text:
Should I reply to a university admission offer email?
I got an admission offer email from one of the universities that I've applied to for a graduate course. It seems to be from a departmental email ID and has generic content with my name and address filled in. It also contains details about next steps, documents, deadlines, etc.
Am I expected to reply to this email? Since I am waiting for other universities' decisions, how do I send a neutral reply to this one?
Thanks!

Unless you have specific questions or the email explicitly asks for a response, the answer is likely no.

It is an automatically generated email with no personally written text?

@Drecate - Makes sense.

@daniel.neumann - Yep, templated email.

It isn't necessary to reply to an offer of admission until you decide whether you will accept.
If you feel you must reply, you can simply say something like "Thank you for letting me know.  I will be sure to let you know my decision before the deadline."

To follow up with this approach, I have 3-4 months to make a decision. So that late of a reply won't seem awkward, right?

@shadow: No.  Nobody is expecting a reply until you have made a decision.


text:
Hypotheses that cannot be sufficiently tested
My understanding is that a hypothesis is not scientific unless there is a way to sufficiently test it.
Is it ever acceptable to present a hypothesis that cannot be sufficiently tested?
I can imagine a situation where one has a hypothesis (A) that can be sufficiently tested via available research methods (e.g. a questionnaire) and another (B) that can only be sufficiently tested via other research methods that you do not have the resources to conduct (e.g. face-to-face interviews).
Would it be acceptable to partially test for hypothesis B and collect some preliminary data for it in this fictitious questionnaire, despite knowing that this would be an imperfect test? But then, if the testing method is imperfect, would this truly be considered a hypothesis or something else?

You mean like the Riemann hypothesis?

@NicoleHamilton No, I'm talking about far more down-to-earth hypotheses that one cannot test sufficiently given the resources (time, money etc.) that are available but which one can nevertheless collect_ some_ data on.

Please don't forget to change your title from "fully tested" to "sufficiently tested".

@scaaahu Good point - have just corrected that.

It sounds less like you're offering an hypothesis and more like you're posing a possibly interesting question and an inexpensive way to decide whether it'd be worthwhile to investigate further, which sounds pretty reasonable to me, depending on your audience.  Apologies for poking fun.  Also, you might revise "this fictitious questionnaire" to be simply "a questionnaire".  If you do it, there's nothing fictitious about it.

Thanks for your comment @NicoleHamilton, it's helped clarify this.

Acceptable to whom? Obviously every hypothesis could be tested more thoroughly - there is no "perfect" test. A hypothesis does not need a magic amount of support before it becomes a hypothesis (however, a peer reviewer may evidently argue that your results are not yet strong enough for publication).

@NicoleHamilton One question: where do you draw the line between 'posing a possibly interesting question and an inexpensive way to decide whether it'd be worthwhile to investigate further' and a hypothesis? When does the former become the latter? I would grateful to hear your thoughts on this.

@xLeitix assume that this is not for journal peer review, just grad school level.

As scientists, we seek the truth, not simply to confirm our own biases.  If you honestly can't know  if something is true without extensive testing, your position as a scientist should be that you don't know, not that you think you could prove your opinion given enough money.  To be a hypothesis, there has to be already be some evidence to suggest there might be a relationship, exactly the kind of evidence you might collect with your questionnaire.  Right now, it sounds like you're in the "I wonder if there's a relationship" stage, not "here's what I think the relationship is".

@NicoleHamilton I would upvote you if I could. Great comment.

@NicoleHamilton: I would be extremely cautious when using the term "truth" in a scientific context. Science is not, and cannot be concerned with ontological truth. The truth that we as scientists can only ever discern is what one might call "technical truth", meaning a statement, or set of statements, is true within the set of axioms and theorems that constitute a model. We can also ask, and test, how close our models match reality as we experience it. Whether or not our models bear any relationship whatsoever with reality as it is is a different, and I would argue non-scientific question.

You know, as I struggled for a word, I wondered if someone would nitpick me for it.

Bose-Einstein condensation was predicted in 1924 and only actually seen in 1995.
Gravitational waves were predicted by Einstein in 1916. It was proved that they followed from general relativity in 1958. They were observed indirectly in 1974, and observed directly in 2015.
If "science" had been restricted to hypotheses which could be tested in the near future with available methods, then these predictions would not have been considered science, and it would have set physics back by decades.
I would agree that hypotheses which cannot be tested in principle are unscientific.

This question seems to be related to Popper's falsifiability criterion. Note, however, that the question there is (certainly for Popper, anyway) whether a hypothesis can be tested in principle. Whether or not you have in fact the means to perform such a test is immaterial.

In statistical terms, you cannot partially test a hypothesis, you either test it or not. Also, there is no such thing as a "perfect" test.

You are right. I should have been clearer. In my example, I'm still testing for hypothesis B, it's just that the data collected is not adequate due to resource limitations.

Inadequate in what respect? If the data collection method is inadequate, then your statistical analysis will be of little or no use.

Given that the OP explicitly mentions qualitative research methods (interviews etc.), I am pretty sure that he does not interpret "hypothesis" in a purely statistical sense. I assume this answer is technically correct and totally useless.

Inadequate in the sense that one is unable to use the most appropriate research method to test it due to resource limitations. You are right to say that this means that statistical analysis will be of little or no use but could one claim that this still has qualitative value insofar as you're getting some data, despite the using a research method that is not ideal? Moreover, would this be considered a 'hypothesis'?

@xLeitix understands my point.

@user5508297 if you are using both quantitative and qualitative methods in one study, then you are adopting a mixed-methods research paradigm and it usually adopts another type of research design and terminology than what you have described here. I suggest you take a look at it, it will likely help you in your research.

I believe the standard term for what you are talking about would be "preliminary results," and there is indeed a good place for work of this sort in the scientific literature.
The test for whether something is publishable is not whether it conforms to the idealized scientific method.  The test is instead whether it makes a meaningful contribution to the pursuit of knowledge.  For work that can be (usually retrospectively) fit onto the idealized scientific method, this test is fairly easy to pass.
There is also, however, a place for many various types of preliminary work, such as:

clearly formulating a problem and explaining why it is interesting or important to solve
developing a method for attacking an unsolved problem of interest
reporting a study that shows suggestive results, even though these are not definitive, this helping to motivate a more conclusive study.

All of these can be valuable in a number of ways, and all of them demonstrate incremental progress towards one's goal.  The question of whether a particular such piece of work is publishable then boils down to whether the partial result is significant enough to attract interest in the venue in which one proposes to present it.
For this reason, "preliminary" work is less likely to get published in a field's top venues (though it most certainly can be, if enough people care about the problem)---the bigger the problem, the more that people will likely be interested in chipping away it little fragments of it (for example, think about all the preliminary work published on hunting the Higgs boson or chasing P=NP).
There are generally also more informal venus like workshops, symposia, etc., which are quite well suited for discussion of preliminary work.
In short: if you think the partial results are interesting, then it's entirely reasonable to try to present them in the appropriate context.

source: Stack Exchange

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

sort: votes


text:
HR will get back ASAP
A week after the submission of my CV for an academic position, a person from the HR department answered me:
"Thank you very much for your application and your interest […] We are currently screening all incoming applications and will get back to you as soon as possible."
The position will be open for more than one candidate, and the application deadline is it within one month. Based on your experience, does this answer actually means that I'll have to wait and hope, or does it mean that they are considering other candidates first?

The email only indicates that you submitted an application.  There is no other meaning.

The fact that I submitted it is self-evident from the fact that I sent an explicit e-mail in the first place. From other people's experience (mine included), in some cases it might happen that the receiver never provides feedback/replies. But, in that case, it doesn't necessairly mean that they haven't received it.

The fact that you submitted it is self-evident to you, but the fact that they received it is not. I would suggest that @AnonymousPhysicist is nearly right, and the only meaning to this message is that HR have received your application ;-)

I'm just a novice, and in some cases online I found conflicting opinions. I was seeking a (somehow) more authoritative opinions rather than some random website's nonesense :)

@Flyto If we want to be technical, then it means an HR computer received the application.   The message may be automated.

