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We are a UK programming company with a maths discovery, but we cannot get into contact with any mathematicians. Help?
Over the past several months we have developed a new way of handling very large numbers in order to turn handling these numbers into a storage problem rather than a processing problem.
The system is now operational but we cannot get into contact with any university departments in order to check the software and tailor it to what the mathematicians need.
Could I please have some advice as to how to proceed?

Edit:

Very few mathematicians work with large numbers.

OK, then do you know who these people are so I can tailor my search?

Chinese remainder theorem

No, I am not using the Chinese remainder theorem. My method is much more  elegant. I am actually hunting Mersenne primes, and have found a neat way of storing the very large prime numbers for later use. I can't go into detail here because quite frankly I need the money from the uses this could be put to.

Get into contact with departments directly.

I have been on the phone/e-mail trying many diferent maths departments. None even bothered replying, so I am clearly approaching this in the wrong way which is why I have come here for advice.
The software is effectively complete, but I don't have the money to complete construction of the hardware. On top of this it would be useful to have a contact in order to tailor the software for how the mathematicians want to use it.

Edit 2:
Received a comment to the effect that since I am cagey with the details I come across as a flake. Well I can't deny that, but the problem is that if I give away enough detail to make a firm case, then whoever I give that detail to could go away and do it themselves leaving me high and dry. In the interests of transparency, I do need the money I stand to get from this so I need to meet any prospective partners in the middle.

Edit 3:
I have a functioning version of the software that I can run as a demonstration without giving away how it works. What I need is for the person I am demonstrating the software for to provide with enough hard disk space to run the software up to the largest number that he/she desires.
In testing we are creating lists of Mersenne primes and checking them against GIMP list in order to validate output. With the larger bank of hardware we can get up the number line to more exciting sizes of numbers but due to the world being the way it is we cannot currently afford the hard disks.
This is why I am asking here. It would cost a pittance for universities to front the hardware that is invaluable to me.

Comments are not for extended discussion; this conversation has been moved to chat.

Let me try to answer your question.

It's highly likely that almost nobody wants what you have made. Above, say 20000 digits, there is little demand for integer arithmetic that I know of. The GIMP is a bit of fun for geeks, it's not serious mathematics, and nobody will pay you (except the GIMP team) for being able to find another Mersenne prime. They are way too big to do cryptography with, and also completely terrible for cryptography, as there is literally a list of them. Finding another one is of no mathematical significance.

Why do you think your discovery is novel? There are current methods to work with integers of arbitrary size. Magma computes with multiplying 10000-bit numbers almost instantaneously. (The recorded time to multiply them is 0.000 seconds.) More than that (20000-bit) seems overkill for public-key cryptography. Magma uses the Schönhage-Strassen FFT-based algorithm for multiplying large numbers. Is yours better than that? And why?

If you aren't willing to publish the algorithms behind your work, mathematicians will not be interested, full stop. Regardless of how good it is, any algorithm not publicly described is fake, and not to be trusted. Publication before purchase is necessary. Universities will pay for software, but mathematicians will not pay for software whose inner workings are secret. That's a hard no. Open source is not necessary -- Magma is closed source -- but it tells you which algorithms are used in every part of the code.

Fancy seeing you here! Say hello to Prof. Flavell for me :-)

"Magma computes with multiplying 10000-bit numbers instantaneously. (The recorded time to multiply them is 0.000 seconds.)" I am sure you know that no computation is instantaneous, if only due to the finite speed of light. What that probably means is that the multiplication time is less than 0.001 seconds or 0.0005 seconds, and is either truncated or rounded to 0.000.

#3 is the death knell. If you want to keep your technique a secret then it cannot be used by research mathematicians, because there would be no publicly verifiable proof that it is correct. Empirical validation (e.g. by finding Mersenne primes using your technique and comparing with a list of known Mersenne primes) is not sufficient.

@Obie2.0 Sure. I thought I wrote almost instantaneously, actually.

Academics might work "for free" on things that advance knowledge for the public in their field of research.
You shouldn't expect them to work for free on developing your idea that you hope to make money on.
You need to hire an expert consultant it seems, not find an academic mathematician to check your work for free.
It's probably worth it to you to offer a substantial hourly rate if an hour of an expert's time will save a lot of yours.

Thank you for the answer. My project relies on input upfront for a payout at the end, so clearly I am looking in the wrong place here for any potential partners. Now I know this I can stop wasting my time here. If I had the money to hire the consultant I could just straight up buy the hardware I need and then publish the research.

