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How can I write a paper that will convince the reviewers that the results are non-trivial?
I submitted a paper in math/cs/economics to a top-level journal. The paper involves a new variant of a well-known problem. All reviewers agreed that the results are interesting and non-trivial, but they rejected the paper as not being general enough for their journal.
Encouraged by the positive feedback, I submitted an improved version of the paper to a medium-level conference. The improvements include simplifications of some of the proofs and additions of stronger results about the same problem. Now the reviewers rejected the paper claiming that the results are too weak and unsurprising!
What should I do in the next time I submit (to a different journal), in order to make the reviewers believe that the results are indeed surprising and non-trivial? I don't want to write the proofs in their more complicated version, as in the first revision, because this is unscientific. But writing it in a simple way seems that doing so creates a false impression that the results are too simple. What do you suggest?

Why on earth would you want to convince the reviewers that the results were difficult?  I think the word you're really looking for is significant or perhaps surprising.

@JeffE - Or the results were difficult to attain. I wonder if difficult here is intended as a synonym for "not trivial."

Sorry, I still think this one is a dup. After reading both questions, I have a thought. If you can write this question to distinguish it from the other question, you can write your paper to convey why yours is not too weak and unsurprising. I think the answers to the other one (including yours) did not really solve the problem. The answers just told you why it is a difficult task.

@J.R. No. If the results are significant, it doesn't matter how hard they were to attain.  On the other hand, if the results are not significant, it doesn't matter how hard they were to attain.

@JeffE This is what I thought, but the reviewers probably thought differently...

@JeffE: The "significance" of a result is often subjective and/or difficult to evaluate.  To perform this evaluation, it's natural to take into account the "depth" or "difficulty" of the arguments.  If when refereeing a paper you meet a result that you had never thought to establish, it is very natural to stop and see if you know how to establish it, or have a sense of what would be needed to establish it.  You are also of course looking for "new ideas" and "new techniques", but it's a similar story; such things are much more convincing when there is no other easy way to solve the problem.

That said, I take the point that difficulty ought not to be valuable for its own sake.  In my experience, prestigious journals can lean too heavily on wanting to publish things that look hard and/or showcase exceptional technical skill (versus a more novel approach that doesn't look as hard).  My very first referee report, a rejection, contained the passage: "Admittedly, Theorem X is a nice result.  The proof, however, is not overly cumbersome."  To which I always react: "Wait!  Give me another chance: I can make the proof much harder."

@PeteL.Clark: And now, with a lot more experience gained after your first paper, do you see any way out of such situation for papers in mathematics (other than going to a lower-rank journal or making the proofs to appear complicated)?

@just-learning: For this first paper I submitted, the passage I quoted was weird but the verdict itself was reasonable.  In fact, I look back at the experience of not having a published (solo) paper that was written while I was still a student as an overall positive one: the paper was not as strong or mature as other papers I've written (and there were some problems with it, though the referee didn't catch them).

@PeteL.Clark: Thanks, I see your point. But what if the result is indeed important (as confirmed by some colleagues, not just the authors, but alas these colleagues are not editors in the top journals to whom one could submit the paper) but straightforward to state? And the proof is easy too (the idea uses a simple formalism, just from a slightly different area), so it all looks obvious to experts after they see it (but somehow this was not discovered for >20 years). In your opinion, is there any way to get such a paper into a really good math journal? Many thanks in advance.

@just-learning: first, I thought I had a followup to my last comment, but I remember now that I didn't get around to posting it.  I certainly have no magic wand for getting papers accepted by really good math journals: I have written over 30 papers, none of which have been accepted by what I would call a really good math journal!  But what is probably my best publication -- it is in Crelle -- is my shortest (non-MAA type) paper and I am proud of how easy the proofs are.  The trick was: I answered a 50 year-old question of Lang and Tate.

Maybe that's a moral if you are truly "just learning" (including some information about yourself on your profile would help me target my responses, BTW): there are serious, professional research mathematicians like me who never even submit papers to the very top journals.  It doesn't mean that my work which is published in, say, the Journal of Number Theory is not "important".  It just means that it is not the world champion of impressive mathematical work.  If you're just starting out, it's more important that your work get published in reputable journals than fail to appear in top ones.

As a general rule, if you're solving a problem that no one had pointed out before and your proof uses only existing tools and doesn't have a feature that can be pointed to as especially hard or tricky: yes, I think it will be difficult or impossible to publish it in a top journal.  Let's ask: why would such a paper deserve to be published there?  Because of the implications of the new result?  If so, show them.

@PeteL.Clark Thanks again, your comments are quite enlightening. To understand your point of view better, I'd appreciate knowing your take on two rather mundane things: i) in your view, the Advances is just a reputable or a top journal? ii) I thought that quite a number of better universities (and even the universities seeing themselves as such :( ) essentially require publications in top journals for promotion to the full professor in math, am I wrong on that count?

@PeteL.Clark: If you don't mind, instead of moving to chat we can continue the discussion in my blog post with the snapshot of our part of the above discussion: https://justwonderweb.wordpress.com/2014/10/22/top-journals-and-all-that/

In the end, the significance of a scientific advance is determined not by how complicated it is or how much hard work was put in, but by comparison with what was known / possible before.
It sounds to me like you need to have a much clearer and stronger comparison with the prior state of the art, particularly emphasizing why the new result makes a difference to larger or deeper issues.  Depending on the nature of your work, this might mean anything from a little improvement on the prior work section to introducing new sections with explicit comparisons.
For example, if you were able to mathematically compute the Nash equilibrium for preference of donuts vs. muffins, that's a nifty little result, but it might seem obvious or insignificant.  If you can explain that this was something impossible with prior methods, because nobody had previously been able to deal with the breakfast uncertainty principle, then that is surprising and interesting.  If you can show that your result accurately predicts sales in major chain stores, then that is also surprising and interesting.  In either case, you are showing how your result has implications outside of just being a result.
Now, you could probably also make your work appear harder and more significant by obfuscating the mathematics, and that might "work" for purposes of getting this paper accepted.  I personally, however, consider that to be scientifically dishonest, and would strongly recommend against that.  Remember, that your colleagues are not stupid, and sooner or later, people will realize that you are fluffing up your results, to your detriment.

"In the end, the significance of a scientific advance is determined not by how complicated it is or how much hard work was put in, but by comparison with what was known / possible before." I wish this was an universally accepted fact, but it is not.

(there are still plenty of people that state that it ain't science if it ain't complicated - and yes, I am saying "complicated" instead of "complex" on purpose ... this is a huge pet peeve of mine)

@xLeitix I absolutely agree with you, and I think it's an ongoing frustration for many of us.  Scientists are, after all, human.  I do think, though, that in the long term, significance does tend to sort out.

The reviewers agree that the results themselves are new, important, and were not known before, but they claim that the techniques we used are not new. In other words, although no one asked this question before, anyone asking this question would come up with the same answers easily.


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What referencing style is this?
My school has provided me with a referencing system but has not stated where it is from. I would prefer to use an online tool such as MyBib however, I don't know what my school's referencing system is. I have attached a screenshot below. Could anyone please help me identify it?

It is not obvious what style (if indeed any) matches the examples you gave. I used the CSL Search by Example (CSLSE) webpage and was unable to find anything that matched exactly.
CSLSE does not list every known style but it does list thousands of different styles including many that are variants of well known, named, styles. My unsuccessful search suggest that you are unlikely to find an exactly matching style to use with MyBib, Zotero or Endnote.
If you want to try using the CSLSE site, you should use the tabs labeled "Previous" and "Next" on the linked page  to scroll through the list of publication types that CSLSE shows you until you find a publication type (e.g., Book) that matches the attributes of one of the publication types on your own list (e.g., single-authored books). Then, using the author, book title, publisher, etc. that are shown to you by CSLSE, together with the style in your own list, make the CSLE publication match the style you want to produce. Then click Search. CSLSE will show you a list of publication styles that match your list with regard to that specific publication type.
If you are unable to find a style that matches your needs exactly, you could create your own style file. Advice on how to do that is available on the website.
However, an all-round simpler solution might be to ask someone knowledgeable at your school what the style is called ... and even whether they have a style file for a particular citation manager!

"an all-round simpler solution might be to ask someone knowledgeable at your school" <-- this.

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aggressive co-worker and bullying at the lab
I've recently started doing postdoc in an European country.
Since the first day, I am having problems with working in the lab environment. The research group is too individualistic (there is no shared protocols, project and any kind of support) and some people are behaving in quite toxic ways.  One of the lab members doesn't even look or talk to us (me and another student) since we arrived here. He ignores and turns away whenever he sees us, as if we are not worth it.
The main problem is the postdoc though. He is too assertive, aggressive and sort of being a bully in lab meetings, trying to get involved in every project and confront you without significant reasons. He even interrupts when he thinks it is boring and not delivered very well or wants you to prove (show RAW data) when he doesn't think it is enough. The PI does nothing and she is so dependent on him, lets him to be a co-PI or the kind of bad boss.
So, basically, I don't know what to do. I know that I can't stay it more and be productive here, but I am in a small country, where all the academic world knows each other.
Do you have any suggestions about finding another position or doing applications at the same university? If you could give some ideas, I'd be very grateful. I totally feel paralyzed.