@AnonymousPhysicist heh, true! But The distinction I made is a meaningful one, because emails can get lost in spam traps, and emails with attachments such as CVs are more prone to going missing than those without. Having an acknowledgement, automated or otherwise, is helpful

You have to wait for the closure date to be reached.
Others have the right to apply until that time, just because you applied early won’t give you an early result.
Once it has been closed then you will receive a reply, but that delay is not certain either - might be a week or two... or longer, you have to be patient.
If you have not received a reply after 2 weeks you might consider politely asking for an update.

They’re probably going over several candidates, I would wait and see. I’d imagine you received a template response to your application.

I sent this application via e-mail (generic HR email) and then I got the reply from a different address (person name and surname), so I sense it was a human reply. For other applications, I filled an online form, that provided me an immediate automated reply.

Template does not necessarily mean non-human. I mean that you got the same email as a bunch of others

This email means that HR have received your application. It is purely an acknowledgement, and you should not read anything else into it.
(You should, however, be pleased to get this acknowledgement, as many institutions don't respond at all unless somebody passes the first round)

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


text:
How to work on a joint math paper effectively?
Now, I am working on a joint paper with some collaborators. The research is about mathematics.
This is my first experience of working in collaboration.
Another author has sent a manuscript about our work. The manuscript is about 40 pages. When I checked some part of the manuscript, it takes a lot of time to read the content and unfortunately, there are a lot of gaps and mathematical mistakes in it.
In addition, there are also many typos buried inside the manuscript.
Although, I can fix some part and adding some details and proof, I still do not understand about 50% of the manuscript.
I have to mention that we can communicate via email only.
The following are my questions:

How do you manage to work collaboratively in research?
How do you detect the mistake and fixing it quickly?
When should we keep trying to understand and fixing the argument or rather asking the explanation directly to the collaborators? Is 4 days-checking without asking question too short?
How to judge``grey part", like simpler proof, simplified definition, notation, sentences, etc?

Thank you for your advice.

Welcome to the site! Actually, this is three questions in one and as such not well suited for this site. I recommend that you take some time to explore the site (if you haven't done so) as there are several questions here already that address several aspects of you question, e.g. Q1. Q2 seems very specific your particular situation, and would probably not be a good fit here. Also Q3 does not strike me as a good fit as there is no universal answer here and an answer would very much depend on the situation. I do not understand Q4.

@Dirk Could you give me the link of several questions here already that address several aspects of my question?

Sure: http://academia.stackexchange.com/questions/71547/collaborating-online-with-researchers-from-other-institutes-countries, already a duplicate of http://academia.stackexchange.com/questions/6035/how-do-researchers-from-different-institutions-get-to-know-each-other-to-begin-a and (but this is somehow different). Also http://academia.stackexchange.com/questions/40881/how-to-integrate-partial-version-control-data-exchange-and-research-assistants is relevant.

As mentioned before, by other answerers, there is no way to answer this question accurately - it is a matter of taste, and the preference of  who you are working with. The best suggestion I think I can give is to use Overleaf
You need to work collaboratively on maths - Overleaf uses LaTex as its back-end, and allows real-time collaboration. Google docs also allows realtime collaboration, but you will likely suffer from formatting issues. Change control is done with git, which means you can also work offline and use git for conflict resolution in the content. You can use either the gui or the command line.
The rest of the questions (2-4) are purely issues of this particular paper, and thus impossible to answer definitively.

Unless there's some special reason to fear that your responses will bother the collaborator, you should make one pass through the paper for mistakes with English, one pass through to fix and clarify math things where you can already see what's wrong and how to fix it (for these first two steps, you are working in Track Changes), and one pass through writing Comments in the side margin, asking the collaborator to clarify or rework things.  At this first stage, your comments can be brief, and you need not address every single flaw or unclear bit.  Towards the end you can make more of an effort to make sure you didn't miss any problems.
Write down your responses to a draft.  Take a break to do something else.  Come back and proofread your responses.  Send.  In other words, do proofread your response, but only once -- don't agonize.

This seems to presuppose that Word is used for typesetting; Latex (and the like) is much more commonly used in mathematics. Though perhaps there is some markup/comments facility for Latex that I'm not familiar with.

@ShaneORourke - Yes, I was using MS Word as an example, to give the OP an idea of a sequence of steps with some structure to reduce the going-around-and-around or agonizing I was getting from item 3.

For specific software recommendations, there is a special stackexchange site: http://softwarerecs.stackexchange.com/

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


text:
What is the best way to deal with cranks?
Imagine you are minding your own business when you receive an email from someone who claims to have discovered the Answer to the Ultimate Question of Life, the Universe, and Everything. He provides some "details" about his theory, then says he wants to meet you and / or arrange a time for a phone conservation to discuss it. What should you do?
The only thing I've seen is this 1983 article by Underwood Dudley about what to do when the trisector comes. Dudley says not to examine the trisector's proof, and also not to direct the trisector to the proof that trisection is impossible. Instead one should send computer-generated results showing that the trisection is imperfect. Problem with this is that it only works for questions that can be attacked by computers - there was a recent question here on Academia SE challenging conservation of angular momentum which this won't work for.
What are some general guidelines for dealing with these situations?
Edit: ignoring an email is easy, but what if the crank calls or visits in person?

http://insti.physics.sunysb.edu/~siegel/quack.html

Related 1 Related 2.  Additionally, an approach I remember seeing somewhere, but couldn't find: When sent a proof by a crank, the professor would send them a previously received crackpot proof, and state that they would go over the new crank's work if and only if the crank could find at least one of the errors in the other one.

I really like this article, which could be seen as a modern follow up to Dudly (and also one that is focused more on physics than on math): https://aeon.co/ideas/what-i-learned-as-a-hired-consultant-for-autodidact-physicists

Comments are not for extended discussion; this conversation has been moved to chat. Please do not use comments to answer the question.

The answer is 42....

This happens far less frequently than inappropriate requests for postdocs that have absolutely nothing to do with your area, invitations to participate in conferences that have nothing to do with you, invitations to serve as section editor on predatory journals, .....
Handle them all the same.  Use your delete button.
A call or visit is harder to deal with.  A polite "... very interesting, but I don't have the time to follow up on this"  might get you off the hook.  If the person shows up at your door more than once, I recommend calling security.

I agree with most of this; however, calling security on a person merely for visiting multiple times seems like an unreasonable escalation to me, especially if you have never previously escalated beyond the polite on previous visits.

@Ben  First visit: I don't have time.  Second visit: I don't have time, you are interfering with my work.  Third visit: "Hello security?  Please come to my office."

I wouldn't call security to ask them to remove the person.  I'd call them after the second visit to say "I may be in a situation".  I have no way of knowing if the crank is a known problem to them or not.  That's their job.

Ignore the crank.
Unless you are in some location where you are required by law to respond to communications (I remember reading here about one country where it was indeed the case that it was required to answer emails as part of "open records" laws), you are under no obligation to waste your time on a crank's musings.
If it amuses you to respond, feel free to do so, but you waste your time at your own peril!

@Roland, perhaps you could clarify whether the legal obligation is satisfied by a reply which states simply "Your correspondence has been received and noted."

There are expectations to make citizens feel heard and taken seriously.

The last line seems incomplete without some reference to James Veitch, so I hereby add that. For more entertaining details, search YouTube or TED.com.

"There are expectations to make citizens feel heard and taken seriously" Then invest in some "random answer generator". Even the first attempt (the famous ELIZA) was good enough to make people feel like there is somebody really caring about them at last, and now there are much more sophisticated versions. I have never seen a human who would be more patient and sympathetic with random complaints than a machine :lol:

@fedja: That's actually pretty interesting; an AI-powered crank email responder honeypot. Wow!

I honestly would like every governmental university (or research institute) to answer such questions in some way. Many of these questions are genuine. It is sad that most academics talk so bad about "cranks" which are just so unfornate to not have collage educatoon and do thus not understand the rules of academia.

