publication, there is no benefit to including the reason in your letter of recommendation.  A correction to the author list could benefit you, but only someone familiar with the details of your work could determine if that is appropriate.

This is the appropriate (and completely non-confrontational) way to deal with this - ask the letter writer to state what your contributions to this paper were. Everybody can then draw their own conclusions, there is no need to spell out whether or nor you should have been a co-author, or whether or not you should have been acknowledged.

It would of course be a tremendous feather in your cap to be a coauthor, even one of zillions, of an article in a prestigious journal. And even if not a coauthor, it is personally satisfying to be acknowledged. However, no one else pays much attention to acknowledgements.
What you now need to achieve is fair recognition of your contributions in the letter of reference. The facts, as you present them, support the hypothesis that the PI likely has forgotten the nature or extent of your contributions, was never wholly aware, or confused your contributions with someone else's. That happens. Regardless, every reasonable recommendation letter writer appreciates a "cheat sheet" from the recommendee, so I'd suggest you write something like:

Dear X, ... This is to request a letter of recommendation from you for ...  Since it's been a couple of years, for convenience let me summarize that I worked on your team from ... to ...  My principal contributions were .... and ...., which I described in my senior thesis and which was used in the publication [insert citation]. As you can imagine, given my hope for an eventual research career [or whatever], I think to the extent you are able to connect the dots between by work and the publication in particular would be very helpful.

Basically, swallow your injured pride (and don't expect any acknowledgement revisions!), but in a respectful fashion make sure the PI has the information to now be able to represent your contributions accurately. Present it factually but impersonally, implicitly assuming forgetfulness or lack of awareness, not trying to prove it with bullet-proof evidence.
Finally, I'm writing this all taking at face value the facts as you have presented them. Do be open to the possibility that your picture may not be fully complete either. Could your "database" have needed significant rework or updating, for instance? I'm not trying to challenge you and know nothing more about your situation, but after several decades in applied research, I've encountered various instances where valued but junior contributors accidentally overvalued their contributions as well.

Tell the advisor you were pleased that the work was published and it reminded you of how much you learned from participating in the evaluation of data (or whatever you did). Reminding the advisor that you participated in the research, hopefully, will prompt the advisor to mention this in a letter of reference for you.
I think it not wise to force the issue of not including you as a co-author.  The advisor should be prompted to provide a correction to Nature based on your correspondence above, but I would not force the issue as it may hurt the letter of recommendation.

What do you expect? A correction to extend the acknowledgments?


text:
What is the difference between a research statement and a research interest?
is there any difference between the two?

This would depend on who is asking, of course. But I'd expect, generally, that a research statement would be more detailed with a plan for how you would go about things like obtaining funding and incorporating students, etc. A research interest might be as little as you area of special expertise, though it might be a mistake to make it too narrow. For example, in mathematics, Algebra might be a bit too wide, but not so narrow that only a few people in the world are interested.
But, it can vary. Ask the asker for guidance if you can.


text:
When do you send in your research proposal when applying for PhD?
do you send it with your first email to your prospective supervisor or after a few exchanges?

I'm assuming that you are in a place in which the advisor/supervisor actually hires you. I'm also assuming that you want to work on your own research program rather than that of the supervisor, which is often ongoing.
I'd suggest that you say something about your research interests, but, perhaps, not make a formal proposal. You can do that in the first mail. You can even say a few things about why this is your interest and what you have already done in that direction.
But some advisors might want you to take up something in their program, rather than work on your own. For others it might be the opposite. Unless you know which situation applies, I'd try to keep your options open.
If you introduce your ideas without expressing too much commitment to them then you might get either a request for more information (hence the full proposal) or a suggestion about what s/he would rather you do for the degree. And take the phrase too much literally. If it sounds like a demand, then it may wind up as an obstacle.
Of course, you may already know something about the professor and have an idea about whether it is better to push or not.

Just for completeness, in some places and fields, proposing research normally is done after acceptance and even choosing an advisor is also done later.

Thank you. Maybe I don't understand how this works (especially in UK/EU). I believe that your application success is strongly tied to the quality of your research idea/proposal. A good proposal would improve your chance (and research group) of getting funding. Do let me know if any of this is incorrect so that I can have the correct perspective.

My experience is US, not UK. Making a proposal isn't likely to hurt you unless you imply that you aren't open to other ideas. You want to show aptitude and ability primarily. But if you can know beforehand how committed a prof is to her/his own program you can adapt your approach.


text:
Citation Style (CSL) with angular quotation marks?
I'm writing a chapter to go in a book produced in South America, and they want us to use angular quotation marks. Two example formats I have look like:

Klaveren, Alberto van. «Doscientos años de la política exterior de Chile: de Hobbes a Grocio». Artaza, Mario y César Ross (eds.), La política exterior de Chile, 1990-2009. Del aislamiento a la integración global, USACH-RIL editores, 2012, pp. 51-69.

Witker, Iván. «La anarquía latinoamericana desde una perspectiva neorrealista», en Estudios Avanzados 12, diciembre 2009, pp. 23-41.

I tried using the CSL Search By Example page, but nothing with angle-quotes appeared in the search results.  Furthermore all the examples found put the year in the wrong place (they put it near the beginning and I need it near the end).
Can anyone suggest an appropriate CSL format and where to find it, or else how can I modify a "similar" CSL file to meet my requirements? (I still find the Visual Editor super-confusing.) Thanks.
(Writing in Google Docs, with citations managed by Zotero and its Google Docs connector.)

Adding the angle-brackets was as simple as using the Visual Editor and clicking on titles for article examples and then adding the « to the Prefix and » to the Suffix fields down below.
Moving the year took a little more than just dragging and dropping it. Downloaded the modified CSL and applied it to Zotero in Doc, and results seem to be very close to what I need.


text:
Mentioning a professor's work in the statement of purpose when they aren't the first author
I am applying to graduate school (USA, computer science/machine learning), and one potential PhD advisor is Bob. Many of the papers that he coauthored overlap significantly with my interests. One of these papers is

Moving basket weaving out of water and onto land improves efficiency
Authors: Alice, Bob, Charlie

Bob is Alice's advisor, and Charlie has since become faculty at a different university.
Would it be OK to include a line like:

Professor Bob's research on the effect of the basket weaving environment is interesting because blah blah

despite Bob being second author?
This is Bob's only basket-weaving-environment paper, but he has many papers (in several different author positions) for related fields- these already received mentions in the SOP. I have not talked to Bob.
But the specifics don't matter too much, I am mainly concerned with writing "Professor Bob's research on blank" where "blank's" primary author was not Bob.