The things you state: "assertive"/"aggressive"/"trying to get involved"/"interrupts when boring/not delivered well" may be unpleasant, but is not yet the hallmark of a bully; it might be someone trying to enforce higher standards. Can you be more specific about the bullying? I am not saying it is pleasant, and the culture of the lab may not be for you - but it may be a functional, albeit high-pressure lab.

There are other things, which I don't want to write here to keep my identity private, but you are right about the lab culture. It is not for me. I am looking a way out of it, I do not know if I can manage without moving into another place.

If so, then get out, fast. Do not waste your time. Keep a firm face while you search for alternatives.

It is a shame that you received no other answers; I have to record my disagreement (and disapproval) of the answer provided by Industrialacademic and I will try to provide my own.

Securing a position in academia, even a first postdoc, is an achievement which everyone can be proud of. After so many years of learning and preparation, this is finally the time when you are not only producing new knowledge, but also are recognised and payed to this. Academic jobs market  is extremely competitive and should be proud of yourself that you are on top of this competition. Getting there takes a lot of time, effort and commitment. An advice to leave without a proper fight is in my opinion extremely immature and ill-considered; it ignores the sacrifices you made to get the position you wanted and the responsibilities that come with it. You should not leave because of a single petty bully.
Our academic training prepares us to deal with high-level abstractions, tons of literature and terabytes of data. It does not teach us how to deal with rudeness, aggression or neglect. It is OK to feel insecure, lost and paralyzed when these things first happen to you. You don't know what to do, because, ideally, you don't have to. There is no place for rude and humiliating behaviour in civil society, particularly in workplace, and academia is not an exception here. A statement that academia is somehow more prone to bullying can be only explained by very limited experience outside academia.
So yes, bad things should not happen, but unfortunately, they do. Bullying still happens in many countries, job sectors, environments. It does happen in academia, too. What can we do when it happens to us?
Before anything remember that you are not alone. Universities do have systems in place to help any student and staff who feels uncomfortable and threatened in their workplace. These people are not immediately obvious, but it is easy to find them as soon as you decide that you need to.
However, before you do, take a deep breath and try to make a clear record of the situation. Is this person really a bully? Cultural norms may differ from place to place, and many things which are "normal" in some country can be considered  extremely rude in another. Examples include putting feet on chairs and tables, pushing someone's shoulder to say hi and bye, cleaning nose in public, cutting fingernails in public, asking personal questions, asking difficult questions, interrupting someone's speaking — add yours! If a person is doing something that is offensive or unpleasant to you, it may be not because they are a bully, but sometimes, perhaps, because they have a different understanding of a norm. It may be hard to talk with them about it directly (although it is often the best way to clarify things), but remember that you are not alone and you can seek help here. Just don't assume bad intentions when there are maybe none.
Your supervisor seems to "ignore" the problem, which may or may not be so. She may have a different perception of it, and genuinely be unaware of your feelings. You should consider making an appointment with her and formally discuss this. She may be the best person to correct the unwanted behaviour. It is quite possible that she is also not happy with this behaviour, but for some reason prefers to let it slide as soon as no-one is harmed. It is true that people often do not start the fight only because it is a right thing to do. People sometimes need better reason, and you should make your feelings known to give her this reason.
If talking to your PI does not change things, go to the Head of Department and talk to them. It is their job to help you solve the problem. They may need to use their power on your PI, but in many cases it is not necessary, as there are already systems in place to delicately solve such issues. But if you remain silent about the problem, these support systems can not help you.

tl;dr: Academia is hardly a paradise for anyone; it is definitely not a paradise for bullies. You are not alone. Talk to your PI and HoD to seek help and solve the issue. Good luck.

It is unlikely you can fight this culture, and academic settings have practically no good ways to address bullying of this nature. If you find what seems to be one, look for evidence that it has worked for past students. Recently.
Alternately, make the bully your friend. This is not advisable.  Alternately, work with people the bully cannot impact, which is a version of leaving. This may be unavailable, depending on your situation.
Calling out this bully may help, but if it does not it will make you a target.  Again, it is highly unlikely your institution has any kind of meaningful recourse available.
Your best strategy? Leave. Keep your head down, and start planning your exit now. After you have an exit, cite the bully as the reason to both your PI and HR; it may help others.

I really wish there were better answers. Academe is such a paradise for bullies....

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Can you defend your thesis without any slide presentation?
You speak and present your thesis without a slide presentation, probably with a pen to explain something on the board. This question came to mind when I was wondering "why do we need a slide presentation?" and "have all thesis defenses in the world been done using a slide presentation?" and "will you be penalized if you defend your thesis without a slide presentation?".

Clearly your field isn't pure mathematics.

Where are you? As well as which field? In the UK, in physical sciences, a presentation isn't the norm, for example

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If the answer were: "In 2016, a congress with representatives from all universities and colleges in the world reached a consensus that is unprecedented in the history of science. Liberal arts, natural sciences, applied sciences, law and medical schools agreed that in order to guarantee a globally comparable quality of postgraduate qualification, all PHDs and doctor titles had to be defended using Microsoft PowerPoint in a version not smaller than 15.0, from 01/01/2017 0:00 UTC on." Would you believe that? If not, the answer must logically be "no", and I must ask back: Why are you asking?

Of course, slide presentations are a very recent development. Even the humble overhead projector didn't exist when I defended. We wrote with chalk on a slate like material.
Yes, you can do a presentation without slides. In some ways you can make a better presentation unless you are very skilled with slide creation. Most slide presentations are incredibly boring. They have been described, somewhat accurately, as the private notes that a speaker would normally keep to themself rather than making them visible. I know a couple of people who can do a good job, but it is, in my view a poor technology in general.
However, the expectations of your audience should be taken into account. If they expect slides, then you should probably do it that way. If you distribute the slides, printed perhaps, before the presentation then the audience has a place to take "notes in context". So, the "penalized" question is an entirely local one. Make sure you understand the local expectations. And, don't be boring.

At one university where I studied, the chalk boards were actually slate and there was a chalk tray at the bottom. The classrooms were very seldom cleaned and after several weeks a small cone of chalk dust would be growing on the floor just below the end of the tray.
Since the boards were seldom washed, just dry wiped, it sometimes occurred that the writing on the board would start to slide down the board on the "lubrication" of the still remaining dust from earlier uses. It would get distorted as it slid, of course.

I wish I could upvote that +100: "Most slide presentations are incredibly boring. They have been described, somewhat accurately, as the private notes that a speaker would normally keep to themself rather than making them visible." One of the best talks I saw was one where the speaker spoke for two hours and ten minutes. The first slide with a diagram appeared 45 minutes into the talk. Another one developed a mathematical field on the board, like a puzzle, filling in the gaps, and the talk ended with filling a hole left in one location on the board, by a new theorem that the speaker discovered.

Disagree that slide presentations are a "poor technology". People just don't know how to make good slides. Slides need to give small bits of information or show graphics/figures. If you spend 3 minutes on a slide, you should be able to read the contents of the slide in 30 seconds or less.
I see too many people put long proofs on slides - if people want the full proof, they'll read your paper. And putting your "entire notes" on the slide is another big no no. These are basic presentation tips that many folks have never bothered to learn.

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It depends on the field.  If you have a lot of data to show, will be hard without slides.  The question could also be asked for lectures.

In the UK it is very rare to have slides in what we call a Viva, which serves the same purpose as a defense. In general, a viva last 2-3 hours, and for the first 10 minutes, the candidate will describe their "thesis" - i.e. what it is they are claiming we know now, that we didn't know before they started. The rest of the 2 hours 50 minutes is the examiners (panel members) challenging them, and asking questions about their work.

I have seen people doing the work on the chalk board or in some countries they sit down together and go over the pages of your draft. Then again, in a formal setting where you have to present your work with a time constraint you might not be able to cover everything you did without slides.

A little bit of a different perspective here - public speaking in general vs. a thesis presentation. But I believe the same things that work in one type of speech work in another. Obviously the expectations of your particular field, your university/department and your advisor are most critical. But assuming that you are either expected or encouraged to have a slide presentation, here are a few things that I have learned from Toastmasters over the past few years. If you have not tried Toastmasters, I highly recommend it. Nearly all clubs are virtual (Zoom, etc.) right now and most encourage guests.

Keep the number of slides to a minimum. I'd suggest no more than one per minute, and that is for a short (5 - 15 minute) speech. For a longer speech, such as a thesis, you might have a handful going over key points and then spend most of the time explaining your thesis with perhaps a slide every 5 - 10 minutes.
Keep the slides simple. 1 - 3 images and/or 5 - 10 lines of text. Sometimes even just 1 picture and 1 line of text is enough. This helps accentuate key points and also keep people from spending their time trying to read everything when they should be listening to you speak.
Do NOT hand out the slides (paper or email) in advance, unless you are required to do so. Hand them out (or email them or send a link to download them) at the end of the presentation. Otherwise, 1/2 the people will be distracted by the slides in their hands (reviewing old slides or jumping ahead to the next one) instead of listening to you speak.
Pick a simple theme and stick to it. Colored border, simple graphic background, etc. Otherwise the background and other irrelevant stuff (unless your thesis is about graphic design) gets in the way of listening to you speak.
Practice, practice, practice! It is too easy (been there, done that) to use the slides as a crutch. Don't let that happen, especially on something as important as your thesis. In fact, practice it at least a few times without the slides. That will (a) help make sure you really know the speech well and (b) take care of the unlikely, but possible, situation of technical failure with the presentation (e.g., projector dies just as you get started).