Follow the peer-review model with some tweaks:
If the work is clearly flawed and so off the mark that nothing can come out of it, ignore. [Desk reject]
If the work may have some iota of sense, but it isn't worth your time to get into it, write back suggesting a different forum, like a blog post. [Reject and suggest transfer]
If you are marginally interested, but not sure whether it's worth it, ask them to try presenting it better/differently with more proof. [Reject and resubmit]
If you think it deserves a chance, but can't get into it yourself, lightly share with your colleagues/students over the coffee table and if anyone seems interested, let them take it up. Alternatively, as suggested by @jpmc26, you could ask them directly if they would be interested to detect preliminary errors that could be pointed out. Purely voluntary, of course.[Assign reviewers]

Would asking your students to review it for errors or if they're interested in doing so be a reasonable variation on the last one? This might act as a sort of initial smell test.

I read somewhere that a professor dealt with this issue by introducing such cranks to other cranks. "You might want to talk to Bob about your theory, I'll introduce you."

I remember reading about a study where three people, each claiming to be Jesus Christ were set in a room together.  Your answer seems similar in spirit, great idea!

https://en.wikipedia.org/wiki/The_Three_Christs_of_Ypsilanti

I agree with @aeismail that you should try to avoid the crank. That may not be possible though. Underwood Dudley wrote a book "Mathematical Cranks" (an MAA press book) about the subject. He has a chapter (Case Study of a Crank, I think; if not, The Making of a Crank) devoted entirely to a crank he refers to as G. K.. This person happened to be an alum of the school at which I taught. When I assumed the Chair of the Mathematics Department, I began to receive "stuff" from G.K., which I stuck in my files and ignored. My luck ran out one day when he happened to reach me by phone in my office (we did not have caller ID at the time). He asked me what I thought about the things he had been sending and I told him that I thought his ideas were without mathematical merit. He proceeded to call me all sorts of vile things and eventually hung up. I have no idea what he said about me in subsequent writings, and don't really care.
Interestingly enough, he had called my residence some time before this and my teenage daughter fielded the call. She reamed him out about it and invited him never to call my home again, which he never did.
Along the way (cranks can be very persistent) he asked me for a recommendation for the national medal of science or something. I ended up calling the organization for advice on what to do. They asked me who the person was and I told them. The person on the phone laughed and told me to throw the form away.
Among G.K.'s mathematical achievements were the "discovery" of "subzero pi," and the recognition that since $e=mc^2$ we must have $e=m(a^2+b^2)$ via the Pythagorean theorem.
I corresponded with Dudley and George Andrews about my encounters with G.K., which they found quite amusing. Although I found G.K. to be harmless, a colleague of mine in the department, who had been a classmate of G.K., was afraid he would come to school and use his military commando background to harm members of the department who didn't praise his dubious achievements. That didn't happen, but I cannot say I dismissed his concerns completely.

+1 since $e=mc^2$ we must have $e=m(a^2+b^2)$ via the Pythagorean theorem --- This is totally priceless! I must confess to spending more time than I should have 15-20 years ago reading stuff by this guy, especially the diaries he posted on usenet when he made road trips.

@Dave L Renfro - This is the first I have heard of Archimedes Plutonium. I'm going to look into him further. My guy was also a megalomaniac. He had translated the bible into verse, and received some award from the Beaux Arts Society in New York. I recall a piece about him, I think on CNN, after his bible translation. He always insisted that his name be followed by the letters FRM, for being the world's foremost renaissance man. I would mention his name, but I don't want to speak ill of the dead (he died just a few years ago).

@Dave L Renfro - A small edit: the initials were RM. for being America's foremost renaissance man.

I made perhaps a couple of dozen posts around 1999-2002 or so under the name Megalomanious Kryptonium to satirize AP, in which I adopted certain writing mannerisms of AP that regular readers of AP's stuff would immediately recognize, such as one from October 1999 that I reposted at the bottom of this post. Most, if not all, of my Megalomanious Kryptonium posts can be found using this search.

@Dave L Renfro- Thanks, Dave. I'll check them out.

Can you please tell us what $a$ and $b$ stand for? If you don't, I am in great jeopardy of becoming a crank in order to find out.

Oh my. I just spent a few minutes wandering about the internet, reading about G.K. His obituary reads as though he might have written it himself.

@AlecosPapadopoulos, $a$ and $b$ are left as an exercise for the reader.

@shoover - Considering he filled out his application for the national science medal and expected me to just sign and submit, I'm sure he had an obit composed and ready to go.

I knew a very eminent astrophysicist who would receive hundreds of these emails claiming to disprove Einstein and relativity, discovering life on Mars, alien visitations, space mirrors, critiques of the big bang, flat earth, etc.
He would respond in a vaguely positive way, "This is very interesting work, but I don't know the answers to these important points you raise.  Let me point you to someone who can help:"  and give them the email address of another random crank that had previously contacted him.

Don't treat someone as "a crank" to begin with
I'm going to put forward a slightly alternative take on this than the other answers.  While I agree with some of the practical suggestions for a polite dismissal of interest in work that is not fruitful, I think it is a bad idea to begin with the dehumanising premise that a person is "a crank".  People described in this way can more accurately be described as amateur analysts with substantial gaps in their knowledge, which lead them to attempt to solve problems that they are ill-trained for, or use methods they misunderstand.  Sometimes (though not always) this is combined with a skepticism of existing authorities in the field.
I agree with the general view that one should ignore non-meritorious contact, and in most cases a deleted email is the solution.  However, if academics do choose to engage in discussion with amateur analysts of this kind, I think it is incumbent on the academic to show the same kind of basic humanity, decency, patience and politeness that would be used with an undergraduate, grad-student, etc.  If the work at issue is extremely poor, it will not generally be frutiful to wade into its details, though one might outline some basic errors or false premises if that is simple to do.  Irrespective of this, a reasonable thing to do here (if you choose to communicate at all) is to direct the amateur analyst to resources that they can follow to allow them to discover the problems with their method on their own.  If the analyst is operating at a level where those resources are too hard (e.g., they lack sufficient training in a particular field), you might instead recommend courses or books that will give them more training in a particular subject.
One of the things that can be observed about extreme cases of so-called "cranks" is that if they are cut off completely from academic feedback, particularly in the early years, this may lead them to proceed hermetically, and some can work for many years ---or even decades--- developing a long and detailed theory without merit.  I suspect that early cases of hostile or condescending rejections from the academic world (combined with the snarky dehumanising attitude exhibited on forums like this) sometimes leads such people to believe that academia is corrupt and insular, which makes them more inclined to proceed without any effective check on their work.**  I'm not sure if anything can prevent this, but it seems like it might be worthwhile if such people were directed early on to useful learning resources, in a way that grants them some dignity, and some sympathy for the fact that they are trying their best to solve problems with the skills they have at their disposal (not unlike our students).
The final helpful thing in dealing with such cases is to highlight the benefits of blinded peer review as a useful tool for amateur researchers.  We all know that peer review has its problems, but whatever its faults, it is an extremely useful source of assistance in academic writing, particularly for researchers who are inexperienced in publication of work in academic journals.  Use of blinding protocols should put amateur researchers somewhat at ease if they are concerned that academia is an exclusive club that discriminates against outsiders.  Helping such researcher simplify and clarify their work, and present it to the rigours of blinded peer review, is something that could potentially be very valuable for any researcher with the patience to assist.  As professional academics, we are extremely patient with our own students (many of whom are appallingly ignorant) so let's extend that patience and courtesy more broadly.

** And let's be honest; academia sometimes is corrupt and insular.

Yes, indeed. Very good points. :)

Thank you for calling for a bit of empathy.

This is best answer. Before ignoring a "crank", I will first politely suggest some readings. I will start to ignore that "crank" only if he clearly misunderstand all readings I suggested.