I'm going to remove my other comments because this has gotten quite chatty, but I hope you can update your question with some of the additional details you've mentioned (comments are ephemeral and are not meant to last). Key points: you haven't had any correspondence, Bob's last-author papers re: your interests, etc.

Let us continue this discussion in chat.
Edit: That button did not do what I intended, but at least it has a log of the comments.


text:
Term to describe paradox where those with less subject matter expertise can sometimes make better teachers?
A teacher of teachers in a field I'm involved in frequently says:

the best teachers are often those who only recently learned the material themselves

The rationale for the statement is that someone who has recently learned the material is more intimately aware of the stumbling blocks someone goes through when learning it, and can therefore be cognisant of those when teaching it to other beginners, thus making them a better teacher.
By contrast, someone who has known the subject matter for many decades may have completely forgotten what it was like when first learning the material, and could be therefore prone to impatience, or underestimating complexity or learning time.
Question
Does this concept have a name? Or is there any study that backs up the idea that more experienced instructors can sometimes be blind to the most basic concepts in their discipline (since they take them for granted), and therefore (paradoxically) make worse teachers than those with less subject matter expertise?

I posted a question on whether the curse of knowledge is a real effect, for those interested in discussing that. See here.

Comments are not for extended discussion; this conversation has been moved to chat. Please read this FAQ before posting another comment. We can only move comments to chat once, but you can use the chat as long as you wish.

This is called the curse of knowledge. From Wikipedia:

The curse of knowledge is a cognitive bias that occurs when an individual, communicating with other individuals, unknowingly assumes that the others have the background to understand. [...]
For example, in a classroom setting, teachers have difficulty teaching novices because they cannot put themselves in the position of the student. A brilliant professor might no longer remember the difficulties that a young student encounters when learning a new subject.

Writer and organizational psychologist Adam Grant nicely illustrates the concept in this article:

Two decades ago, I arrived at Harvard as an undergraduate excited to soak up the brilliance of professors who had won Nobels and Pulitzers. But by the end of the first month of my freshman year, it was clear that these world-class experts were my worst teachers. My distinguished art history professor raved about Michelangelo’s pietra serena molding but didn’t articulate why it was significant. My renowned astrophysics professor taught us how the universe seemed to be expanding, but never bothered to explain what it was expanding into (still waiting for someone to demystify that one).
It wasn’t that they didn’t care about teaching. It was that they knew too much about their subject, and had mastered it too long ago, to relate to my ignorance about it. Social scientists call it the curse of knowledge. As the psychologist Sian Beilock, now the president of Barnard College, writes, “As you get better and better at what you do, your ability to communicate your understanding or to help others learn that skill often gets worse and worse.”

To all those discussing if the effect is real, I posted a separate question about this, see here.

Comments are not for extended discussion; this conversation has been moved to chat. Please read this FAQ before posting another comment. We can only move comments to chat once, but you can use the chat as long as you wish.

It is often said but I have never seen firm evidence of it to be true. (I have seen bad teachers hide behind the equally false pretence that "therefore" they must surely be brilliant scientists!)
The biggest confounders are the Dr Fox effect and the Dunning-Kruger effect, which lead students to make erroneous assessments as to how well they have been taught.
Teachers who have themselves not mastered the material often fall back on the same coping strategies as poor students: "Do not try to understand this. Just, whenever you see an equation like this, follow these three steps..." Clearly the poor student believes that this teacher speaks their language, but it is far less clear if anyone is learning anything in such an exchange.
This happens mostly with TAs. It is nice to get positive feedback on the module because the TA follows this pattern, but not so nice to see what the students' heads have been filled with, come exam marking time.

I hadn't heard of the Dr Fox effect before - very interesting!

Another related model is Dreyfus model of skill acquisition.
The premise being that someone at the Expert level might struggle teaching someone at Novice level since they way they perceive the domain and problems are very different.

It is not a "paradox" unless one assumes - incorrectly - that an expert in a field must ipso facto be an excellent teacher as well. As has been mentioned, teaching is a skill and requires experience and training that a substantive expert in the field may not have. Similarly, an expert in a field (scientific, humanities or otherwise) may not be a good writer. Those are simply different skills. It is commonly - and correctly - stated that lawyers (my field) are often poor writers.  I am not aware of any specific name for this misconception.

The supposed paradox is that if there are two people who are equally skilled at teaching and one knows more than the other about a certain subject, then — if the claim is to be believed — the one who knows less about the subject would likely be better at explaining it than the one who knows more. This is a stronger statement, and a more counterintuitive one, than just saying that teaching ability is not correlated with subject matter expertise. Now whether this claim is true or not is open to debate, but your answer doesn’t even acknowledge there’s anything surprising being claimed.

-1 “It is not a ‘paradox’ unless one assumes - incorrectly - that …” I think you can say this about all paradoxes. More importantly, this is not an answer to the question posed.

@DanRomik "The supposed paradox is that if there are two people who are equally skilled at teaching and one knows more than the other about a certain subject, "  That's a possible question with assumptions that someone might ask, but that is not what the OP asked.  The OP asked simply if there is a term to describe the  statement that "the best teachers are often those who only recently learned the material themselves."   And I did in fact answer the question  - no such term afaik. As for whether all paradoxes are based on incorrect assumptions, who knows, but this one certainly is.

@BrianDrake well, "this sentence is false" is a paradox with no prior assumptions. Good for detecting people who are secretly robots, though.


text:
How important are undergraduate and masters studies transcripts in applying for a faculty position?
I am going to apply for a faculty position via online system. In the announcement of the position  they have just asked for cover letter, contact info of references and C.V. But in the online process of application I noticed that there exists some taps related to uploading transcripts of B.Sc, M.Sc and Ph.D. I do not know whether they need transcripts or not? Can a bad transcript have bad effect on applying for a a faculty position?

What sort of institution is this? Primarily research or primarily teaching?

@Buffy It is primarly teaching institute.