I generally agree with everything here except "Do NOT hand out the slides". The printed (PRINTED) slides can be helpful as a place for notes. If the other advice is followed it shouldn't be a problem. And Toastmasters is also a good way for extremely introverted people to become more comfortable in public settings. The same for people on the autism spectrum.

Uh, 5-10 minutes per slides... Here they urge students to manage to stay within 30 minutes. So much in this topic depends on local specifics. The UK viva mentioned elsewhere are even more different. FWIW I do not recall ever seeing someone handing out slides.

A lot depends on local specifics and a lot depends on the subject matter. As far as handing out slides, that is quite common in some places.

My PhD advisor demands a presentation without slides even though we are in a field that works with a lot of images, for example from electron microscopy. We only have a blackboard/whiteboard. There was only one exception where an industry partner wanted a powerpoint presentation. This was continued even during the pandemic, so that we have to draw on a tablet or something similar instead of showing prepared slides. My advisor's reason for doing so is that without images, the defendant has to focus more on the ideas and abstract concepts of his work instead of showing one sample after the other.
So I agree with the other answers, that this is very much a cultural thing, and not even necessarily determined be the field. Speak to your advisor.

Yes, it is certainly possible.  One of the good things about starting a viva with a brief talk is not to transfer useful information (we have already read the thesis very carefully) but to give the candidate a chance to get "warmed up" and deal with any nerves they may have.  So I would be happy with whatever form of presentation suited the candidate, it is largely for their benefit.  It is perfectly reasonable to have some nerves* and few people are ready to answer difficult questions right from the start.  For similar reasons, I often make sure that early in the viva I have prepared a question that has an easy but non-trivial answer.
I also advise my students to pre-prepare some slides containing any diagrams etc. that they think they may need during the viva even if they are not intending to use them in the initial presentation.
* just occasionally** there has been a candidate for which I wasn't completely nerveless myself ;o)
** they usually end up being the best vivas ;o)

I have been the independent chair of a successful PhD thesis defence (within the past few years) where the only visual aids were a couple of pieces of paper. However, that's just one, compared to a lot that did use slides.

authors: Vladimir F Героям слава


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Nice vs. ugly numbers in homework and tests
This question revolves around using integers (−1, 0, 1, 2, 3) or simple fractions (½, ⅓, ⅗) vs. real numbers (−1.254, 42.72) in teaching concepts, assigning homework, and preparing tests for math, science, or engineering. For the rest of this question, I will call integer or simple fractions nice and real numbers ugly.
For the sake of simplicity, let’s say that you are teaching a math class, and the first topic is basic addition. The first time that you teach it, I would assume that you would want to teach it using nice numbers. For example, using 2 + 2 = 4 would be preferred over 1.234 + 5.678 = 6.912. Sometimes you can get lost in the weeds of the calculations ("just plug these numbers in here and get the answer out") and completely miss the concepts. While concepts are important, it is important for the students to be able to apply the concepts for more complicated problems. While part of me thinks that learning concepts should be the same for nice numbers and ugly numbers, my personal experience says that there is a difference (perhaps just a small one) between these two.
In order to facilitate better learning and better application of course material to real-world problems, should you also include homework with ugly number inputs and answers? How about tests? During my engineering studies, it seemed like there were lots of problems that had nice inputs and/or answers. Most of the questions did not have really ugly answers. Is this typically done to make it better for the students learning, or is this done to make grading easier? Perhaps calculator use can also influence the type of number being used too. Overall, it would be nice to understand why professors and/or teachers often select nice numbers for assignments.
If it would help to know, the main drive of this question is that I would like to automate some of the homework or maybe even tests for classes. I would like to be able to generate multiple versions of homework or tests so that students can’t simply copy answers from each other. If I am generating homework, it might be tricky to find nice solutions vs ugly solutions. I think I have a method for automatic grading, so that is not a problem. The main thing that I want to maintain is a good learning experience for students.
Note on π and other irrational numbers: For my studies, π was of course in lots of the problems, and this technically makes problems have answers that are irrational. For most problems, it is acceptable to include the symbol π in the answer instead of including the numerical form in calculations. These problems could be still written nicely with implied multiplication like 2π or 3π/5.

While I do not think that your question is off-topic here, it is almost certainly better suited for [matheducators.se]. In fact, a duplicate already exists.

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I am a physics student, so I am naturally inclined to despise working with ugly numbers [I  prefer letters :) ]. However, I remember being frustrated when I was younger to show my work when working with hard numbers. Writing down a bunch of decimals was so frustrating when anyways I was going to put it into a calculator, and so I would just write the final answer without showing any work. When one is working with nice numbers, showing the work is much easier and clearer.

I think I'm going to be fundamentally disagreeing with a lot of the answers here.
Nice numbers definitely make problems easier, and I make a habit of using them when first introducing a concept; they make the students more comfortable, and let them focus on the key idea that I'm trying to teach. But I never rely on nice numbers for tests or assignments. There's three major reasons here:

I have had many students over the years who genuinely stop understanding a concept when presented with "ugly" numbers. For example, I've had students who can easily find the average of 2 and 6 but when asked to find the average of 2.3 and 6.7 don't even know how to start. This isn't an issue of getting confused by the calculations; it's that they think about "nice" numbers differently than they think about "ugly" ones. In the case of the average, the issue was probably that the student in question thought of the average as "the number in the middle", not "the sum divided by two", which makes sense when working with integers but not otherwise. The problem is that you can't capture failures of comprehension like this without using ugly numbers at least occasionally.
Not a grad student and Per Alexandersson pointed out that many students use the "nice number" test to tell whether their answer is right - they tend to trust the answer if they get "2", not so much if they get "2.134". So from the perspective of "be nice to your students", you should use nice numbers; but the thing is that, in literally any application they will have for this material later in life, they won't be working with problems that were carefully curated to produce nice numbers. If you're teaching them something you expect them to use later, it's a disservice to allow them to continue to use the "nice number" test.
Loosely speaking, there are far fewer "nice" numbers than "ugly" ones. I've had students "solve" problems by assuming the answer will be a whole number and then guess-and-checking their way to success.

That said, if you're using ugly numbers, you do need to make some concessions to make that work. Here's what I do:

I allow scientific (not graphing) calculators on every assignment and test.
I allow unsimplified answers, except when the problem is about simplification; so, they're welcome to leave their answer as a complicated mess of radicals if they want to.
I warn them specifically that the numbers involved in some problems may be messy, and I go through "messy" problems in class.
I take some class time to teach techniques for judging whether your answer is correct that don't rely on niceness of number; my preferred one is "ballparking", where you use the context of the question to estimate the general size of the answer (is it positive or negative? Bigger than a thousand? Etc.).
Problems that involve ugly numbers tend to take longer than ones that involve nice numbers - even I find that I go slower when a problem involves weird fractions or decimals. Take that into account when writing tests.
Problems that involve ugly numbers are more prone to minor error than ones that involve nice numbers; for example, you probably don't want to be counting an answer in a calculus class as "completely wrong" because they typed "2.146" instead of "2.156" into their calculator. I always offer extensive partial credit based on work shown, and do not generally mark off for errors that don't show a lack of comprehension or change the difficulty of the problem. For online tests, to make this work, I allow students to submit their work alongside their answers.

One other point: at least in science students should also round their result to the correct number of significant digits (+-1 or so). (Doing proper uncertainty propagation is usually too time consuming, unless that is exactly what they should learn in that course.) They won't learn that skill if all numbers are always "nice".

"I have had many students over the years who genuinely stop understanding a concept when presented with "ugly" numbers."
I've seen similar. I remember a classmate who couldn't figure out what the derivative of pi is.

Personally I think nice numbers are best used in Mathematics instruction and ugly numbers in Science and Engineering classes, but otherwise I think this is a great answer. One thing interesting to me is that when averaging, I would say 2.3 and 6.7 are quite nice numbers, as 3+7=10, and of course pi and e are very nice numbers, despite being transcendental.

+1 Make sure to tell students that you are no longer using nice numbers in exams when previously you taught the material using nice numbers.

+1 for the 6th point, and yes, as a physics & mathematics student, I definitely agree with the above answer.

in literally any application they will have for this material later in life, in most cases never...

(4) is a surprisingly useful life skill -- not just for double-checking calculations, but checking data analyses and even framing business decisions ("is this likely to be worth our time?").

I disagree with your point (2).  A professional should check his answers using methods that are not in the scope of a math class, let alone appropriate for a mathematics exam.  If, during the course of a math test, I found that an integral turned into an ugly number, I might move on and try it again if I have time.  If I found it ended up being $\sqrt{\pi}$, I'd make a quick double check of sign errors and the like and just move on. I have taken exams where virtually every question uses ugly numbers, and forced us to use sigfigs, etc.  Having to practice calculator discipline was wasteful.

@nomen I'm not sure I understand your position here. Are you saying that, in a math class, one shouldn't be teaching the techniques for checking answers that are appropriate in practice? The strategy you describe is a good strategy for taking tests; but I'm not preparing my students to take tests, I'm preparing them to solve problems. If a student double-checks their work because an answer was unexpectedly messy, that's fine; but if a student believes that they're wrong just because an answer was messy, I haven't prepared them for real problems.