Introducing a crank to another crank is always a grand idea. They never have any trouble accurately diagnosing the other one.
In any given field, there are lots of enthusiasts out there in the gen pop that lack the competence (formal training, background, or just the intellect) to play a role at the top professional level. In sports, we have "grass roots" activities - amateurs who are not anywhere near major leagues but still spend their time meaningfully. In art, lots of people paint and sculpt without necessarily believing they are the next Michelangelo. In astronomy, we have the star gazers who can make a real contribution. Birdwatchers - ditto.
But in maths and physics, we somehow do not manage to have a healthy relationship with a broader population of enthusiasts, and in the final analysis we must admit that this is unfortunate.
Very rarely I come across an enthusiast who is at least vaguely aware that he (almost always a he) is but a dabbler and willing to admit that he has probably made a mistake or two. Such an enthusiast is not a true crank, by Dudley's criterion that a crank is someone who will not consult (this also applies to academics, at times!). But most will not be told, and simply cannot be told, because of the Dunning-Kruger effect (often aggravated by some sort of paranoid-megalomaniac resentment that eerily surfaces before too long in almost all conversations).
Before the internet, cranks would utilise purple ink and mimeograph and mass mail and complain about being ignored. These days, they can put their stuff out there and stand a good chance that a professional (often a young one) will bite and patiently explain that, e.g. limits just don't work the way the crank believes they do.

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


text:
Can't shake doubts about quality of research, but want to continue
I'm late in my PhD career, and I recently switched advisors. I'm having major doubts about my work and my choices seem to be: stay on this project or drop out. I'm looking for advice from people who were in similar situations. Sorry for the long posts, PhD complaint posts are probably always long. :-)
I was given a project: read paper "A" and followup paper "B" and figure out how to follow up with "C". While Paper A initially caught my eye as interesting and promising, I now seem inevitably led to the conclusion its logic is basically bogus. It was a real emotional hit when I began to see that -- if Paper A were plausible, my life would be a lot easier right now.
I have mentioned my skepticism to others who have familiarity with Paper A. They say that I am right to have doubts, that the paper is not great and there are flaws, but they still think the general idea is true. I feel like I am not being heard -- if they understood me, they would see that I am saying that the general idea is probably not true.
A relevant fact I should mention here is this: all the people I've talked to so far who have read Paper A participated in publishing Paper B. I am not so naive, and I suspect perhaps cognitive dissonance is at play here.
My SO suggested I briefly write down my doubts and the reasons for them, plus potential other directions for research, and bringing them to my committee. I think this is a good idea.
I will just leave these things here:

My doubts aren't being heard. My advisor said, "You can do this project, or you can find another advisor." I mentioned this to a member on my committee, ready to quit. They said, "Don't worry about that, it's not true and it's just a misguided way of trying to motivate you."
My advisor's techniques seem really outdated. I am trying to show him recent papers which have amazing results we could build on. He both hasn't read them and doubts their methods. How both can be true I'm not sure.

This list was going to be longer but it is painful to write. I am hoping someone can tell me: "look, man, there is a way to solve this", but I think I know what kind of answers I'm going to get.
What sucks is this: I feel like I was made to do good research. I see myself as methodical, precise, skeptical, and a highly motivated problem solver. I have good relationships with my peers, and I'm pretty respectful of others. And I keep ending up with advisors who seem like they don't really give a damn about anything except publishing. Help please.

Have you written down your doubts and reasons for them and show it to your advisor?

”You can do this project, or you can find another advisor." — I recommend the latter.

If I have understood your question correctly, you are doubting that the methods used in Paper A (and followed in Paper B) are "correct." The question of whether or not Paper A's methods are "good enough" to get the "right" answer to this problem is an empirical one you can investigate.
You should consider proposing and writing a paper where you look at a similar problem as Paper A with two methodologies and see if there are different results. You could do what your advisor wants and also solve the problem a different way and compare. This would be a valuable contribution and would make your point for you (or not).
You could do this while also starting Paper C to make your advisor happy. You may also consider publishing Paper C with a simple method as a "first pass" and including caveats about the method and how it may be affecting the results. Then when you get the results to the comparison paper it will become obvious if Paper C also needs to use the new method, and you could publish a follow-up paper (or add to Paper C if it is not yet submitted).


text:
Advice for thinking about whether to pursue a PhD
I've included lots of context because I thought it may be useful. If it's too much to read, I've marked the important parts of the question.
I graduated from college last May with a degree in Computer Science and Math and just recently turned 23. I'm in San Francisco now working in tech. The money is nice but I've found it's not quite the life I want. Over the past 7 months, I've developed a near insatiable taste for curiosity that I had never seriously indulged in the past (I was naively focused on getting a lucrative job that might be a stepping stone to maximizing my wealth and "success", not learning for curiosity's sake). I've learned some Statistical Mechanics, Bayesian Statistics, Topology, Logic, Information Theory, Social Psychology, and the list goes on.
I think this part of me came out partly because I feel disillusioned with tech and partly because I feel free from the college->job market rat race and can pursue what I am genuinely interested in.
Important 1 Start
I'm considering switching to a PhD track for 2 reasons:
1) So I can better shape my life by what I'm passionate about. It's frustrating to work knowing that I would rather be learning something else.
2) In learning more I've discovered how little I really know. This smallness not only humbles me but also motivates me to learn more and use what I learn to reshape my worldview. I feel particularly lonely with this feeling and know very few people in my social circle who relate. While I'm aware there may be other social circles that I could join with more people who feel this way, I expect students pursuing PhDs and professors share this feeling as well as they've surely learned more than me.
I am considering a PhD track because it seems like it may satisfy both of the issues I described above.
Important 1 End
I'm setting my potential start age of a PhD to 25 because I want to take the time I have (especially with the current pandemic) to think extremely carefully about this decision before I devote at least 4-7 years of my life. I also want to be mindful of other options that may satisfy both (1) and (2) above. I'm finding over the past 7 months I've begun to understand my emotions and personality much better than I ever thought possible. I see this new understanding as overwhelmingly positive since it helps me make the best decisions I can for myself. I'm willing to take the time now to think about this decision if it will lead to a more fulfilling life 20 years down the line.
The final question I have is how someone decides where it is they want to focus their research. I find that I get easily distracted by new information as I learn. I may have an interesting idea that leads me to explore one path down some material. As I learn more, the material sparks a new question or idea that leads me down a new path. While this feels like a great strategy to self-learn with a constructive and natural progression, it doesn't seem like an effective way to research. How does one decide they're ready to study a very specific question that may close doors to other material and questions in related fields they find interesting?
In my case, I spent a lot of my undergrad time learning about machine learning and working with a startup that explored some research questions related to its business. I find machine learning interesting because of how natural the algorithms can feel to think about. The ideas feel intuitive while my math education helps me wade through the more nuanced derivations and implications. On top of that, both the advancement of computers and my familiarity with them helps me solve seemingly difficult problems. But at the same time, I feel more drawn to questions on causality, truth, logic, observable effects at large scales, and efficient problem-solving. I have found physics fascinating since I was a kid but never started learning anything beyond basic relativity and quantum mechanics until recently. It seems like that opportunity is gone; to pursue physics long-term I would have needed to study it in undergrad. I enjoy math as well, but more so as it comes up as an abstraction to a concrete problem I'm thinking about. I would not like to spend my "passion-time" solving unsolved problems or proving various conjectures simply out of my enjoyment for math. I enjoy having a tether back to our world and the means to produce and use any result I find.
Important 2 Start
In short, I'm not looking for an answer to my life question (I must answer that myself), but rather answers to these 3 gaps in my reasoning:
1) Is it more common at a PhD program to find others who share a humility and sense of wonder at the immense amount of knowledge both discovered and undiscovered?
2) How do PhD candidates decide what question(s) they are interested in pursuing, potentially closing doors on other related fields and questions they find interesting?
3) Am I expected to be set on a question to pursue before I join a program? How flexible is this if I learn something that makes my question seem unsolvable?
Important 2 End
That being said, if you feel that you have life advice to give, I will gladly welcome it. More information will help me make a well-informed decision.

Is it more common at a PhD program to find others who share a humility
  and sense of wonder at the immense amount of knowledge both discovered
  and undiscovered?