Sorry that I'm a bit late for an answer, but there are some things you should consider. The answer of Clément provides the basic guidance, but, since this is a teaching institution, rather than a research one, it may be that undergraduate performance is more relevant to a decision than otherwise. Normally, the things you have done long in your past are treated as less relevant to how you will perform now, but teaching institutions have a need to know how you will deal with students and their myriad problems.
If you have a poor undergraduate record, then the reasons might worth examining. Let me give two scenarios.
First, it is possible that you were just less engaged with your education as an undergraduate and only learned later the importance of hard work.
Second, it is also possible that you just struggled as a student for whatever reason, but pushed through but with a less than stellar record.
You might be asked by such an institution why you have a poor record and it would be good to have thought it out in advance. Neither of the above scenarios is damning, and either can give you some insight into students and how to teach them effectively. But think about how you were able to improve things later and what it took: internal fortitude, helpful advisors, ... , whatever.
Let me also describe the alternate scenario of someone who always did well and has a near perfect record. It might well be that such a person has no idea whatever about how students struggle and how to help them. Everything to them was easy and they expect it to be easy for others. It will take that person a long while to become an effective teacher; one who is not overly judgmental.
Teaching is much, much, more than the flawless presentation of material.
These are extreme cases, I realize. But think about your own situation and how you came to succeed and how that might make you a better teacher.

You are perfectly correct that for primarily teaching-oriented institutions, those scenarios reflect the possible importance given to transcripts. Thanks for complementing my answer.

Your answer includes some important points, which I definitely consider them. Thank you very much

I do not know whether they need transcripts or not?

There are two slightly orthogonal aspects when you apply to faculty positions:

What the panel will use to determine if they will offer an interview,
What the administration requires for your application to be complete.

The announcement will focus on 1., but when actually applying, you may realize that 2. is a bit different.
If the application platform requires your transcripts, upload them, and don't think too much about them: they may or may not be reviewed by the panel, but what you did during your PhD and your cover letter will have a greater weight than those transcripts.
If the application platform does not require the transcripts, then I guess it's up to you. You can probably just upload them later on if the panel would like to have a look at it, but as Bill Barth noted in the comment, that is probably not a good idea to give the panel a possible reason to filter out your application before even looking at it.

Can a bad transcript have bad effect on applying for a a faculty position?

As I wrote, they can, but whether they will depends on multiple factors that are hard to assess. I believe it is reasonably safe to say that your PhD, cover letter, and possibly letter(s) of recommendation will have a greater weight, but that does not necessarily imply that your transcript will have a zero weight.
Good luck, I hope your application will receive favorable reviews!

I wouldn’t take a risk and fail to include requested application elements, even if in the end the committee doesn’t want to look at them. Don’t give them a reason to filter out your application before looking at it. There may be hundreds of other applicants and they may use incomplete applications as a pre-filter before reviewing individual apps to reduce the load.

@BillBarth Good point. I've edited my answer. Thanks.

@Clément Also I appreciate you for your answer with positive words


text:
Advisor ignoring his Ph.D. student after getting tenure
I am Ph.D. candidate, and my advisor got his tenure about 9 months ago and called me on zoom and said no one could fire him anymore, and that was the last time we talked. Since then, he has completely ignored me as his only Ph.D. student. He does not read or comment on my papers(2 paper drafts were sent five months ago). My results get continuously beaten, and I have to make changes to keep my papers state-of-the-art constantly. He refuses to set up a zoom meeting since no one is going to school; that is the only way to meet him. He was active with fundings, papers, and proposals before he got tenure.  He responds to my emails with irrelevant suggestions, or he says he will read my papers sometime next week(he expects 2-3 papers to graduate me). He is not supporting me financially anymore since his fundings are over, and I pay for my Ph.D. from pocket.  School officials can not do anything, and changing my advisor after four years of hard work will result in a complete reboot. I'm an international student and can not just quit. My goal is to get my OPT and a job. It looks impossible to graduate with this advisor... What would be the best option to do in this situation.

Why can't you just quit? What good does it do to pay for yourself? Can you talk to someone in the uni (like another prof) who could say"my collegue behaves horribly, so I'll take you as a student, just write everything together and defend tomorrow"?

I don't know what an OPT is, but have you actually tried finding a job?

If you can finish your PhD in a few months, do so.  Otherwise, you need a new advisor who will provide funding.

I find it interesting that someone (your advisor) would put forth so much effort (get PhD, get an actual tenure track job, get tenure) into a career that is heavily involved with doing things that he/she apparently intensely dislikes.

@user111388 OPT is a United States visa type.

@AnonymousPhysicist: And what does OP mean by "to get it"? Do only people with phd diploma get this visa?

@user111388 It is Optional Practical Training. Students who graduate with a degree in the US are eligible.

This is country specific and domain-specific and could be university specific. Not the same in France (European Union) and in California (USA), and not the same in history and in computer science.

As noted below, I am surprised that the university cannot do anything.  At my university at least, there are policies to protect students in your situation.  We also have a students advocate.

Your prof actually might be burnt out. Can you submit the papers on your own?

I'm really sorry to hear about this situation.

School officials can not do anything, and changing my advisor after four years of hard work will result in a complete reboot.

This surprises me. Every university differs, but in general you should bring these sorts of issues to your Associate Chair/Director, etc. of Graduate Studies in your department. If they aren't able to mediate with you and your supervisor, or aren't willing to, in most universities that I'm familiar with you should escalate your complaint. Perhaps you have an Associate Dean of Graduate Studies, or if there is a Faculty of Graduate Studies, there is somebody that you can consult there.
Barring this, you should seek advice from either your graduate students association. There may be informal avenues of support that you can pursue.
Most universities have policies around the change of supervisor, as this happens more commonly than you may think.

Exactly. You should discuss with the other individuals on your committee and perhaps ask one of them to take over as your advisor: the current advisor won’t mind this as he doesn’t care about advising you.

...and a change of supervisor =/= complete reboot or even alteration of the research topic, especially this close to graduation.

This is of course atrocious. I can show you a list as long as my arm of former PhD students who will all sing my praises in the "always being there for them" department. So I have a right to state what I think of such a supervisor. But I won't, as it is just a string of very bad words.
Now, a good PhD student should actually be able to produce a top-notch thesis with literally zero input from their supervisor. However, not all PhD students are that good (why it would seem that most of them aren't) and supervisors do have a duty of care toward their students.
Your department may have procedures that allow for a "no fault" ("least said soonest mended") supervisor switch. Discuss this option with the departmental senior academic tutor.
A kind word of warning: you are unlikely to get your own back with this supervisor. In the fullness of time "the system" will have its own way of dealing with this sort of attitude, but this will only happen many years after you have left the department. So please stop expending any further thoughts or emotional energy on this **** right NOW.


text:
What to do to speed up the paper publication process?
One month ago, I have submitted a paper in a journal under Taylor and Francis. 3/4 days later after the submission,  the status changed to "under review" and till now the status remained unchanged. I am in a hurry and need to get the final decision as soon as possible. What can I do to speed up the process? Should I send an email to the editor? How long it will be in "under review" stage?

thanks. those answers are helpful. Actually, the journal is not so slow since I know that the editor already assigned the reviewers. I just wanted to know if I  can do something to make the whole process even faster.