@Reese: calculator discipline is rarely relevant to any kind of modern practice.  We use computers now.  And we use different techniques for checking a solution than doing the problem over again, which is frequently/usually the only option on a test question that tells us to "simplify" or similar.  So what is being tested?  That we can push the buttons fast enough?  It's pointless.  I'd rather do another interesting homework problem than spend 3 hours practicing button pressing.

@nomen I'm sorry, I still don't understand. A computer is essentially a highly powered calculator; it is exactly as prone to basic typing mistakes as a calculator is. And you're correct to say that a test that is entirely pressing buttons on a calculator would be a waste of time; such a test would have to be entirely arithmetic, and it's not appropriate to allow calculators on an arithmetic test. In a test at the level of algebra or above, even involving "messy" numbers, calculator work will at most cost a few extra minutes. As for what is being tested, I think I was clear in #1.

@Reese: "essentially" does not mean "is".  A computer typically is programmed using a high level language, and any syntactic error results in an error or crash, not a fake and wrong answer.  A computer also allows the expression of logic in a calculation, which means that the results of calculations can be passed around implicitly, rather than rekeyed.  Calculator mistakes happen, and can you really remember if you used x or y or t for that last variable?  A calculator, on the other hand, will give a fake and wrong answer for a typical typo.

@Reese: furthermore, why even waste those "few minutes" (per question!) on mechanical button pushing, when that hour could be used to demonstrate mastery of useful technique?  No one thinks I can't do polar coordinates because the test answer was pi^2 / 6.  In fact, my answer demonstrated mastery.

@nomen I see. I'm pleased to hear that messy numbers apparently do not harm your comprehension of mathematical techniques; that was the case for me as a student, as well, and it's been a useful skill. However, as I stated in #1 in my original answer, in my experience that is not the case for many students. I will also point out that in #2 above, I explicitly give the option of "pass[ing] around implicitly"; in #6 above, I explicitly discuss partial or even full credit for minor calculator mistakes. Finally, when I said a "few minutes" I meant a few minutes, not per question.

@Reese: As long as the policy is sane, fine.  Here's where I'm coming from:  I have taken a few professional exams where you get 6 minutes per problem, analysis takes 3-5, and doing the calculator takes 2-3.  They're testing something (like time management), in addition to mastery, but at a cost to the demonstration of mastery.  And the reality is that a professional would be using automated testing methods, under much looser tight time constraints than a student taking a calculus final.  So I'd much rather see "notable" numbers than not, especially since the college tests were such a joy.

You write "I think I have a method for automatic grading, so that is not a problem.". If you are going to depend on automatic grading, you should use easy, simple numbers.
There are two ways of getting a wrong answer, not getting the method right and making a mistake copying from question to calculator and from calculator to answer sheet. During manual grading you can distinguish those by requiring the students to show their work and grading that. Automatic grading tends to give the same weight to not knowing how to do a calculation and entering one incorrect digit.
Using simple, easily checked numbers reduces the risk of calculator error.

Nice observation and it's challenged me to find the wrinkle here. At some point any answer, no matter how simple, has a possibility of transcription errors. So I'd argue there's a continuum and you basically need to pick how much precision/rounding is required in the submitted answer. This is directly supported by LMS platforms, and interfaces particularly well with the OP's engineering focus.

By automatic grading, I mean to say that questions would be marked correct or incorrect. If a question was marked incorrect, I think it would be important to go over the question to see where the student had a mistake and give partial credit if required. Even if the answer was marked correct, I would plan on randomly sampling some tests to see how students showed their work.

Please see o.m.'s answer for why your objection to automatic grading is incorrect; calculator error can be eliminated by providing enough ugly answers as options.

While part of me thinks that learning concepts should be the same for nice numbers and ugly numbers, my personal experience says that there is a difference (perhaps just a small one) between these two.

I'd expect a difference: Ugly numbers get in the way of applying and learning a concept. E.g., average (−1, 0, 1, 2, 3), (½, ⅓, ⅗), and (−1.254, 42.72). The first I can do in my head, simply by applying the concept of averaging, the addition is trivial, the division easy, I'm just thinking about the concept. For the others, I'm not think about the concept, I'm think about fractions and more complex addition/division.

In order to facilitate better learning and better application of course material to real-world problems, should you also include homework with ugly number inputs and answers?

I've just argued that ugly numbers are a barrier to learning, so nice numbers are preferable, imo.

How about tests?

The same. (Plus, do students have calculators?)

Ultimately, it depends what you're trying to teach.

@zabop ;-) Although: Complex numbers are a barrier to learning! (Edited and fixed, thanks.)

I always liked tests and homework that you could complete without using a calculator.

A computer science professor of mine would often say that since “we can name our variables anything, we’ll call this one Fred”. It made following a day’s lesson one step even further away from easy comprehension.

-1 Handling 'ugly' numbers is an important part of learning how to do these sorts of problems. Sure, it's best to start with 'nice' numbers when going through a new concept, but I genuinely believed as a teenager that if I didn't get a 'nice' looking number (or expression for that matter) out of the problem, that I had made a mistake somewhere along the way. This included for calculations I was doing in my own spare time which wouldn't have been 'coerced' into niceness by the problem setter. It took me a while to train myself out of this pattern.

When working out the average of (-1, 0, 1, 2, 3) I observed that they were a linear progression and just picked the middle number, doing no addition or division. This is a good example of numbers that can be too nice. You want to make sure that the easiest possible path to a correct solution is the path you're trying to teach.

@Ingolifs Indeed: Ultimately, it depends what you're trying to teach.

Since this is a website about higher education, I will answer in that context.
The only "difficult" thing about "ugly" numbers is doing concrete basic operations with them, like adding them and so on. Everything up to that is typically done algebraically using variables (x, y, z…). University students are already supposed to know how to perform basic arithmetic, even with "ugly" numbers. This is never what you want to teach in higher education. So either let your students use a calculator, or use "pretty" numbers in your data. If you are concerned about real-world applicability, then surely you know that today everyone who has to perform this kind of tasks works with a computer that is hugely more capable of performing mathematical computations than any human.
As for computer-generated homework questions, I have had the unfortunate duty of doing it last Spring, like many of us, I guess. It was not particularly hard to produce "pretty" numbers, even when I needed to produce complicated linear systems to solve for example. Make it so that your question depends on a few parameters (let's say 3-5) and make sure that these parameters are taken to be integers in a reasonable range (for example [-5,5]). Then unless you get crazy with how you derive questions from parameters, you will mainly get "pretty" numbers. And since I assume that you wouldn't dare giving a question to students that you haven't even looked at, when you do a cursory check of the automatically generated questions you would quickly pick up bad edge cases.

Certainly when teaching college-level mathematics, such as abstract algebra, linear algebra, probability, discrete math (including combinatorics), and analysis, I don't see any benefit to using ugly numbers in problems. The concepts are challenging enough and the numbers will quickly become "interesting" if not "nice", such as pi, e, the square root of 2, the cardinality of the natural numbers, and the cardinality of the reals. For most of my college math, there were no numbers, nice or ugly, there were mainly true/false, definitions, and proofs on tests.

I want one question on the test to have ugly numbers, since I want students to learn to trust their calculations, and not use "the answer is a nice number" as a verification method. Ugly numbers are great for teaching you to trust the method and the knowledge. But most of the time, they are simply annoying.

But trusting ugly numbers doesn't equal trusting the method, it equals trusting your calculations - something which very easily can go wrong sometimes even for the best of us, especially with more ugly numbers, even if you applied the method 100% correctly. I'd argue that it's better to have clean numbers so students don't have to go over their calculations 1:1 every time just to be safe.

But doing the calculations is applying the method. And what is good about making your students not have to check their working?

I'm not an educator. I'm simply a math graduate working in related industry but my answer would be a hard no-no on nice numbers. Some answers claim that makes students use intuition to know whether the result is correct. There is absolutely no scenario where intutition is a good verification for the result you get (not saying it's useless for choosing the right method of calculation).
You absolutely do not want to teach students to rely on the result being nice. Another answer mentions that using them gets rid of the need to verify their calculations. This is an absolutely crucial step, you should always verify your calculation at least once. It is a process that never has any drawback.
Otherwise you might hear news stories like "building collapse kill 50 people because civic engineer made a mistake but the number looked nice so he didn't check again".
EDIT: I actually more often checked my calculations when the result was actually nice. If it wasn't then I assumed that I have used the best method I could think of and the worst that could happen was loosing a point for the wrong result.
Luckily I mostly had professors and teachers that graded the method, not the result.
EDIT 2: You want to teach your students to think of a solution, not how to game the system. Those same students might learn to later look for legal loopholes to deliver a half completed and sometimes dangerous product instead of doing the expected (see dieselgate scandal, why work on the solution when you can just game the result).