Yes, but it's also more common to find people completely jaded and disinterested in their work due to poor research progression, troubles with supervisors or colleagues and deep financial worries. Research itself can be the wonderful, carefree pursuit of new knowledge that you describe, but getting a PhD is often the opposite. Go in with your eyes open: the reality is, it's very hard work and takes a long time, and there will be many days/weeks/months where your feel like you're banging your head against a brick wall and like you're not learning anything at all.

How do PhD candidates decide what question(s) they are interested in
  pursuing, potentially closing doors on other related fields and
  questions they find interesting?

I did a lot of reading. There are (and always will be) a ton of things in physics I find interesting, but in terms of finding a topic for my PhD it was pretty much a case of "what's the coolest thing out of all these interesting things". And in fact, I've grown to love my research area more the more I've worked on it and the more depth of knowledge and understanding of the field I've gained. Plus, if you stay in research after your PhD, there's plenty of time to work on all the ideas you've had on the back burner.

Am I expected to be set on a question to pursue before I join a
  program? How flexible is this if I learn something that makes my
  question seem unsolvable?

No, although having an understanding of the field and the big open questions helps. A null result is still a result. You can change direction at any time.
Good luck.

I would keep very much in mind that a PhD is a professional degree. If you are not certain you want a research career, then it's likely not the right correction to go in. Luckily in computer science a research career doesn't strictly mean an academic career, so there are some options. That said, going into a PhD program driven wholly by a sense of wonder at the landscape of human knowledge, with insufficient attention to concrete career goals, is a common failure mode. You need to work into your plans the possibility that all this stuff might seem a lot less wondrous once you've spent five (or six, or seven...) years trying to compete with a lot of other really smart people to prove that you've got the best insights on it all. Even if not, you still have to get a job!
The smartest PhD plan I ever saw was an old colleague who worked as a coder for a long time, almost ten years, spending lots of nights at home getting familiar with the research landscape. After a while he knew exactly who he wanted to study with and went and did it, with great success. While as others have said, you're not expected to know what you want to work on on entering a(n American) PhD, it bears keeping in mind that the vast majority of PhD students do not end up in research careers at all. Those who do are often over-prepared. It's not necessarily a waste to do a PhD and then go into a pure teaching job or back to coding, but far more people end up on such a track after their PhD than intended to on the way in. Make sure you know what you're aiming for, and what it takes to get there.

Losing my sense of wonder is something I hope never completely happens, but over time could be possible. On the note on preparing, I find that my research questions tend to break into 2 categories:

Questions that build off current research I've read. These are usually already being explored by other researchers
Questions that are new or unexplored. I usually know what pieces in my understanding I'm missing and how to find them, but the question is a much more of a "stretch" problem.

I find (2) much more motivating, but I'm unsure how interested a research program will be.

@jet457 As a PhD student, you should not expect to break open highly novel areas of research. There is an enormous amount of work to do just to get from "great undergraduate student" to "person capable of producing interesting research at a reasonable pace." You want to have as clear as possible an idea of the area you want to do work in, but you should assume you're totally incapable of assessing which specific projects in that area are good targets until proven otherwise-usually quite late in a PhD. The single best thing you can hone in on is: who might you want as an advisor?

The other comments are great, but based on my experience at an R1 school in a CS department with a large international student population and strong connection to industry sponsored grad students:

1) Is it more common at a PhD program to find others who share a humility and sense of wonder at the immense amount of knowledge both discovered and undiscovered?

Not necessarily. Although PhD students on average may relate to this, I've never thought to describe grad students as such. People's motivation will differ. I know some international graduate students who want to stay in the United States and being in a PhD program helps ensure they can stay. Others may be doing it because where they work needs trained scientists/engineers and the company sponsors them.

2) How do PhD candidates decide what question(s) they are interested in pursuing, potentially closing doors on other related fields and questions they find interesting?

Unless you are reading papers for work or connected to people who are familiar with the literature, it is going to be difficult. One strategy is to look up the proceedings of a conference in a field you are interested in, for example CVPR or NuerIPS, and browse the papers that catch your eye. More realistically, and which is my case, my current research direction is fairly different from what I put on my grad school application and has largely been dictated by my advisor's interests, collaborators, and data available. In fact, most programs have classes or structures in place for PhD students to find a suitable advisor and research direction in their first 2-3 years in the program.

3) Am I expected to be set on a question to pursue before I join a program? How flexible is this if I learn something that makes my question seem unsolvable?

Mostly answered above. You aren't expected to be set on a question, though having an area of interest, such as machine learning, would be helpful for the admissions committee to pair you up with an initial advisor. If a problem appears to be intractable, get feedback from others or try to solve a constrained version of this problem. Your advisor should be able to help you navigate this.

Too few people around the world have the option to actually choose what they will do as their life's work. If you have the chance to do so, pick something that you feel passionate about and forget the rest.
Are you driven to do research in some field, say CS or math? If not, don't bother. It is often said that "You don't choose mathematics. Mathematics chooses you." That was my experience. I also really wanted to teach and be a productive faculty member.
But the goal is a ways off and there are many hurdles. Do you have the drive and the patience to push through them? Including disappointments?
From the basic sound of your question, I'd think that you would be a good candidate, but it is up to you. Do it if you really can't envision spending your life any other way.
You only get one shot at life. No do overs. If you aren't forced into something unpleasant by circumstances. Grab it by the ...


text:
Academic CV: Including declined postdoctoral fellowships under "Awards and Honors"?
I have seen many people list declined graduate fellowships from big tech giants, NSF, etc., on their CVs. Many of these are respected researchers working as tenure-track faculty in top-tier R1 institutes. I don't have such fellowships that I have declined, but I did get multiple postdoctoral fellowships (all from very good places) that I did decline (to accept my top-choice postdoc).
I wanted to ask if it looks obnoxious to list these under "Awards and Honours".
I am sure this varies with context, so here's the context: I'm applying for travel grants with the AMS and also for some summer school short courses.
My reason for wanting to list these declined fellowships is to signal that multiple places thought I was good enough to be offered a postdoc. I didn't get any graduate fellowships, and my "Awards and Honors" section otherwise looks quite scarce, with only minor travel grants. That's why I thought I'd add these postdoc fellowships (they are all I have).
Of course, though, I do get that this can look really icky; I'm not entirely sure though since I have seen senior people do  it. I thought I'd check here. Thanks!

I don't have an 'Awards and Honours' section of my CV. Sounds like there is several lines worth of space better devoted to something a potential employer might actually care about.


text:
Letting grant funder know that funds no longer needed?
I am a English PhD student (focusing on literature), but this year one of my assistantships through my university has involved some grant writing for local non-profits. Recently I've been working on a small grant for a local non-profit, which will help this non-profit pay for some consultants to help it develop a strategic plan and more effective organization. (The grant is offered by a foundation that focuses on capacity-building support for non-profits in the city where I live.) Because of the impacts of COVID-19 on the non-profit sector (i.e., many of our organization's donation funds are likely to dry up), our hired consultants have generously offered to do their work pro bono.
Here's my question: what is the etiquette of letting a grant funder know their funds are no longer needed for a specific project? To clarify, I was pretty far into the grant writing process (original LOI / project proposal approved, directed to the next steps in the application process) when we learned we'd no longer need the funds for the consultation fees. (The foundation that has offered the funds is a major donor to local non-profits, so there is a good chance that we'll be applying to them again in the future--just for a different project.) Since I corresponded a lot with a representative of the foundation, I feel like I should follow up to let them know, especially as we may be applying to them again in the future ... what are others' thoughts on this issue?
(If there's a better StackExchange community for posting this question, I apologize!)

Please talk with some senior people about this grant and how the people act first. For the grants I know, the advice mostly is "buy anything related just to use the money" and "if people give back money, the next time they get less".

I would ask the representative. Procedures differ wildly from funding agency to funding agency.
However, I would not be worried: everybody acted in good faith, and you are asking for less money. So in all likelihood the response will just be a short email thanking you for letting them know, and telling you that they look forward to receiving new applications from you in the future.