The answer is generally "No", especially since reviewers have already been chosen.  What are normal review times in your field, and how good is your reason for needing it to be done quickly?

You can't make it go faster, but you can make it seem faster if you work on something else. It is out of your hands for the moment.

I have found that it takes 42 days on average to get the decision which will end in a few days. The problem is I can't attain my thesis defense without the acceptance notice(even accepted with minor review will work). And I need to let the office know about the status in 2 weeks.

The review process currently takes longer than it used to because we're in the middle of a pandemic. You may want to ask the exam office if a submission rather than acceptance notification is enough in this case, due to the special circumstances.

@pritom An unfortunate situation, I feel for you. Your situation is unusual; at my university, thesis defenses aren't contingent on anything happening outside the university. You might write to the editor, apologize for being a nuisance, explain your situation, and ask if your request could be forwarded to the referees. Simultaneously, I'd make a backup plan. Unfortunately, the end of the semester is a busy time for everyone, and I suspect that people aren't likely to prioritize review work until after final exams. I would try to find out if the deadline is at all flexible. Good luck.

You cannot speed up the process.  Everyone’s in a hurry to get their stuff published so your own situation is repeated with pretty much every submission.
More importantly, what are the odds the manuscript will be accepted as is, with no revisions?  Be ready to quickly make revisions, and be sure to address all concerns of the referees, and this will speed up the process.

3/4 days after the submission, the status changed to
"under review" and till now the status remained unchanged. I am in a
hurry and need to get the final decision as soon as possible.

If you are in a severe hurry, then consider whether or not you can post it to an e-print repository such as arXiv, bioRxiv, ChemRxiv, or even GitHub, or your own website. If you're in a hurry because you want to claim that you were the first to discover your findings, then this will solve your problem, except if the journal does not accept papers that have already been posted online (many journals these days allow pre-prints to be released with no negative consequences though). If the journal does not allow you to post it to a pre-print server, then consider re-submitting to a journal that does allow it, or if none of the journals in your research field allow it, you will have to consider what is more important: getting the paper published in a journal, or the hurry with which you need to claim credit for the work.

What should I do to speed up the process? Should I send an email to the editor?

The only thing you can do to speed up the process is to email the editor, but the editor will not be very delighted to see you rushing the process when the "normal" amount of time has not even passed yet, because papers take weeks to months (and sometimes over a year) to get published. You will come across to be demanding in a highly unusual way. Emailing the editor is an appropriate way to speed up the process when, for example, the journal says that referee reports will take on average 4-6 weeks to arrive, and after 7 weeks you still haven't received anything. It is very unlikely that rushing the editor right now will get your referee report produced within a few days: please accept that the time scale is usually best measured in "weeks" rather than "days".

How long it will be in "under review" stage?

If you tell us the journal, we may be able to help answer that for you.
If you don't want to tell us the journal, you can browse their website, perhaps under the "guidelines for authors" section, and see if it gives an estimated turnaround time for referee reports. If  they don't give that information, you can ask politely to the editor, what the typical amount of time would be, but please understand that the amount of time you've waited is not an extremely long time in the journal publication world.

"Four days is not a long time at all" ... The question starts with "One month ago", so more like ~25 days (though 25 days isn't a long time in the review process either).

@muru thanks for pointing that out. I've edited my answer.


text:
Can I write "equal author contribution" in acknowledgment?
One of my papers is now in the proofreading stage. In the revision stage, I didn't add the "equal author contribution" as a foot-note. Is it possible to add that now? Can I put it in the acknowledgment section?
Note: I am not allowed to add any sign beside the authors' names.
Edit:
I was finally able to do that. During the proofreading, I mentioned this issue and they added a footnote. They were very helpful.

To add to the previous answer, I would consider that listing equal contribution in the acknowledgement section generally does not carry the weight as listing it as part of the front page. However, if it is clear that journal policy does not allow any mentioning of equal contributions on the title page, the acknowledgements may be your best options.
However, I think that you should have a clear discussion about this right away between the senior authors, the co-authors, and the editor. Co-authorship can have significant impact on the career of individuals, so you want to be certain that everybody is clear in what is going to happen and is in agreement with the path chosen.

I have the feeling that there is no standardized way to list (or parse) "equal contribution" annotations, so my feeling would be that it does not matter.  (Say, if you put the paper on your CV, you could/would mention this fact explicitly; and I'm not aware that indexing services take this into account.)

You may be right. But there needs to be clarity and certainty. Telling a potential joint-first author after the fact that this was the best option is not really a good way to approach this. You need to be certain about the options and need to clearly communicate these options to everybody to get their consent about moving ahead.

That was not my point. My point was relating to your "I would consider that listing equal contribution in the acknowledgement section generally does not carry the weight as listing it as part of the front page".  I meant to say: I don't see that there is a clear way how such a kind of "equal contribution" label is mapped to relevant information in relevant scenarios (CV, bibliometry, etc.), so - beyond someone actually reading the article - it does not matter so much.  (From the author point, not from the journal point!)  Where would it carry more weight?

(I notice you quite rewrote your comment while I was responding ... I guess we're more on the same side now - as I said: "Ask the editor.")

Ah, got it. Thanks for clarifying your point. And yes, I rewrote my comment because at first I assumed it was the OP who was commenting. I wanted to make sure pritom is certain on all options and clearly communicates them to all authors.

Whether, and what, you can edit at this stage, and what kind of information is allowed in the acknowledgements, likely depends on the journal. You should contact the editor, since they will be able to tell you.  (And, needless to say, you need to have the permission of your co-authors to do this change.)
In fact, some journals (Nature comes to mind) even have an "Author contributions" field in which one can (or even has to) describe how the individual authors contributed.


text:
Questions about Mathematicians
I will be completing high school at the end of this academic year. I have a strong love for Maths, and I am considering becoming a pure mathematician or pure mathematics researcher when I'm older. I have a few questions about the academic world of Maths in general:

I have discovered some formulae, or theorems if you prefer, about a quite specific topic in maths with apparently limited, if any, applications to any other areas of maths. I would like to write a paper about it and try to publish it in a journal, but I'm unsure if it's been discovered before, as it hasn't come up on any Internet searches I've conducted. I've also searched arXiv for it. My question is, is there some sort of archive or database that I could use to quickly check if something I'm investigating has been discovered before?

What exactly do research mathematicians do? Do they simply think all day and write/type their thoughts and results and progress as their job?

If I don't discover anything new as a maths researcher, would I still be employed or would I no longer be payed, ie is it a safe and steady job?