What kind of students are you teaching?  If you are teaching elementary or high school students, then use the kind of numbers that are appropriate to your curriculum.  If you are teaching engineering students, then you should use real world numbers.
You say "During my engineering studies, it seemed like there were lots of problems that had nice inputs and/or answers.".  Wow, what kind of engineering did you study.  After halfway through my first real engineering class, just about every problem I did had no tidy solution - we used trial and error to solve nearly every problem (on first generation programmable calculators (think HP-25)).  The numbers made sense - a heat exchanger might be rated 100,000 BTU/hr, for example, not some oddball number.  But the pipes going in to that equipment might be 4 inch schedule 40 (which are 4.026 inch inside diameter - I always had a pipe schedule booklet handy, along with steam tables in my bag).  When I used the ideal gas constant R, I always used a version with 5 significant digits (and I could rattle those values of R off in 4 or 5 different unit systems - I studied in Canada in the middle of the transition from Imperial to metric units).
When teaching, you want to use numbers that challenge your student to think and to be unafraid to solve the problems that they will see when they do their senior design project or when they get their first job.  There's no sense using numbers with much more precision than they will see in real problems, but you are cheating them if you make everything too "cute" by having problems that feature integers as inputs, and particularly integers as outputs.
If you really want to challenge them (and get them understanding the numbers they are using), get them to buy or borrow a slide rule and give them a "no calculators allowed" test (by the way, if you do that, you probably want to make sure that the problems are reasonably easy to solve using a slide rule - lots of multiplications and divisions and little else).

On a test, you don't want students to be always unsure if they got the right or wrong answer when it comes to algebra, so generally nice numbers are preferred. Also, if you just want to test them on knowing the basic methods and you assume that they can work with more complicated numbers, making the numbers messy is a distraction. At the very least you need to give the students an idea of what to expect. If all but one of the answers have nice answers and the other one has a messy answer, the students who get the messy (but correct) answer will spend all their time double-checking their algebra, when they could be spending their time on other problems.
On HW then I think messy numbers are fine, but I think that writing "Round your answer to the nearest hundredth" would be appropriate.
For lower-level classes, though, using some messy numbers at some point on HW is a good idea. Once during a final exam for precalculus, a student thought that she messed up on finding a vertical asymptote because she got a number that wasn't an integer. Apparently vertical asymptotes can only happen at integer values. Well, she looked again at her work and had a flash of insight when she found her mistake and got that the asymptote was in fact at an integer value.

I’m in the habit of giving mostly nice numbers of assignments and tests.  As “mostly nice” number is Sqrt[2], or Log[6] or e^7, for instance.  This way students can provide answers in exact form (without floating point) without too much difficulty.
I would stay away from things like Sqrt[1+Sqrt[2]]$ which I consider truly ugly. The students know this so if they get an answer like Sqrt[21/213] they suspect there’s probably some bug in their calculation.
Now I also have in some courses assignments questions which are entirely numerical (v.g. plotting some solutions to some nonlinear differential equations).  Even in those cases I will try to find “nice” boundary conditions so that the students can verify if their intuition matches the numerical output.

The the kids are missing out on $$\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1+\dotsc}}}}$$ and the (sad but definitely not ugly) story of Srinivasa Ramanujan?  The reason most folks "hate" math is because, unlike art or literature, teachers of math often forget to pepper their teaching of the human dimension and the fascinating neuroscience that works behind our mathematical thinking. https://www.youtube.com/watch?v=leFep9yt3JY

It has been suggested that I should turn my comment into an answer.

Use 'ugly' numbers for an entire page of assignments.
Take all the results and add a few more 'ugly' numbers as distractors. List them of the bottom of the worksheet.

That means students will practice to work with 'ugly' numbers. They can easily verify that there was no arithmetic error by finding their result in the list, yet guessing will not get a passing grade. If the number is not in the list, the first step is to check if they mistyped on their calculator or got their sums wrong.

There is a pedagogic advantage in using ugly numbers: users will try to avoid them and teach themselves algebra in the process by maninpulating symbols instead of specific integers, fractions or decimal expansions.  The idea is that you simplify the expression as much as you can before plugging in the actual figures.
So it really depends on what you're trying to teach.
By the way, what you call "real" number is referred to as a "decimals of nonintegers", which is a pretty ugly name, as -1, 0, 1/2 or 1 are real numbers too.

Unless the point of the homework is to test them on their ability to do basic arithmetic, why not give variables rather than numbers, and the answer should be an expression in terms of those variables.
Going from that to a numerical answer is just some easy but tedious arithmetical calculations.

Using nicer numbers allow calculation in tests to be more fluid. I think this is generally a good thing.
However there are sometimes situations where you explicitly want to teach the basics of symbolic calculations, where for example rational numbers like 1/3 ensure that the task cannot be solved numerically without leading precision. Sometimes with trigonometry questions they might rely on the fact that intermediate results are expressed in pi fractions.
One of the examples mentioned that when asking for the average of numbers, that 2.3 and 6.7 would better test the understanding than nice numbers. However I would argue that those are actually nice numbers as they add to a round number and can easily divide by 2, so the result is a clear 4.5 with no need for calculator or risk of rounding error.


text:
Applying for a postdoc. Should I mention that I completed my PhD with no supervision?
I'm hopefully in the last half a year or so of my Ph.D. in a subfield of mathematics/theoretical physics and am considering applying for a postdoc within the next three months.
My supervisor works (partly) on field X, and I've pursued my Ph.D. in the direction of subfield Y (with the thumbs-up from my supervisor) – however, my supervisor neither has experience in subfield Y nor much familiarity with the type of mathematics involved. Furthermore, my supervisor is the only person working on field X at my institution.
I've therefore been working with zero direction/advice from my supervisor (I like them, I'm not complaining!) – essentially complete research freedom (which I guess is strange for a typical Ph.D. experience). Of course, this has its pros and cons. The cons mainly consist of working in complete isolation (internet aside) without any supervision in the traditional sense, and with no people in area X (let alone Y) to talk to – my own doing, I know it's what I effectively signed up for! This has been slightly daunting at times (given I had zero research experience before the Ph.D.); it's been 99% laissez-faire.
I have managed to attend a few relevant workshops. The discussions there have been great and have often left me feeling positive/excited about research – I guess if I managed to secure a postdoc in an environment with a group of people in field X (even better with some in field Y), I'd get to experience the stimulation/collaboration experiences that I've thus far missed out on.
The question: When applying for a postdoc, should  I mention any of the above? I'm not sure if having done the Ph.D. in field Y in 'isolation' will be a mark for or against me. If I should mention it, what would be the best way (roughly) to word things?

essentially complete research freedom (which I guess is strange for a typical PhD experience) - It's not that uncommon, and the situation should be clear from your reference letters.

I don't mean this as a negative, but just for students in a similar situation who are still in grad school and reading this: I would be much more impressed if you had initiated connections with researchers in area Y (outside your institution) and then learned from and published research with them.  That shows some important skills that will serve you well later in your research career.

Just to be clear: Supervision does not necessarily mean supervision om the research field. There are lots of supervising task that do not require knowledge of the field, but of management. Help you get on track of writing chapters, going to conferences, meeting people, etc. Did your supervisor not help with any of that either, or did them only not help with that particular subfield of maths? Because if its only the latter I'd say you still got plenty supervision

Be positive about the situation, above all.  To get a PhD it is assumed that a) you can do research on your own b) that you are willing and able to work under supervision, and usually with some sort of team-format.  To the extent you worked with others (labs, any TA work, etc) emphasize that as well as your ability to do things on your own!

@AnderBiguri I know, I didn't receive any help/guidance with any of those things either. It honestly has been "99% laissez-faire"!

Just a wonder... if your nominal supervisor doesn't understand the area you are working in, who is going to be authoritative in examining your work?

@houninym 2-3 external referees/examiners

If your subject is sufficiently obscure (i.e. not currently overrun), everybody in it will know that your supervisor had no clue what you were doing. ;)

@Karl True that!

I don't think having an advisor working on X while you are doing you PhD on Y is that much problematic, but "no people in area X (let alone Y) to talk to" would be a serious killing blow for me.

Should I mention that I completed my Ph.D. with no supervision?

Definitely not.  "I had no supervision during my PhD." could be interpreted as "Nobody taught me anything during my Ph.D. so I am unqualified." or "I am incapable of giving credit to other people who deserve it." or "I am so obnoxious my supervisor will not interact with me." or "I refuse to work with others."  It is likely none of these are true, but the misinterpretation is a possibility.
What should happen is that your supervisor writes a letter of recommendation saying that you have shown a high degree of independence and that you now have more expertise in Y than they do.

Thanks, those are great points. I have a good relationship with my supervisor, I'm sure they'll make my case in a way that highlights the pertinent points in a recommendation letter. "Nobody taught me anything during my PhD so I am unqualified." That is a scary thought.

@CoderInNetwork If it were me, with my best intentions, all I could get from that sentence is: "So... The faculty doesn't care about its students? Why did this person put this sentence here? What's the purpose? I should ask."

@CoderInNetwork if you get a recommendation letter through from a supervisor who clearly worked with the student and the student has claimed to have done everything alone what would your conclusions be about the situation? Would sound like an inability to give credit to me.

Where you write X you mean Y, right?

@Vincent No. When someone says: "There was no elephant in the room.", I start to wonder - wait, I never thought about that - should there have been an elephant? Is there usually an elephant? Did they expect an elephant? Are they disappointed that they could not shoot some ivory? Has china been broken and they are looking for an elephant to blame? Is there actually an elephant in the room and they try to divert me from the fact by denying it? In the moment you state something highly unexpected, the attention level towards relevant ramifications increases significantly.