First, think about whether there is some other use for these funds that would contribute to this project. If you can think of something valid, tell them of the situation and propose that the funds either be returned or applied to the other purpose.
But don't do anything frivolous. I expect you know that, however. But be specific about any other needs and say how they would contribute.
But if nothing comes to mind, just inform them as suggested by Maarten Buis with your thanks.


text:
Can an applied (e.g. applied computer-science) postdoc compensate for pure PhD (e.g. Pure Mathematics)
I have graduated last year from a PhD in pure mathematics and I intended to do some machine learning in industry. However, seems like no place takes me seriously so I began asking colleagues from industry why. They claim I am on the one hand overqualified to do a "usual" programming job but on the other hand under-qualified to do a "serious algorithms job"  as I have never worked in my PhD on applied computer science/Machine Learning.
One colleague from a technology  company said

Doing a PhD in pure math was a sin. Repent for your sins by doing a post-doctoral degree in applied Machine Learning.

What do you think about this idea of doing applied postdoc just in sake of "cleansing" a pure PhD from the cv? I feel deeply traumatized from the academic poisonous environment I had to suffer during my PhD training and I don't think it'd be any different committing more to the same evil. On the other hand, can it really help improve my value in industry ? Let alone when applying for bigger companies?

There's nothing "sinful" about doing pure maths, at worst it is "useless". On the other hand, doing machine learning in industry without proper mathematical understanding...

@leftaroundabout ...is extremely common. You'd be surprised how little theory you need to know to have a machine learning job.

@PasserBy I'm not surprised by it, only appalled.

Some large companies I know offer postdocs, might be good experience and exposure.

I have worked in AI and Robotics for about a decade now. Most companies will have a trail of Phds that look good on paper but fail to deliver. This is exacerbated by the fact that the Phds at a company will typically have a hiring rubric closer to, you guessed it, what you might want in a lab.This does not always meet commercial needs. You have to show you can deliver in some aspect while respecting the Iron Triangle.

Well, people do enjoy caricaturizing other people... and, yes, sometimes, self-described "pure math" people are amazingly narrow... oh, but, wait, sometimes lots of other people are also amazingly narrow. It seems that you yourself are not so narrow, but other people need/want to see tangible evidence.

@PasserBy - math too, IMO.  basically you just need to know arithmetic in large quantities.  (IMO one of the big lies of ML is that it is "linear algebra".  They swiped the term "tensor" from physics because they're dealing with large multi-dimensional arrays of numbers - but left off all the actual "math" of tensors, 'cause not needed.  But it's much more cool to talk about "tensors" than "rectangular arrays".  (They're not even matrices - when was the last time an ML guy talked about taking the determinant of one of his arrays?))

@davidbak I'm absolutely certain there is no way that "just knowing arithmetic in large quantities" would've sufficed to complete my PhD in arithmetic (!) geometry. On the other hand, I do know that I'm thriving in a machine learning job now using nothing more that high school maths. It does help that I'm the only person in the data science department that understand what a linear regression 'actually does'.

@DenisMarcinkov Make sure that you can show some 'hands-on' experience in applied computer science. If you have a PhD in pure mathematics from a half-decent institute, everyone will understand that you'll pick up the ML theory necessary for industry in a few weeks. The question is whether you can implement it in practice, and work on large collaborative projects effectively. Getting another degree is a complete waste of time.

@Servaes  I did graduate from a good place. I had been freelancing as a software engineer since graduating but did only fullstack jobs so far. That didn't quite help.

@DenisMarcinkov, I'm in a situation similar to yours, but I have a year to finish my PhD. Could you update on your current position?

Since I have a pure math PhD but worked in CS (academia) throughout my career, I don't see any need to "expunge" a degree. You are in a good place to learn computer algorithms in a short time since you have the background on which they are based.
The problem would only be gaining some recognition in a different field. I've also done that. Plan to attend some (many) conferences and get to know people. Industry folks go to these as well as academics. Try to form collaborative relationships and work (with others) on a few papers. It would (IMO) be faster and easier than taking an additional degree, much of which would bore you, I suspect.

I can understand why a company would be worried about hiring a pure math PhD who doesn't have applied experience. I have known a lot of mathematicians, engineers, and people who have migrated in one direction or the other. It's not a guarantee that you can implement something -- or even develop something that CAN be implemented -- just because you can write a mathematical proof about it.
So: The piece that appears to be missing from your resume in order to get a serious algorithms job is proof that you can take things from the conceptual high-level pure math domain and implement them in code. If you want those jobs, the question you should ask yourself is: How can I fill that gap?
A postdoc is an obvious way to do that, which is why your colleague suggested it. You will be hired to do some specific implementation work which will result in products (papers) that you can point to, and you'll have someone who can be a reference and vouch for your ability to make those connections. That puts you in a very strong position.
If you are traumatized enough by your experience as a PhD student that even spending one or two more years in academia feels unmanageable, break down those two benefits and look for other ways to get them. You could implement some aspect of your PhD work in a code base that you put on GitHub. You could write about that and put it on ArXiv. You could reach out and make contacts with people who you think might have applications that your code base would be useful for, and ask if they would be interested in collaborating.
Just the first thing -- the GitHub repo -- might be enough to get you hired. If it's not, each subsequent step will put you in a stronger position. But each of those steps takes time. Again, this is why a postdoc is handy: You get paid.
The other option you mentioned was "usual" programming jobs. You say you are overqualified, but you also didn't mention your level of expertise in software engineering. Could it be that you are underqualified in that regard? Again, GitHub repositories will help you if you have that problem. You can also take one of those coding boot camps, but it is much harder to get placed with a company through one of those programs these days than it used to be. There are programs aimed specifically at people who did a little programming in their non-CS PhD program and now want an industry job that uses a lot of programming that might be helpful, though.
If you are already extremely proficient in programming, so the only problem is that you are overqualified, I will remind you that you can list your PhD as work experience rather than education. If you focus on the transferable skills and minimize the cachet you expect a PhD to have, it will probably read less to a hiring manager that you are overqualified. But I suspect, given your background, that it's more likely that you are simultaneously too expensive to hire (because of the PhD) while also being underqualified in other important areas (ie with practical experience collaborating on large code bases) for the lower-level software engineering jobs.
From the perspective of a hiring manager, the PhD can mean you will require a higher salary due to company policy, or because they expect you to negotiate harder because you have the degree. The PhD can also mean that you'll ditch this job as soon as you get one where you can use the PhD, which is expensive because replacing and training people takes a lot of time. I haven't been on a hiring committee for machine learning jobs in industry but I've had an inside look at several hiring processes over the years and the jobs tended to go to someone who would grow into the role rather than the most highly qualified candidate because they were expected to want to stay longer in the position. If you're really good -- much better than the other people applying -- the hiring manager is more likely to be willing to take that risk. If you have an equivalent level of practical experience with software engineering to someone without the PhD, they may not be willing to take the risk. (Also, please understand that not all hiring managers will feel this way -- a minority will view a PhD as a plus no matter what.)
I hope some of this is helpful for you.

The key issue here is that your qualifications do not match employers' requirements if you are looking for AI jobs. They seek (and find!) employees with a software and algorithmic background, and for all of the hard work that went into your PhD (of which you should be proud!), you just don't have those qualifications. It is, then, not a surprise that your applications do not lead anywhere: You would also not be hired as a sociologist for a think tank, or as a welder by a steel manufacturer, PhD be damned! Having a PhD does not make you qualified for jobs outside your area of expertise.
The way forward then is to either (i) work on having the qualifications the employers for your dream jobs seek, and being able to document them, or (ii) change your target for jobs to things you actually are qualified for already.

it's some sort of a circular path I am afraid -- for having the qualifications employers seek (i.e., experience programming) I need to be hired by other employers which seek the very same skills.

Perhaps, but that's just how it goes with jobs. It's true that I'd like to have the job of CEO of a Fortune500 company, with a salary of $20M pretty please. I might even believe that I'm qualified for it. It's just that those who hire these people don't agree. You don't get jobs because you want them, but because you can demonstrate that you're qualified for them. But you don't actually have to have a job to demonstrate you're qualified -- as others have pointed out there are many other ways.