I would really enjoy being a pure mathematician/pure mathematics researcher, but is it a good job in terms of salary? I don't think job satisfaction would be an issue.

To be a research mathematician do I need to very good at maths or be spectacular at it?

Thank you for your advice, it is really appreciated.

These are all good and valid questions and I do think you would benefit from a local mathematician who you could have a talk to. Could you ask your teacher to put you in touch with a mathematician? (Or, if not, maybe even another researcher?) Or does your nearest university has any person/program for people who'd like to study maths? You might want to check it out.

@user111388 thanks, I'll ask my teacher if he can put me in touch with anyone. I'm not sure if he'll be able to though; are there any mathematicians on this site?

The career advice section on Terry Tao's blog might help with some of your questions: https://terrytao.wordpress.com/career-advice/, and I encourage you to try and find the websites of other mathematicians (or even twitter profiles) for other opinions. My own thoughts: a career in academia is very unstable and permanent jobs are hard to come by (this can depend on your field somewhat). It's better to be aware of this from the beginning. To be a good researcher I'd argue that perserverance, hard work and a strong interest in your subject are far more important than talent.

I also added the united-kingdom tag as I assume that is your location, but please correct it if not.

I was a terrible high school student. To be a research mathematician you don't need any of the skills that you get in high school. You need perseverance, tenacity, the ability to cope with the fact that most of the time you're wrong about something, and if you want to be a great mathematician, also an incredible creativity. But you can be a very good mathematician even without being creative. There's a lot of things that require collaboration, and at least one of the collaborators can do the heavy technical lifting, there's no "shame" there.

Go to university and study math. Mathematicians are sought after and well payed in industry and banking and insurances and whatnot. Decide on your next career step when you have the first degree. Then you will also have met enough profs to decide if thats something for you.

https://academia.stackexchange.com/questions/44183/what-do-mathematics-researchers-do-if-they-arent-good/44187#44187

@astronat thanks for the interesting link, it was quite helpful. Do you know any form of an answer for my first question?

We've had similar questions in the past, perhaps try searching this site for "publishing while a high school student" or similar. It's important to be aware that your result might not be as novel as you think it is. Math Overflow is possibly the right place to post proofs and solicit discussion, but check their question policy before posting. If you really do have a publishable result, you'll almost certainly need help writing the paper itself. I echo user111388's advice: talk to your maths teacher or email PhD students/postdocs/lecturers in maths at some nearby universities.

In terms of quickly checking if a result's already been found, literature reviews are often anything but quick :) I suggest taking time to go through arxiv more carefully, and reading some review papers if you can (these will be long, probably expository and contain many references which you can follow up). Working methodically is also a good habit to get into if you want to do serious research.

Look also into theoretical computer science, it is very close to math (e.g. abstract interpretation...)

I worry you're getting a bit ahead of yourself. I would suggest going to university and getting a degree in mathematics. There you'll have access to professors and you'll be able to have a much clearer idea of the deliberations you'll need to make to decide whether you want to go further into pure mathematics by getting a PhD.

@transitionsynthesis thank you for your advice. I definitely plan on doing a degree in mathematics, as you suggest.

Let me try to give you some perspective on mathematics and mathematicians.
First, there are lots of kinds of mathematics. Algebra and Geometry were studied early in human history and other fields split off from them. At first glance these two seem quite different, but now there is Algebraic Geometry, a field of its own. There is also Analysis which studies certain kinds of relationships and Abstract Algebra which studies certain kinds of operations on things. No, there is more to it than that, but it gives you an idea. Topology is something like Analysis in some ways and something like Geometry in others. So there are some overlaps.
But the differences between mathematical fields are big enough that it is possible, even likely, that you can have true insight into only one or two of the many fields. And it is insight that is required for mathematics.
Mathematicians study problems. Applied mathematicians study "real world" problems and apply mathematics to their solution. Pure mathematicians study problems in mathematics itself. They study what has been shown to be true over time, but try to imagine what might be true and then set out to explore whether it is true or not. This is where insight is required.
It is unlikely, but not impossible, that you have discovered something new. It is less likely, but still not impossible that what you have discovered is significant. It may have been noticed in the past and not explored deeply, for example, seeming obvious to someone who has studied it deeply.
But, one thing that mathematicians do a lot of is work with others and share ideas. They bounce "new" ideas off of colleagues and get feedback. So, for someone in your situation, teachers and professors are the people most likely to be helpful at this stage.
If you want to be a mathematics researcher then put yourself on a path to eventually earning a PhD from a good school. Most pure mathematicians are also academics, though there are exceptions. Even an amateur can be a researcher, but will probably need to build up a circle of contacts and collaborators over time in order to be effective.
In a certain sense mathematicians work literally all the time. There are no breaks. But you don't sit at a desk for most of it. Your mind will work whether it feels like "work" at all. I often go to sleep thinking about some sticky problem and wake up with the solution. The insight comes sometimes when you let your brain relax, rather than trying to force it through some complex logical argument. The crux just falls into place.
Working with professors, especially on a doctorate, will give you a sense about what problems are important as well as ideas about how to attack them. But it is the "imagining what might be true" that makes a mathematician. The proofs are hard work and require training and practice, but it is that insight that makes the difference.
Only a few of us are "exceptional" as the word implies, or spectacular. But we all work toward excellence. Do that and you should be fine.

As a young person, I suggest you study widely (and not just mathematics). There is plenty of time to specialize later. And if you want to do serious work in any field, get in the habit of carrying a notebook (or equivalent) so that you can quickly jot down any insights or ideas that pop into your head while you are doing other things.

Thank you for the extensive answer, I appreciate it. Do you know of anything that would be helpful for my first question, apart from discussing it with my teachers? Also, I'm not exactly sure what benefit there'd be from discussing my formulae with my teachers; do you mean for proofreading and finding possible holes in my reasoning?

The problem with your first question is simply that the mathematical literature is so broad. Discussing your ideas with a teacher is probably best as they have a wider view. They might be able to put you in contact with someone who is a specialist through their own contacts.

Thanks for elaborating, I will try to discuss my ideas with my teachers as you suggest. If my teachers don't have any useful contacts for me what do you suggest I do? Do you think it'd be a good idea to approach a journal with my paper, and tell them my age, once I have completed it?

Your age will be irrelevant to them. But there are one or two journals that publish student work. Mostly undergrads. Sorry I don't have names.

I see. What do you use to check if something you've found is indeed completely original and hasn't been found before?

Also, today I spoke to my Maths teacher and unfortuantely it seems he has no useful contacts for me.