My comment seems a bit mysterious now as the Anonymous Physicist changed X to Y and so there is no X anymore. @CaptainEmacs: I agree that it would be helpful if the advisor, who is an expert in X, would say something highly unexpected like the candidate now having more experience in X than they do. However I also don't expect that that is going to happen, especially if it is not true. The applicant having more expertise in Y than their adviser might actually be true given the original post so, like the Anonymous Physicist, I can imagine that they would write that and agree that it would help.

@Vincent Hopefully a good PhD student should have more expertise in their particular subfield than their adviser. That's the whole point of a PhD. If the adviser has no expertise at all, though, this is quite a meaningless lower bound, though. Why point it out?

Tread carefully to avoid a doesn't play well with others impression.
I was in a somewhat similar situation (Ph.D. supervisor in a different area), although I had plenty of contacts in my own area. In my applications, I never explicitly brought this up but did claim that I was rather independent in setting and pursuing my research goals. The evidence I brought up was here's some single-author paper and here's a bunch of papers coauthored with all sorts of different people. I left it to the letter from my supervisor to say anything more because he is in a much better position to put this positively.

Certainly one of the things I'm keen to avoid - thing is, I just haven't had a chance to coauthor a paper (would really like to if the opportunity arose), so my papers are single author.

Let your supervisor comment on your remarkable independence in their letter.

@user2705196 This should be the answer.

You shouldn’t say it, because it’s not true.
Of course, I’m guessing here and this isn’t based on any specific information in your post, but “my supervisor didn’t advise me on the mathematics in my thesis” is not the same as “I received no supervision”.
I am fairly confident that your supervisor taught you many things about X, the philosophy of doing research in math/theoretical physics, career advice, productivity and writing tips, and probably other things. Those workshops you attended - how did you hear about them? How did you obtain funding to attend them? Was your supervisor really so “laissez faire” that they gave you no assistance whatsoever related to anything that you can attribute your success to? (In that case, in what sense were they your “supervisor”? And why do you like them?)
To summarize: I congratulate you on your independence, but this quality is best attested to by others. Be mindful of how things you say about yourself are perceived by others. When you say you received “no supervision”, it sounds like you’re saying you got no help. But everyone gets some help along the way, and denying that, or appearing to deny it, makes you sound petty and ungrateful.

Oof. No, we never really talk about technicalities in field X / productivity and writing tips. Found the workshops using Google  / through contacts made at previous workshops - funding through the project of course. I like my supervisor because we get on well (more like friends) - but still absent in the ways you mentioned. This question wasn't meant to be a complaint - it was just a question as to if/how I should word the independence of anything I've done. The answers have been eye-opening to say the least !

Thanks for your response though - like others, it does an effective job at illustrating how me claiming the above could really backfire!

@Meths ok, evidently I guessed wrong then, sorry for that. It’s still the kind of guess that others may make as well if you aren’t careful to not give them reasons to make such a guess. Good luck with your job apps in any case!

Nothing to apologise for whatsoever - totally legit answer, applicable for others who might chance upon this question and "It’s still the kind of guess that others may make as well if you aren’t careful to not give them reasons to make such a guess" - definitely! Thank you.

I think a careful inspection on your supervisor and your PhD subject/publications will reveal the truth. Therefore, no need to explicitly express it but you can mention it in your application.

When applying for a postdoc, should I mention any of the above?

I was in the same boat as you, one leg in one discipline, another one in a completely different one. I had one thesis director but the referees were from both fields. I also had the opportunity to discuss with them in the course of my PhD.
The experience was amazing. I made sure to highlight exactly this: the opportunity to be responsible, engage with people from different fields and end up with a thesis which bridged both. I was very grateful to all of them.
Turn it to your advantage by showing that you had a good time and that you are a team player

Excellent answer

The ability to work independently and attain significant accomplishments is noteworthy.  Your letters of recommendation should speak to your many qualities.  Your published contributions should speak to your research accomplishments and your ability to publish original work.
We are talking a form of a job interview here.  And people are hired not just for what they can do, but also for how they fit into an organization. If you are considering a place which values independent work, your story will work well for you.  On the other hand, if you are considering a place which operates with a tightly coupled team, there may be reservations.
Understand what the interests and expectations there are, and figure out how you can give them what they want, then sell it with as much evidence as you can extract from your past.

Do you have the experience, the knowledge and the expertise?
Was your thesis published and peer reviewed?
If so, what is the problem?
You need to sell you so think sales and marketing
Be honest in interviews and what you write down but no need to reveal details that do not affect your ability to do the job
I think you should keep it to yourself


text:
Conflict of interests of reviewing paper if I have talked to the author
I found an interesting poster during a workshop, and I had an engaging communication with the authors (even in a banquet). They told me that their work was just submitted to a journal.
Quite surprisingly, next day I received a review invitation from a journal editor, and the paper is exactly that of the poster in the workshop.
I am definitely keen on reviewing the paper, but is this a conflict of interests?

Is the review intended to be double-blind? A strict publisher might want to know you're not blinded in this particular case, although it's not terribly uncommon and I wouldn't expect it to be disqualifying in all cases.

You could email the editor and find out what they think? That would be my advice. While I am sure most answers here will probably be reasonable, and probably correct, only the editor of the journal will be able to tell you if it is definitely appropriate or not.

After a while in academia, you tend to know and talk to everyone in your subspecialty. People have sent me entire preprints to comment on before they submitted them... only for the journal to send me the submission for review. Once you are an expert in some niche, you are the logical person for both conversations and reviews. And no, I don't see a conflict of interest. (Plus, at some point you already have collaborated with pretty much everyone, at which point the question becomes a little more interesting, but then the editor is presumably aware of your earlier collaborations.)

Having talked to the author would make you biased, but not be a conflict of interest.

My one concerned is how well can you judge if the paper explains the concepts well enough for someone who are comming across them for 1st time.

Knowing the author whose paper you are reviewing does not imply any conflict. You have no reason to do anything other than what you should do in reviewing the paper, giving advice to the author and to the editor.
It would be different if you had a professional or personal relationship with them that goes beyond such a meeting. Such things could cloud your judgement, arising in a conflict.

But the catch is that if the communication is "engaging enough", doesn't this lead to a personal relationship?

If it is engaging enough that you've agreed to support it or collaborate, then yes. But if it just left you intrigued and wanting to know more, then no. You still are independent enough to make a judgement about the paper overall and in the details.

@null remember that many fields are so small that pretty much everyone knows each other, at the level you describe. If you cannot review the work of anyone you have ever met, then you either don't review at all, or you stay home and never attend a single conference.

No, I do not think that having a conversation about someone else's science with them creates a conflict of interest.
If you were collaborating with them or seeking to collaborate that might be a conflict. If uncertain, you can let the editor know but unless you have a problem reviewing you can still say you're willing to review the manuscript (e.g. "I haven't worked with these authors in the past or on this manuscript, but we've had conversations about a future collaboration. I'm willing to review the manuscript unless you feel this poses a conflict that should disqualify me.").
If you've offered them advice about the manuscript while it was in preparation you might let the editor know but I don't think it would make it necessary to exclude you from review (especially when editors are so often having trouble finding reviewers).
More generally, if you have any question it's fine to disclose to be on the safe side but not necessary to automatically recuse yourself.

To add to the other (excellent) answers:
I have noticed that junior researchers often overestimate the presence of a conflict of interest.
Many specialized research communities are, at the end of the day, quite small; a given paper may have only 5-10 people who are established experts in it. (And this is also a Good Thing; science progresses when people specialize, because we need different people working on different topics so as to not to overcrowd any one particular topic!)
What does this have to do with conflicts of interest? Well, given that there may only be 5-10 experts in some particular specialization, it follows that many of these experts know each other. In fact, they have probably seen each other at conferences, discussed each other's work, and reviewed each other's papers. But that does not mean that their reviews are biased. In fact, if they are truly experts, then they know the important problems in their field, what related work has already been done, and what results would constitute progress.
So the idea is simple: experts should try to review papers on their scientific merits alone (with clear arguments that can be independently vetted by the editor and by the other reviewers).
On the other hand, a conflict of interest is usually reserved for clearly problematic cases: such as between advisor/advisee, being a coauthor on a paper, any financial relationship (e.g. being at the same institution, or at the same company), or any close personal relationship (e.g., family, romantic relationship now or in the past, etc.).
Beyond these cases, you can still declare a conflict, but only if you think it is impossible for you to be unbiased (i.e. you can't evaluate the work on its own merits independently of its authors). This doesn't seem to be the case here.

While you may be able to remain objective in your review there could be a perceived conflict of interest if people were to find out you met the author previously, which could discredit your review. It is because of this that I think you should reach out to the publisher and let them know in advance that you met the author previously.


text:
Can I submit articles in top math journals from my master's thesis (after the defense)?
I am writing my master's thesis and my advisor is taking the total hands-off approach (I am mentioning that because I am still waiting to hear his feedback on the work when he reads it). He wants me to submit the thesis and defend it as soon as possible because there is a deadline for the master's program.
Q1: If I defend my thesis first, can I extract articles from it to be submitted to top math journals?
Q2: I have an idea that is an extension of one of the chapters in my thesis, and planning to work on it for a few months after my defense. Can I use multiple background sections from my master's thesis to be included in the second paper I wish to submit?
How can I ensure that my master's thesis will not be stolen in whole or in part after submitting it to my university/reading (or thesis) committee? - I may seem skeptical but, I live in a country where there are lots of people who may steal each other's work in whole or in part.