This quote seems like a silly attempt at a joke, combined with a serious attempt at gatekeeping. The majority of people working "senior" AI / dev jobs do not have any serious background in maths, be it pure or applied, and won't be competitive with a candidate with Pure Maths PhD. They have some advantage by "knowing the ropes", i.e. the processes in their current workplace, libraries, people one need to please to pass a review, some tricks of the trade, etc. But doing a PhD prepared you intellectually to do serious research at a much more rigorous and detailed level.
Don't let anyone tell you that working hard for your education was anything other than a noble and difficult act. Don't let anyone tell you that you don't deserve your dream position because your educational profile is different from theirs. You have a terminal degree, there is no degree higher than a PhD. Keep applying to top companies and eventually your achievements will be noticed by people who value and recognise them. Good luck.

This answer is all nice and good but does not address that the OP's qualifications are not helpful for the job they seek, however hard these qualifications were earned.

I take the point of view of this answer to be a denial of the assertion that the OP's qualifications are not helpful for the job they seek. This is a point of view which accords with the experiences of myself and of my department colleagues, who have placed several math PhD's in data science jobs.

@LeeMosher Yes, many data science programs are in mathematics and place large numbers of graduates into such jobs. But that doesn't apply to the graduates in pure mathematics.

idea of doing applied postdoc just in sake of "cleansing" a pure PhD from the cv

I work in the industry and hire people. I do not know what a "postdoc" is.
I see on your CV that you have a PhD in "mathematics", we want to hire for "machine learning".  This does not really match.
I look at your experience in machine learning and I do not see anything.
Next.

You may be more lucky but it is likely to be the way your CV is perceived.
The only reasonable way to get out of this is to show that you can do machine learning. Depending on where you are, the industry and the alignment of planets, this may be

a degree that says "machine learning" (or "data science" - close enough). The fact that it says "postdoc" does not change anything, it could very well be a new degree from scratch.
a serious set of things that show that you have experience in the matter (projects, etc.).

Please keep in mind that the path your CV takes into a company is of uttermost importance. If you apply on the web site your chances are slim. If the CV goes through someone inside the company who can advertise your added value then the chances are much higher.
Your degree in math can be very valuable to companies that take machine learning seriously, to the point of enhancing the mathematics behind (and not just throwing data and hoping for the best). You need to find the companies that are in the first case and then apply to the people who work on the enhancements.

There are no real post-doctoral degrees, but I agree with your colleague, though not with the facetiousness:
You have shown a great collection of skills by getting a degree in Mathematics.
An employer might worry about getting you up to speed on ML, which has considerably evolved in the last years. People in your situation that are doing research work have progressed quite a bit, including in the personal skills that they now possess. Doing a Post-doc in ML would be great to overcome this problem. In a related manner, writing papers in ML would also help.
There is no need to "expunge" your doctorate. If you can prove that you acquired ML skills, your degree gives you some advantages over people who do not have the degree of abstraction, intuition, and precision that you acquired. Others in ML of course have acquired those through a different road.

Actually I taught classes in classical ML and have a project with neural networks in my cv, yet I am not hired.

Classical ML is not what people are currently using in industry. Your project with neural networks might similarly be too theoretical, too basic, or not demonstrate how you can connect your theoretical work to practical implementations. Or it might just be that one project is not enough to demonstrate a level of proficiency high enough to overcome the additional expense to hire a person with a PhD.

Your sample is non-representative. I have at least 1.5 acquaintances who have a theoretical math Ph.D. and post-doctoral work - category theory - and have gotten work doing on some some deep-learning-AI-thing, or cryptography.
Also, you are not over-qualified for a usual programming job - you're under-qualified for it: A "code-monkey" requires knowledge and experience with programming languages and development tools more than they need deep abstract insights which a Math Ph.D. affords them.

What do you think about this idea of doing applied postdoc just in sake of "cleansing" a pure PhD from the cv?

You're thinking like an academic. Don't do that. Take some time to:

Read up on ML classically (maybe this) or the fashionable deep-learning-by-neural-networks stuff.
Study and practice a programming languages (Python is quite popular where it comes to ML), perhaps contributing to some relevant FOSS project if you find one that interests.

As you do this, you can add relevant items to your resume; and in an interview, you could explain how you are making your way into the field. Also,

Try to find some "meetup"-like activities in your area regarding ML or the sector of industry you want to get into, and attend


text:
How to accurately digitize plot data from figures available as vector graphics?
Measurement data in publications is often provided only within figures, while the original data is not available. There are some very useful tools around to digitize such data, such as the web application WebPlotDigitizer, the app Engauge Digitizer or within the software Origin, but to my knowledge they only support raster images.
Since publications are usually available in digital form and figures therein are often embedded as vector graphics, a more accurate digitization would be desirable. Are there tools around which allow to directly digitize vector paths from figures (similar to the aforementioned methods)?
This question goes beyond precision (see further remarks below) and also addresses an efficient and semi-automated workflow.

Remarks

The achievable accuracy of course depends on the quality of the figure, or more specifically on (i) how the figure was originally produced, and (ii) how it was processed during the publication process. Since often high-quality plotting tools are used (e.g. guaranteeing proper resampling) and journals don't always mess up, figures in appropriate quality should now and then be available.

The problem goes beyond precision in terms of reading out values (which could be resolved by rastering figures in high resolution and using the aforementioned tools). In complex figures graphs could (i) cover each other up, (ii) overlap themself due to scatter and line thickness, and (iii) have varying sampling rate. Hence, rastering involves misinterpretation of data. Using a vector graphics editor for preparation before rastering (e.g. hiding individual graphs) would help, but is time-consuming and does only solve some of the problems.

At first, it should of course be checked if the original numeric data are available, as required by some journals (unfortunately not in many fields). Also, the corresponding author could be contacted, which often won't lead to success for many reasons such as unavailability (of data or author, after some time) or unwillingness.

Thanks to Martin and Massimo Ortolano, whose contributions inspired some of the remarks.

https://academia.stackexchange.com/q/158356/13240 Just turn it into a bitmap with the required accuracy and then use the previously mentioned tools.

PostScript just is not meant to be converted into data tables.

Thanks @AnonymousPhysicist, but I'd like to avoid rastering graphics, since even for high resolutions information is distorted, i.e. either original data points are lost or fictive data points are added.

How big a difference can that possibly make? Surely the error involved will be negligible at high resolution.

Is your actual problem that the data points cover each other up?

Thanks @JHare, I added additional information to the question.

Thanks @AnonymousPhysicist, I added additional information to the question.

I suggest that this is impossible because the software that made the graph might have omitted some of the data that is covered up.  In any case, it is a bad idea.

@AnonymousPhysicist, assuming a properly prepared and processed figure is available (which should sometimes be the case), why would it be a bad idea?

Vector graphics were designed not to work this way, as I mentioned above.

Well, i used to do this a lot, open in illustrator -> Clean export points. This works. BUt several times it would have been easier to grab the data from a image, Since there is no guarantee that the data is not consisting of millions of trimmed triangles with extra points and object expended into million of pieces. But yeah if its a well behaved graph then its a 2 minute job

This is an amusing programming/hacking challenge, but my guess is that in 90% of cases the best solution lies in the realm of human affairs, and that’s simply
to email the authors and ask for the data.
Why? Two reasons:

When it works (and I expect it would most of the time), you’ll know with certainty that the data you have is exactly what the authors were working with rather than some approximation recovered by trying to reverse engineer an unknown sequence of human and algorithmic processes to convert the raw data into a figure. (Vector graphics may offer the illusion of lossless encoding, but that’s assuming no lossy steps were applied by the human or software at any step along the way — a dangerous assumption to make in practice.)

In the infrequent occasion when it doesn’t work because the authors refuse to share the data, you’ll still learn something useful about how trustworthy their data can be assumed to be (i.e., not at all). You can still try to revert to a technological solution, but in most cases I’d just assume the data is invalid and not worth relying on.

About point 1, I'd be surprised if it works half of the time, for two reasons. First, many groups, especially in competitive fields, are not so willing to share their data. Second, there is a problem of data preservation. If you ask me the data from my experiments from 25 years ago, or even those from 10 years ago, I have long lost them.