Buffy, do you have any advice for me on account of recent developments?

@A-LevelStudent Judging by your username, I'm going to assume that the teacher that you asked falls into the usual mold of an English school-level maths teacher (that is: did a batchelor's degree in mathematics, possibly many years ago, and no significant mathematics since). If all of your maths teachers are of that form (or, more specifically, if none of them have names starting with "doctor"), your best options for questions like that are to either search ArXiV (which is something of a pain) or just to ask on Math.SE (then MathOverflow if you don't get an answer on Math.SE).

To answer part of your question about financial concerns - If you are passionate about mathematics and likewise good at it, you should not ever have a problem finding employment, although it need not be a strictly math field. The knowledge one gets when learning higher level mathematics is applicable in nearly all technical fields, however it is more than that. It's not just about the knowledge you get, but rather, the intuition you end up developing about the world and logic in general.
Mathematics at its most basic level is abstracted from the study of logical structure and axioms. While most people are "logical", a mathematician inevitably develops the skill of automatically thinking about the subtle differences of objects and their properties, at a far more rigorous level than a person in any other field. A mathematician learns concepts that nobody in any other technical field ever gets exposed to; concepts which are universally applicable to pretty much everything in existence.
One thing I came to learn that nobody really talks about is that learning mathematics to a high/abstract level inevitably makes it far easier to learn pretty much any other technical field. Not only will the mathematical concepts in less technical fields be far easier to comprehend, but the mathematician will be able to recognize abstract features of topics in those fields that someone who specializes in the field may have never even thought about.
In short, while mathematics can be challenging, it is by far the most rewarding and universally applicable field a person can really study in my opinion, although this usually isn't obvious to people when first introduced to things like algebra and calculus. Another way to think about this is to consider that much of higher level mathematics involves the study of very abstract concepts and structures - and then ask yourself: What is the point of "abstracting" anything? The entire philosophy of abstraction is about making things easier, simpler, better, and so on. Such philosophy of abstraction is what we owe our entire civilization to.
But again, I wouldn't suggest someone jumping into pure mathematics if it is not something they are truly passionate about. However you define "passion" in that regard is up to you - people are passionate about different topics for different personal reasons.

The other answers are focusing on "should I go into mathematics as a career?", but no-one has answered your first question, about what to do with your research results. There are related questions (with answers) on this site:

Is it possible for a high school student with no academic qualifications to publish a research paper?
What to do with research results while being in high school?

Your particular question about "how do I know if my work is novel {without established connections to university-level mathematicians)?" has not previously been answered, as far as I can tell.

in addition to ArXiv, you should search for published papers (ArXiv is only for preprints, and only a subset of papers are posted as preprints before publication).

mathscinet is probably the best index for math papers, but most access is through universities; I don't see an easy way to get access as a high school student (you could check into the London Mathematical Society, but membership ordinarily starts with undergraduates and isn't cheap).
Google Scholar is second-best, but has the distinct advantage of being free (it will find papers published in journals as well as on preprint servers like ArXiv: if you have trouble getting access to the text of papers you find, you could take a look at this question ...
someone suggested MathOverflow; I don't know whether that site (or Mathematics Stack Exchange) is an appropriate venue for this kind of question, but you can browse the questions & answers and read the information on those sites about what kinds of questions are appropriate. (If you find answers there you might not need the rest of my answer below ...)

if you find papers that contain exactly your results, you're done (for now), although you can and should pat yourself on the back for discovering a non-trivial mathematical result

if you don't find your result already published, look for papers that are closely related to your topic, and note their authors/e-mails (a contact e-mail is always listed in a published paper; it's also typically easy to find academics' e-mail addresses via web search).
Provided that your maths teachers have looked over your work and think it's good, I would say it would then be OK to write a polite letter to one or two academic mathematical researchers who you have identified as likely having the expertise to evaluate your results and ask them what they think. (Do be polite (proper salutation etc.), and keep your e-mail short; state your results briefly and attach a slightly longer description that they can read if they want.)
It is probably a good idea to write your idea up as completely as you can, in a format as close to a publication as possible (e.g.  in LaTeX); this will make it easier for researchers to read (and they're more likely to take it seriously in the first place), and is the first step toward publication (and good practice!) anyway.

Some addition to the other answers, related to your questions although maybe going a bit off track as I think this may be of interest to you:
(1) There are probably more jobs in which there is some math research besides other things, particularly in academia, like professors, university assistents etc. These involve math teaching, examining, and also administrative tasks. Even people whose job is to be a math researcher in the first place will have to do administrative tasks, apply for research money, write project suggestions and sit on the occasional committee. Also some companies employ researchers who then often work on projects, in groups, that are defined by the companies. Very often this is interdisciplinary and the mathematician collaborates (and actually competes for the positions) with people from, for example, computer science or biostatistics.
(2) Studying mathematics opens many possible career paths for you, and it can't hurt to have an open minded attitude to possible opportunities. There is much work to be done in physics and engineering, artificial intelligence, statistics that requires mathematical competence and often also mathematical research. Quite a bit of the research can be connected to computer simulation. If you focus on being a "pure mathematics researcher", there may not be that broad an offering of positions later (many pure researcher positions are fixed term and people are expected to use them to qualify for a professorship or another position that comes with some additional duties), however the overall spectrum of jobs in which mathematics research is done is very wide, and you may even find out that you love some of the other options as much as pure mathematics research. (I love teaching and statistics for example, so I became a statistics professor - I do a lot of things other than doing proper mathematical research, but at times I do that as well.)
(3) One can easily say you need to be very good, as in pretty much every job that is sophisticated enough. However you have to find out for yourself whether you are up for it and studying and doing a PhD in math is a good way of doing that. The positive thing is that at the point at which you may decide that a pure mathematics researcher career is not for you for whatever reason, chances are that you have lots of other options, many of them related.
(4) Regarding the third question, the "pressure to discover something new" looks very different from "outside the system" than from being in it, at, say PhD stage or higher. At some point when you have a good overview of a field, you will usually see a number of things that can be done with pretty low risk, i.e., you can address certain question of which you know that you have the necessary tools to solve them and chances are that they are not done yet. There may be competition, but very often different people can get a slightly different spin on things so that what looks pretty similar to something else can still be sold as "new". Obviously this is not what most people imagine to be exciting research, and at a sufficiently high level things certainly don't work like this, however there are many researchers who do research that is useful and to some extent new, and can even be some fun, without saying that they discover big new things.