Did you get any external feedback leading you to believe it should be published in a top math journal? I am asking because most professional mathematicians don't publish even one paper in a top journal in their entire career.

How is this question relevant to my question? - I will hear from my advisor soon and I hope that it can be published. Either way, I won't lose anything if I submitted my work to a good journal. My field is computational mathematics. :)

One question worth exploring is whether your advisor should be co-author of papers emerging from your thesis. Even if the supervision was fairly hands-off, formulating the right problem can be an important contribution.

There is a pretty big difference between publishing in a top journal (something that, again, most mathematicians never achieve) and publishing in a good journal (something that a good mathematician achieves on a regular basis). From context I assume you simply mean the latter (i.e. submit to a solid, respected journal), but beware that there is a very significant gap between these two goals that can lead to some miscommunication.

Once you have submitted your master's thesis to the university, this is a form of publication.  You can also post it on arXiv.  If someone else submits your work to a journal, you have the timestamps to prove that your work was first.

Somebody told me that submitted university theses are "non-peer-reviewed" work, so it counts as work sample, but not really as a publication. Same with an unpublished arXiv preprint. (and, the older an arXiv preprint, the harder it is to get it published.)

The answers to your questions are:

Q1: Yes, you can definitely seek to publish worked based on your masters thesis after your defense, and there is no reason not to submit your work to top mathematics journals. The matter of whether it will be accepted for publication or not is much the same as it would be, were you to submit prior to your defense. However, see the additional comment below regarding "stealing".
Q2: Yes, you can use, and build on, the material in your thesis, and seek publication of that new material.

The question of how you stop people from "stealing" your work, is more difficult. Given your comments, it sounds as though the risk in your country increases in proportion to the number of people who are aware of your work, so you might simply try to limit the dissemination of your thesis until such time as you publish.
This also brings to mind the judgement call you will need to make in deciding where to submit your work. There is absolutely nothing wrong with submitting your work to the very best mathematics journals although it obviously makes most sense to submit your work to a journal that fits well with your subject matter and is of a standard commensurate with that which you believe your own work to be. However, it takes longer to be published in some journals than in others, even after the work is accepted. You will need to balance that issue against your concerns of the work being plagiarized or "stolen" prior to publishing it yourself.
Good luck.


text:
Is it normal to submit an abstract to a conference when the research is NOT completed?
I just started my 2nd semester of my part-time master, I was given a thesis topic last week and expected to submit an abstract this week.  Because advisor told me -> I would have not choice. However, I just wonder:
Is it normal to submit an abstract to a conference when the research is NOT completed? Or people normally completed the research then write the abstract?
I read a topic asking about how to write an abstract without having the result
How to write abstract for conference when you have no results yet?
So I have basic understanding of what I should not write in my abstract.

"Because advisor told me -> I would have not choice." This attitude will cause you no end of trouble in grad school.  You have free will.  Or, to paraphrase Thomas Aquinas: your advisor may set the goals (at first), but that should not prevent you from pursuing those goals via your own path.

Or, to paraphrase Miley Cyrus: it's your mouth you can say what you want to.

@DnuorgSpu, I guess we always have to do things that we do not want to do. I do not say that I hate working on my thesis in this case but I feel kind of strange to have the abstract done before my research done.

A small note of warning: while the answers here are correct for some fields, others (especially within Computer Science) place a much higher value on conferences. In these fields, papers without conclusive results are unlikely to be accepted to the conference.

Is it normal to submit an abstract to a conference when the research
  is NOT completed?

Sure.  There are plenty of fields where the purpose of a conference is to discuss research that is "still cooking."  In fact, many journal publications can be viewed as interim reports on larger research programs that are still in progress.
You might use this opportunity to set a goal for (roughly) the piece of your thesis you want to have done by the date of the conference.  It's ok if that piece is relatively small, and nobody at the conference will hold you strictly to what you say in the abstract.
In fact, some people submit abstracts on one thing and then talk about something entirely different... I won't advocate that behavior as an intentional strategy, but I will say that many people (myself included) prefer a great talk to exacting consistency with the abstract.

Thanks - I got lot of confidence now after reading your answer.

@user7226 - I'm in an empirical field and I tend to put something like: "Preliminary results (N=3) suggest that..." This makes it clear there's more to come, and that I'm mostly speculating for the time-being.

Yes. The idea of the conference is to talk about the current research, not about the published articles. Conferences can also be used to discuss works that may or may not evolve into articles. And while conference abstracts are not rated as high as articles, they do help PhD student to support the significance of the work - especially when, because of various reasons, the article at the end have not been published.
However if your work is close to completion, or even there is already an article in preparation, or otherwise the topic is very successful and highly promising, professor may suggest to avoid disclosing details that may help for potential competitors.

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text:
Grading strategies for oral exams
Several recent questions on oral examinations have caused me to reflect on whether or not this particular examination tactic would be worth further investigation for my courses.
From a practical standpoint, I am stumped as to how one would go about grading an oral exam. For example, one of the key benefits of an oral exam from the student's perspective seems to be that the exam can be optimized in real time according to the student's performance; however, a well-prepared student may end up getting a relatively more challenging exam, while the ill-prepared student may receive a relatively easier exam.
All of this has me wondering:

How would one go about grading an oral exam in a manner which is both fair and accurate?

In all kinds of assessments, but especially oral exams, carefully prepared rubrics can help increase consistency and decrease subjectivity. From "A short guide to oral assessment":

One of the advantages of oral assessment is that it can often be
marked quickly on the spot. To support this, the use of a marking
guide or rubric of some sort is usually essential. The use of rubrics
in oral assessment has many benefits:

It provides assessors with a common reference point for their
judgments
It reduces the likelihood that judgments will be based on
extraneous factors
Providing students with the marking guide in advance helps them
understand the nature of good work and helps them to evaluate
the quality of their own work in the assessment
It provides a basis for peer evaluation/feedback
It makes marking more efficient
It provides a useful framework for feedback to students.

Further details depend on the format of the exam, and on whether you want to include things like presentation skills in the grade or not.
In [1], there is a predetermined set of questions that are graded as follows:

Students are told that they will be asked a series of questions
that are designed to evaluate their understanding of the
material. Students are instructed to “think aloud” in order
that their thought process can be observed (9). The grading
system is explained and they are shown a scoring sheet. Four
scores are possible for each answer: 3, 2, 1, or 0. Students
answering a question correctly and without prompting earn
3 points. Each prompt a student receives results in a deduction
of 1 point. Mistakes made along the way have no consequence
on the grade if they are self-corrected. Following
the questions in the order they appear on the scoring sheet
allows for consistency in the administration of the examination.

In [2], the content of the exam varied with each student. Therefore,

Developing a rigid rubric for an oral
examination was not feasible when each student individually
determined the content. This required the evaluation criteria to
remain roughly defined to facilitate evaluation of all students,
no matter which reaction they chose. The rubric shown in
Table 2 was used to guide the evaluators when grading.
Presentation skills included oral and nonverbal communication
(such as writing a reaction mechanism) and delivering
information in an organized manner. Student knowledge
about their chosen subject was evaluated partly through
reviewing the content they had prepared for the session and
whether they presented the required information. The ability of
each student to answer questions was used to assess depth of
knowledge and the extent of the research undertaken and to
gauge how capably a student could synthesize information
quickly, problem-solve, and think critically. For example, one
student mentioned a recent innovation of their selected
reaction being undertaken via solid-phase synthesis. Their
knowledge regarding solid-phase techniques was subsequently
assessed through further questioning to determine the depth of
their understanding.
To limit inconsistencies and subjectivity, which are reported
problems in oral testing, two of the course instructional
staff were present for each examination

In the "poster exam" format described in [3],

The grading of the poster exam occurs in two parts. First
students are graded on the content, organization, and design
of the poster itself, the oral presentation of the poster, and
their ability to answer questions on the poster. The students
receive a group grade, which we chose to score as 60% of
the exam. The detailed breakdown of the poster evaluation
is shown in Figure 1.

...
Individual knowledge of the broad subject matter is
probed in the second half of the test with an individual oral
examination administered to each student in the poster group.
Questions are drawn from a database constructed by the
course designers and instructors, and labeled according to
degree of difficulty. After each poster exam the database is
refined and enlarged. The examiners are asked to draw questions
randomly from the database and score the answers on a
three-point scale of outstanding, acceptable, or unacceptable.
Each student’s response is scored and entered on an answer
sheet, which the students do not see, and returned to a folder
that remains with the group. The next examiner then has access
to the folder and does not repeat the prior questions asked.
In this way each student receives at least two different oral
exams, and most are given three. Examiners tend to conduct
this aspect of the poster exam in one of two ways: some ask
each student a different question, while others give the same
question to all students.