I agree with @MassimoOrtolano but would add a third reason not assuming unwillingness or inability: in some fields lots of publications are written by PhD students, who simply are no longer active in research and therefore unavailable.

And sometimes the authors have passed away.

@MassimoOrtolano yes, I was thinking more in the context of recent papers.

(a) You will have to live with whatever graphic format, conversion, compression and thus imprecision has happened to the data. Authors are supposed to proofread and confirm that the data is - at least to on visual level - intact (or correct it - I have had high rank journals messing up with data for no obvious reason). I.e. you may be able to recover numeric data not to the original precision, but this is hopefully neglegible to the imprecision due to statistical sampling. You may not be able to recover "hidden" data such as higher harmonics.
(b) Consider that even the original data before upload/conversion for the journal may contain some drawing-related imprecision, e.g. if folks use Excel-smoothed lines only without showing the actually measured points (what I of course do not recommend for real data, just for symbolic simplification).
(c) In addition to precision, the second layer of complexity is overplotting: the "hidden object" may or may not be invisibly present in a vector graphic. You can use techniques such as opacity (or jittering e.g. in case of categorial data as "beeswarm plots" in R), but who knows what the authors have done?
In summary, if you are fine with the available level of precision, you will probably have to inspect the plot manually. I am not aware of a generic software solution that is intelligent enough to tell you, which data points in a drawn line are measured or smothed, if data is jittered or overplotted, if there must be overplotted data but is missing below an other object, or even in the first place what kind of plot it is (x/y scatter, categorial beeswarm where x does not matter, heatmap ...), and for some data symbols (e.g. numbers/letters) even if the numeric value is represented by the center or some corner (depending on plottting program and settings).
The alternative is to ask the authors for the data (and tell them honestly, what you are doing with the data). Also some journals require upload of bulk numeric data (e.g. gene expression), so check the journal policy.

Thanks for your efforts! I added some remarks to the question and upvoted your answer, but hesitate to accept it, since manual inspection certainly helps (especially via a vector graphics editor) but it is not the solution I was hoping for.

TL;DR. Extraction doesn't work; rather than attempting extracting, ask authors for raw data.

Since publications are usually available in digital form and figures therein are often embedded as vector graphics

Although many publications are prepared in digital form with vector graphics, such as those prepared in LaTeX, the vector graphics are lost during conversion to camera-ready format, such as PDF, wherein vector graphics...are constructed with paths (source: Wikipedia). I believe   precision is lost during conversion (but I'm uncertain). Further research provides evidence that precision is indeed lost:

what in PDF parlance is called an 'image', by definition always is a raster image. There's no such thing as a 'vector image'. Even if the original file which was converted to PDF included vector graphics, then the converter program could have decided that it includes these as raster image. If you extract this, you'll not get your vector graphics back, but a raster image. Raster graphics which are preserved inside a PDF as such cannot be extracted by pdfimages.

Thus,

Are there tools around which allow to directly digitize vector paths from figures?

Original vector graphics cannot be recovered, assuming non-lossless conversion. Partial reconstruction should nonetheless be possible, with some loss of precision.
Even if original vector graphics could be extracted, it surely wouldn't be known whether they were indeed the originals, or some partial reconstruction, which is dangerous for science.

I didn't downvote, but this is not true. Depending on the PDF format, the vector paths are preserved. Most frequently than not, you can import a pdf into Inkscape (for instance) and successfully import all the paths and objects of the vector graphic. So, in practice, you can even edit a vector graphic stored in a pdf.

@cinico According to Wikipedia, vector graphics are converted. I had expected some conversion, because that's how PDF documents work. I haven't checked the precise details. I don't doubt you can extract a vector graphic from a PDF; I don't believe the original vector graphic can be extracted: Are you claiming to the contrary?

Yes, that's what I mean: you can extract the original vector graphic. You can easily try this yourself.

@cinico I tried. I'm confident it didn't work. I used inkscape to extract a vector graphic containing text. The resulting svg file didn't contain that text (at least not as a plaintext). We can assume that only computers avoid plaintext, leading me to believe the original vector graphic was not extracted. This leads to another point: An extractor can surely never be certain that they extracted an original image, which defeats the purpose of extraction. If you do have a working method, why not provide it?

One thing about text in vector graphics. It's common, as a good practice, to convert text to paths because it ensures a correct visualization anywhere without needing the fonts. So it's possible that you didn't get the plaintext because it was converted to path. What I do, and it works, is that I import a pdf to inkscape and then I need to ungroup (a few times) the objects that I've imported. Then I see the original objects with exactly all the nodes and paths of the original object. If you want to try, create a complex object in inkscape,save as PDF,and then import again

Note that filters and some other things not purely in vector format, like gradients, have to be renderized when you save into pdf with inkscape. Because it's not purely a vector drawing anymore, the objects with gradient filling will lose information

@cinico I think you've confirmed my answer: Original vector graphics cannot be recovered...Partial reconstruction should nonetheless be possible. When you cannot be sure what you've recovered, you can't do good science. That isn't to say extraction isn't useful.

I'm not sure if you misunderstood what I explained or if we are using different definitions of vector graphics. Pure vector graphics as in 'there is nothing else other than vector objects', can be fully reconstructed from a pdf. As soon as you start adding things to the vector graphics that are not vector objects (like gradients), then they information is lost because there is something else other than vector data - gradients will be rendered and will have a finite resolution. If your definition of vector graphics covers hybrid objects, then you're right: they might not be fully recovered.

Maybe I should add that, for purposes of extracting data from a paper, you can be sure of what you have recovered because either you can or you can't reconstruct the object. If you can reconstruct the object, then you know it's the original. What you cannot recover, it simply won't be reconstructed into vector objects and you will know.


text:
What are the benefits and purpose of presenting a paper in an academic conference?
If i have completed all the research work and compiled a research article then why should I present that paper in a conference and not submit it to a good journal for publication ?

@Roland Manufacturing Engineering

@JeffE Editing now done

You're still presenting a false dichotomy.  Why not do both?

@JeffE Is it permitted to submit the same paper to a conference and a journal ?

It certainly is in my field.  Not at the same time, but conference first and then journal is completely standard, usually with some additional material in the journal version.

The answer depends on the discipline.
In many disciplines you can do both. There are conferences where you can present work that has been published in a journal (or at another conference) or that shall be published in the future.
In other disciplines, conference publications are as "valuable" (or even more prestigious) than journal publications.
To know what is the case for your discipline, talk to your advisor.


text:
Rephrasing and Reproducing some part of the Introduction of a Research publication without citing that publication. Is it plagiarism?
I want to rephrase and reproduce some part of the Introduction of a Research publication without giving citation to that publication. Will it be considered an act of plagiarism ?? I am not using and citing any result or any table and figure of the publication.

Unequivocally, yes. Plagiarism isn't limited to results or figures alone. As for automatic plagiarism-checkers, they will make even less of a distinction, and will almost certainly flag it as plagiarised if a certain contiguous amount (I am told it is 2 sentences, but I don't have a confirmation on this).
You mentioned rephrasing - this could help avoid automated checks, but if the changes are trivial (changing voice, shifting subject/object, substituting synonyms), a reader may spot and report this.
That aside, why would you want to reproduce it? Different papers should have different introductions if their motivations are different. Is it to save writing time/effort or something else?

I am writing a review paper.The background information regarding the field must be similar in the Introduction of all the related research publications.

Not necessarily- individual publications will generally have limited scope, and will mention only the relevant background information. A review paper will have wider scope, so the background information should also be more broad, but also comprehensive.

Continuing, even if it is similar, it shouldn't be identical; a review should summarise a lot of information in a concise way. It follows that it should be differently written.

I don't think it takes you anything to cite this reference. Please do cite, otherwise, if you don't like the reference, get a different reference with similar information and cite it.

If someone queries or asks you about that information, how do you
attribute it to the original author?
For many of the things we write, among other reasons, we cite to show who
is responsible.