Thank you for the answer, it's quite thought-provoking. I am just wondering, why is there suddenly activity on my question again now? I've had a couple of upvotes, one comment and one answer (yours) so far today/yesterday.


text:
How to avoid aiding academic misconduct when tutoring online
I have started teaching online recently. Sometimes I am asked not only to teach, but also to actively help in a particular project. If it was a paper, I would ask be included in the list of authors, or at least acknowledged.
How should I approach this issue if the material which is produced is a Masters' thesis for example? I have no concern about teaching some material which can be used by students to advance their thesis, but advising them on how to write the thesis itself seems different.
Is it ok if I ask them to write an acknowledgement where they specify that I have made some contributions to the work, or this situation cannot be saved such a way? I am hoping to be able to be involved ethically in such a project because it helps with my finances but I have ethical boundaries.

My suggestion is to ask the client if they are comfortable with you asking their advisor for guidance, which of course makes your participation visible. If they won't do that, then I'd guess that they want to use you improperly.
But, if they are willing to keep the advisor in the loop then it also allows for each case to be handled individually and in the open. One size may not fit all here.
If they won't do this, then you might consider either dropping them or, alternatively, sticking close to what is more obviously acceptable.


text:
How much money is spent on students' above their tuition fees in the UK?
It is well known at the university which I went to (Cambridge), that way more money is spent on each student than the home-tier tutition fee (it is partly payed for by the exorbitant cost of international fees, and the student loans of home students are payed by the taxpayer).
UK-wide, how much money is spent on average on university students?
This question was inspired by some of the answers to this question: Why are online lecture notes usually not accessible to non-students?

"the student loans of home students are paid by the taxpayer" - this is not universally true at all - people pay off their loans. I paid mine off. Even when they don't fully pay them off, I would bet a reasonable portion pay off the principal. Sure, it depends on a variety of financial factors as to whether it's worth paying off, but the number of students for which it's beneficial to pay the loan off is non-zero.

At the time of studying, I think this is true for the overwhelming majority of students. Yes, you might pay it off later, but when you are at uni, you are essentially always paid for by the taxpayer.

@AdamWilliams I don't think this is true, especially since the rise in tuition fees. The monthly interest on my loan is practically the same as the minimum repayment for my income, so if I remain on roughly the same salary for the next few years I will never pay it off. I believe there is even talk of scrapping the system because it's clear that repayments are only going to continue falling.

I don't think Cambridge is a good comparitor. Its long been the case that educations at Cambridge (and Oxford) is considerably more expensive to provide than that at any other university, due the large amounts of teaching delivered through small group superivisions/tutorials. When I went (20 years ago), this was recognised via the seperate "college-fee" that the college recieves  per student (from the student's home local education authority I believe) on top of the standard tuition fee that the university receives, I don't know if this still applies, but it was unique to cambridge/oxford.

Also, tax payers don't pay, because the government doesn't provide the loans out of taxation, but in turn borrows the money it then lends on to students. It is more correct to say that it increases goverment borrowing, than to say that tax payers pay the costs. The arguement has been about how to account for that borrowing. Until the ONS's ruling, borrowing for student loans didn't count towards the Public Sector Net Borrowing, because the borrowing was offset against the asset value of "owning" the loan, now it does, but still only partially.

Thank you for these clarifications!

@DanielHatton Interesting. Back when I was a student Oxbridge got considerably more income per student than other universities. Seems that is no longer the case. I wonder how they make up the difference? I doubt its from research grants, because these are paid to departments, but teaching is done through colleges.


text:
Should I include details about extracurricular art projects on a grad program application?
I'm in the process of applying to graduate programs in a field unrelated to music. I write, record, and perform original music in my free time. Normally I would not mention this in a personal statement; however, one of the programs I am applying to has an additional statement where I am to discuss ways in which I would add to the diversity of the school. I do have material I hope to discuss that falls within normal parameters of relevance, but I am wondering if it would also be appropriate (or rather, not obviously inappropriate) to mention my creative projects? I would obviously attempt to mention them in a way that demonstrates personality traits about me (creativity and drive), rather than just an irrelevant aside.
Any help would be appreciated. Please let me know if there's any additional info I can provide.

Normally I'd vote to close as being off-topic due to the question being heavily dependent on personal circumstances/a university's policies, but I think that at the heart of this is a good question about using extracurriculars in general on grad applications. +1.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


text:
Refusing the postdoc offer (email acceptance of the offer only)
I have a classical situation, but as it is the first in my live, I would like to know: if it is acceptable to refuse a postdoctoral offer. The contract is not signed, the paperwork are going to start, my official commitment was 'Yes, I am taking your offer' by email).
The reason is having an up-to-the-minute offer from the other University, which I like more. That offer however is agreed only by email, no papers are prepared.
Thank you for any tips.

Officially, you're always allowed to walk out. Particularly before signing any papers. Just make sure you let everyone know as soon as possible to avoid creating expectations and preparations.
Now, you're probably asking whether your peers will be happy if you walk out. Usually they will not appreciate anyone dropping a postdoctoral offer. If you understand exactly why they're pushy about you taking the offer, you will be in a better position to take this decision.
Don't worry about making others happy. Do what you must.
Good luck!

I'm not sure that this is the correct answer everywhere. Laws on what constitutes a contract vary widely around the world. I doubt that the university would press the issue, but if they do, you need to be aware of what the possible consequences might be. In the old days, a simple handshake could constitute a contract even before anything was signed.

@Buffy An informal offer/acceptance is surely just that? Such offers/acceptances are based on incomplete information, e.g., in the absence of a formal employment contract. As such, either party can surely withdrawal. That said, perhaps there exists a jurisdiction where that isn't true...

Agreed. Though I find the email informal exchange unlikely to hold a postdoctoral agreement in Academia. Still, some particularly pushy professor seeking to retaliate might resort to just about anything.


text:
Is it appropriate to include a List/Summary of Theorems in a paper?
I am 16 years old at the time of writing (so I have no supervisors to seek advice from), and I'm working on a Mathematics paper at the moment, which I plan on submitting to a journal for publication. In the paper I have about 9 lemmas and theorems in total; they are all just formulaic (by formulaic, I mean that they are all just formulae rather than an idea or property about something, eg for argument's sake the quadratic or cubic formula).
Is it a good idea for me to include a list/summary of lemmas and theorems in the paper after my introduction, or should I simply include a couple of the main results in the introduction and not bother with a list of formulae I establish?
It just seems to me that to see all of the results without a summary near the beginning would be quite hard; you'd have to scroll down many pages.
Thank you for your advice.

@dodd In the abstract shouldn't I just give a very brief overview of what I do in the paper, rather than listing the actual formulae?