[1] Roecker, L., 2007. Using Oral Examination as a technique to assess
student understanding and teaching effectiveness. J. Chem. Educ, 84(10), p.1663.
[2] Dicks, A.P., Lautens, M., Koroluk, K.J. and Skonieczny, S., 2012. Undergraduate oral examinations in a university organic chemistry curriculum. Journal of Chemical Education, 89(12), pp.1506-1510.
[3] Marino, R., Clarkson, S., Mills, P.A., Sweeney, W.V. and DeMeo, S., 2000. Using poster sessions as an alternative to written examination—the poster exam. J. Chem. Educ, 77(9), p.1158.

"the use of a marking guide or rubric of some sort is usually essential": Mm... honestly, in 30 years of oral exams (student+teaching) I've never used such a rubric and I've never seen anyone using it.

@Massimo Well, now you've met me :)

We could do a research on the assessment uniformity with or without rubric ;-)

Apologies for not accepting this answer sooner.

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text:
Tasteful way to indicate large funding in job application
I am a PhD student in one of the social sciences going on the market. A large organization funded part of my dissertation research, as part of a research partnership. I wrote a report for them with some of the data in return. The total funding was a couple hundred thousand dollars, which is a lot in my field.
I was hoping to list the funder and the amount in my CV and cover letter to demonstrate my record of linking my research with funding.
The organization however insists that specific funding figures are confidential and I cannot use the precise number of the total funding.
Without the ability to put the specific number, what is a tasteful way to indicate in my job application that I received this large amount of research support?

My CV had a "grants and awards" section for exactly this kind of information, including "~100,000EUR". Or is this too specific?

I'm not sure if that's too specific. @FábioDias Are you prohibited from putting the exact amount? If not, why do you put the approximate number? If yes, then you think putting the approximate number is OK.?

My grants are matter of public record. I put ~100k because I was too lazy to get the actual number. And for CVs the approximated value is enough IMHO, nobody really cares if it was 101k or 120k. Now, 100k x 200k is more relevant.

Ask the funding agency if they're okay with "low six figures" or "over $100000".

It depends why you think it is a lot. A 5 year PhD grant that covers tuition, stipend, and a small research/travel allowance could easily be 250k+.

Even if you can't put the exact amount, you can say what it covered! This should be pretty clear about the magnitude - e.g. "covered 2 years of salary" or "funded survey of X people using Y methods"

The organization however insists that specific funding figures are confidential — That is truly weird.  Most funding agencies like to brag about how they use their money.

A large organization funded part of my dissertation research, as part of a research partnership. Did you write the grant proposal?

The (main) reason you can't just blurt that out in your CV is that it's not necessarily relevant:

Company X partnered with my university in a Billion-dollar-funded research project and I'm one of the Ph.D. candidates in it.

Suppose I said that. Well, so what if it was a Billion-dollar collaboration? Did I broker the deal? Did I propose the project? Was I in charge of coordination? If not then it really doesn't matter.
In your case, if you actually had a contribution to the collaboration other than being selected to do a Ph.D. - write a few sentences about what you actually did. Those sentences could at the same time illustrate the large scale (inn terms of people, organizational commitment, impact, time etc.) of the project and why you deserve some credit for it.

Presumably, the money went directly to you, as opposed to being managed through a University account through the University.  If that was the case, and if your University is a public institution, the funding amount can be subject to a FOIA.
Listing the exact funding amount on a CV is expected in the social sciences, at least it would be in R-1 universities (in the United States).  However, if you have an agreement with the funding agency that the amount is confidential, then it has to be honored.  You cannot signal that it was very large.  If you want to signal this information, I suggest you get written permission from the funding agency.


text:
What are the inputs and weights for US News grad program ranking?
The US News website states that their process for ranking graduate programs "involves factors ranging from the personal to the objective. [...] U.S. News is able to present the most current figures on enrollment, job placement, faculty and other critical quality indicators." And they survey "experts who teach and direct programs in these fields to evaluate their peer programs."
Source: https://www.usnews.com/education/best-graduate-schools/articles/rankings-faq#1a
From this we know their scoring function includes weighted inputs of: enrollment, job placement, faculty metrics (citations, publications, impact?), and "expert" assessments.
Does anyone know more about the score formula? What are the specific inputs? How are they weighted?

Actually, I think your premise is not entirely correct. Under US News's methodology, most graduate programs are rated entirely by their reputation, as measured by "surveys of knowledgeable individuals." There is no hidden formula at all. See FAQ #2 in the document you linked.
Specifically, for all fields other than business, education, engineering, law, medicine and nursing, the rankings are:

based solely on the peer assessment data from academics involved in that particular field

where:

The expert assessment data for these areas comes from surveys of knowledgeable individuals in academia and practitioners in each profession. Survey respondents are asked to rate the programs with which they are familiar on a scale of 1 (marginal) to 5 (outstanding).

It is only for the six fields listed above, as well as for undergraduate program rankings, that the expert assessment data is combined with statistical data using a proprietary formula.

Yes, thank you! Following your suggestion, I found the precise info for each field described here: https://www.usnews.com/education/best-graduate-schools/articles/rankings-methodologies

The US News ranking algorithm is proprietary. They don't say what it is.
A few years ago some Reed College students attempted to reverse engineer the undergraduate program rankings.
See
https://www.reed.edu/reed-magazine/articles/2019/usnews-discrepancy.html
https://www.insidehighered.com/admissions/article/2019/07/29/reed-students-challenge-us-news-formula

Very cool, too bad the Reed student analysis doesn't seem to shed any light on graduate school rankings. To your first point, the fact that it's not publicly known is why I asked the question


text:
How to prepare for long-term dissertation fieldwork?
I am a PhD student in the social sciences at an American university. I have completed coursework, my prospectus, qualifying exams, and teaching. I am about to leave for one year of dissertation fieldwork.
As is the case for most PhD students in my position, the project is larger, longer, and more independent than anything I have done before -- conducting one year of full-time original research, writing a dissertation, and then writing a book. Although my prospectus outlines a research plan, it feels too abstract to give day-to-day, week-to-week guidance.
What strategies have you used to succeed in a large, long-term research project, especially when it is based on fieldwork and for a dissertation? Personal anecdotes, experience, advice, and tips are welcome.

Make sure you have all permissions and approvals from your home institution before you leave.  For example: if your field work involves human subjects, advance approval will be required.

For each of the components, have a plan B, even plan C: Be flexible about pretty much everything. For example, if you rely on making copies of questionnaires, would you still be able to collect data if the copier in the field office fails? Etc. It's always good to mentally play a couple what-can-go-wrong scenarios when planning the study. Do so within reason, however, or you may risk stressing out yourself.
Incorporate some immersive observation of the field: If safety and cultural environment allow, try to observe more as a bystander. For instance, a patient with diabetes may tell you that she always wears shoes to protect her feet when walking on the dirt, but in fact the local people may only own one pair of shoes and they only wear them in festivals or when meeting with visitors.
Learn the local languages: Interpreters in some places are not exactly fluent in English, knowing some of the local languages can help you better engage with the process like interview or daily dialogue. It will also facilitate your mixing-in with the community.
While you're there for your research, also think how you can benefit the community: For instance, you may volunteer some time to work, train some locals to empower them, share with them your results at the end, liaise local stakeholders to address your questions and give input to your solutions, etc. If possible, be more "by the community, for the community."
Back up and back up again: If you use field note, get the ones with the brightest cover so that it's easily recognized and less likely to be lost. Written and drawn field notes should be photographed and archived regularly. Computer records should be backed up into at least two other media (external hard-drive and/or encrypted cloud storage.) Don't store your external hard drive and work computer at the same place (e.g. left in the car or office together.) For people who might have picked up your lost notes and wanted to return, make sure your equipment and notes have a contact method (like the address and phone of your host organization) to reach you. If possible, do not leave your personal address if you'd be living alone.
Backward engineer from your products: A day-by-day routine may be difficult, it's easier to set up milestones along the way. I found it useful to decide what the product will be (say, a 1,500 word literature review x 5 parts) and then give them an estimated duration to complete, followed by fitting them into the calendar. Once the big skeleton is in, then do the finer level like weeks/days to determine daily word quota you'll need to fulfill. Give everything some cushion time. Most of the time, I found myself underestimate i) transportation mishaps, ii) local festivals and holidays, and iii) administrative difference, like some clinic can just close for the day because they gave out all their medicine in the first hour after opening.
And I totally agree with another answer that you should start entering and evaluating the data as soon as they are ready. Time to time I've found questions being misunderstood. E.g. I had respondents answering an English-to-Portuguese question "What is your top three favorite foods?" with "Breakfast, lunch, and dinner." Knowing something has been lost in translation allowed us to correct the question quickly.

The most relevant advice (about the research, not life in the field) I can give is to keep on top of the analysis as the data comes in, and do not stockpile data in the hope that you can make sense of it when you're home. Analysis will reveal gaps and problems, which you need to address before you go away. Though if you're stuck with a rigid methodology where everything has to be set up before you go and then you just grind through the questionnaire, then you have my sympathies.

I suggest that you create no more than three Post-It notes to attach to your computer screen.  On these, write your most concise statement of:

Why am I doing this research?
What is significant about the way I am doing this research? (new? different?)
In the end, who will care about these results? How can I make my results vivid for them?

Look at these Post-It notes every day as you do your research and write your dissertation.  If what you are doing deviates, either re-write your Post-It notes, or rewrite your research.
This advise comes from my decades of experience.  My best writing and research  comes when I can feel direct and visceral connection with the people who might benefit from what I'm writing.