Take a look at some existing papers in your area, and see what they look like.

What are you planning to do with the paper? And what do you mean about the theorems and lemmas being formulaic?

@DanRomik I am planning on submitting it to a journal, for publication. About them being 'formulaic', I guess that isn't a proper term, sorry- I mean that they aren't ideas or properties of something, but rather they'reformulae eg for argument's sake something like the quadratic formula. I have now edited my question to clarify this.

@dodd thank you very much for this clarification!

What is most appropriate and would give your paper the best chance of being taken seriously by the research community, is if it conforms to the writing conventions of the field.
The writing conventions of the field do not include having a list of theorems. Therefore, I’d advise you not to include such a list.
Good luck with the paper!

Thank you for the advice and good wishes! :)

If the lemmas and theorems are unrelated (unlikely) then a list might be fine. But if the purpose of the paper is to prove the main theorem(s) then giving that purpose and naming just those in the introduction is probably more standard and easier for a reader to get a sense of purpose.
So, my guess is that your second suggestion works better. If there is one main theorem then focus, primarily, on that. But if one or two of the others has some independent use then you could expand a bit.
Mathematicians are used to following a train of proof through a fairly long argument, but knowing the goal ahead of time can be helpful.


text:
Is there a consensus on how long you should know a person before you ask him/ her to write you a recommendation letter for graduate school?
I was wondering if, in general, the length of time you have spent with your professor/ superior has a great impact on your application.

Could you please clarify what length of time you have in mind?

What I personally have done is that if I get an A+/A/A- with his course I would reach out to him for a recommendation letter. This might not be the case for several Professors (it is a case by case basis), but in general this works. I also would ask for recommendations for Professor's that I have done research projects with.

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


text:
Different results according to the method use
I am preparing a rebuttal letter to reviewers and the editor about one of my manuscripts. The reviewers were concerned about the results and they suggest running the same models but using another way to calculate the response variable. I am totally fine to explore the data with other ways to make results more robust and reliable. However, the results from the methodology suggested by the reviewers are not the same as the other one. This makes me feel dubious about the conclusion drawn from my results.
Although in the first version of the manuscript I had a sharp conclusion based on the initial results, now I realized that I should tone down the message after exploring the data in different ways.
I was wondering if you had a similar experience like this and how did you manage to your rebuttal letter?

I think this needs a deeper look to analyze what you should take from this: what does it mean that the results are "not the same"? p<0.05 one way and p>0.05 another way? What happens to relevant confidence intervals: are they consistent? What is the interpretation of the differences in analysis approach? What are the implications for type I/II errors when using multiple statistical approaches?

It seems like a case in which the reviewers made good suggestions which made you go over your data and conclusions again, thereby improving your manuscript and saving you from making too bold claims. Therefore, the obvious approach is to thank the reviewers for their input and explain to the editor how your analysis and conclusions have changed/improved in the revised version of the manuscript by following the reviewers' advice. The way you explain it, your previous conclusions were not totally wrong. If so, you have no real reason to be overly worried just now. Focus on explaining your revisions to convince the editor that your manuscript is fit for publication.

Thanks @Snijderfrey for the answer! Yep, I actually cannot hide from the suggestions of the reviewers since they are totally fair. It makes sense to not overstate my conclusions after re-analyzing my data. Thanks again!

I think you are jumping the gun by thinking about the rebuttal letter. Your first priority here should be thinking about how these new results affect your paper and its conclusions. Rewrite your paper as needed, maybe even run further additional tests to confirm your new conclusions.
Now that you have written a better paper, writing a response to the reviewers (thinking about this as a "rebuttal" is already a wrong antagonistic mindset) is easy. Simply describe what you have done with the reviewers'  suggestions and how this has improved your paper.

Thanks @TimRias for the advice! Will take into account


text:
Is it possible to hire a phd student or postdoc by hours?
I am working on small projects in machine learning field at my spare time. I love to research on the main ideas and concepts. However, I won't have much time on implementing it. Since the field requires special abilities, I feel it would be better to hire a phd student or postdoc.
When I search online, even part-time postdoc jobs offer around 50k annually. Since my projects are not that big and I do not have much money, would it be possible to hire a phd or postdoc by working hours for the projects ?

part-time postdoc jobs offer around 50k annually In which country? For how many hours?

The last part of the question is a shopping question asking for recommendations, and those are not received very well here. Removing the last paragraph would improve the question.

Thanks! :) any idea about where might be suitable for the last part of the question ? Oops ! Sorry~Is this another shopping question?

Universities hire hourly employees and contractors all the time.  If you are not hiring using university funds, your question is off-topic.

Do you have to use university funds to hire freelancers ? Would it be possible that one hires those collaborators(e.g. Phd students, Postdocs) as freelancers without using university funds and listed them co-authors if there is any publication ?

50k in which currency???

@Sweetie AnonymousPhysicist's point is that if you aren't a university and asking how to hire people, you're talking about something outside of academia. You could maybe ask about restrictions that academics would face while doing outside work, but "how do I hire someone?" in a non-academic context isn't on topic.

would it be possible to hire a phd or postdoc by working hours for the projects ?

Yes, but, can you afford one? You've highlighted the cost of a part-time postdoc [at] around 50k annually and noted [you] do not have much money.

does anyone have rough idea about the price range/hour?

Compute the hourly postdoc rate (from the above salary) and multiply it by some factor (probably greater than two). (The hourly rate is non-trivial to compute, given that many postdocs work more than their contractual hours.)

If the work isn't going to lead to a publication then most people are going to want a lot of money.

@StrongBad That's why multiply [hourly postdoc rate] by some factor (probably greater than two)


text:
If this is my second Visiting Assistant Professor job, who should I ask for letters?
I'm just looking ahead, but I intend to get 1 letter from my current department chair but am not sure beyond that. Should I include a letter from my graduate advisor no matter what? Should I get a letter from my last job as well (1 from current school, 1 from previous school, 1 from grad school) or 2 from my current one? Or where else should I look?

What kind of a position are you applying for?  Is it focused more on teaching (in which case reference letters from the two institutions where you have taught will be critical) or research (in which case a letter from your advisor will be critical) or some mixture (in which case you'll probably want both.)

@BrianBorchers this would form a good answer ;-)

The best choice depends on the schools you have worked for, what you did there, and where you will apply.  If I were hiring, I would look for the job you didn't get a letter from.  Then I would contact that employer to find out what they think.

I'd probably be looking for a more teaching focused institution, but those positions seem to be less frequent so I suppose I might need a research based letter as well?