@Bearishmouse Is the hardware really so specialized that you must "construct" it? If not, renting HPC resources might be cheaper.

Speaking for myself, part of the reason that I'm in academia is that I am not entrepreneurial. I might take a contract, but I'm unlikely (for all the reasons given by commenters) to enter into a partnership where I provide professional services in hopes that I will make a lot of money somewhere down the road, especially if I'm given very little information up front.

Echoing @BenBolker, I've been burned a couple times by "entrepreneurs" needing my expertise, but having no up-front money... my spending time on it... and, in the end, sending me no money at all.

Here's one possible path to monetization:

Go to America, or find a partner who is in America.
Get a Software Patent.
???
Sell the patent, or the products it protects, for cash.

Once you have an open, examinable, demonstrable approach, then you stand at least some chance of being able to commercialize and sell the idea.
There is no way for you to monetize the idea, without giving people something they can take apart to find out how it works, whether in hardware or software.
You cannot monetize a closed idea. As others have hinted, the overwhelming majority of ideas that lay people come up with, don't survive even the most cursory examination by specialists, in any field. Statistically speaking (and math specialists are usually pretty good at stats!), your idea is very unlikely to be different. Is it any wonder, then, that specialists are unwilling to waste time examining the claims of yet another naif who claims to have done something that the specialists could not?
Academic mathematicians get countless papers from laypeople claiming to have proven some outstanding proof or other. These people lay out every step of their logic, and expect no funding or money... and even they get ignored. Why should they waste time on someone who gives no information, and expects money?

This may be exactly the approach I need. Thank you for bringing this up, I will start work on my research on this topic.

Except 2) fails because mathematical concepts are explicitly forbidden from being patented, even in the US?

Indeed, (2) is not applicable (see: What constitutes an original patentable idea in software?, and Software patents under United States patent law). The best you could do is copyright and sell your implementation, but then if the algorithms underpinning it are not publicly known, no-one will be interested in using it.

If your method actually needs you to construct hardware, there's very little chance anybody will be interested. If you just mean assemble regular computer parts, then even if you don't have the money for that, you could rent an instance from AWS with 512GB of memory and 16TB of storage for around $6/hr. Seems like you could record a demo for not much money, which would give people a much better idea of whether it's interesting.


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Transforming Development and Management Practices
Disclaimer, I already posted this on StackOverflow and got advised to post it on "The Workplace" where I got advised to post it on "Academia". Please don't send me back to StackOverflow. In my opinion, it's deeply related to all three of them, so probably people who are active on all three subs have the best perspective.
We are currently an academic institute of around 50 people. The institute does typical industry research, batteries, metals, magnets, etc. Recently, we began more and more relying on algorithmic developments for evaluation. Most of the recent research results depend in one way or another on custom-built solutions a.k.a software, some even required a User Interface to limit the burden on less tech-savy people.
We are currently building these solutions internally on a per-need basis. I joined the team 1 year ago as a "Machine Learning Expert" but my origin is in computer science and programming. I have some experience in DevOps, Software Project Management, and CI/TDD, and also other people have concepts of how things could be organized. If it's relevant, I will be working on my Ph.D. there. Also, we are doing industry transfer. 4 or 5 more people have at least some experience coding so I am not all on my own with the following mess:
We have data management by chaos and network drives, there is no CI or TDD, no common code-base, everything is pushed on network drives via mercurial (if at all, often it stays local) we slowly have to start using docker because some of the hardware requires it, but we don't have the time to get to the point where it starts saving time, we have high fluctuation and that's only some of the problems you can imagine. Also, we have tons of meetings on how to structure stuff and improve the situation (theoretically). Nothing changed in a year.
The management structure is "by objective" and the DevOps horizon ends at excel. How you do DevOps in excel? You don't. So nobody really cares what we do, how we do, or even who does what as long as you document your stuff in PowerPoint and application guys can use it. There are multiple people supervising multiple students, which sometimes have some sort of coding experience and add to code-abyss. As long as stuff gets published no one cares. Later on, we have a "knowledge" transfer program in cooperation with industry partners ("knowledge" basically means software), that's where everything comes crashing down. In my opinion, working like this and continuing in such a way is tremendously short-sighted, to put it gently. I love this institute and I want it to play in the SotA league. Currently, nobody is holding us back other than ourselves. Freeing time for actual reproducible research by having modern infrastructure and fitting management, sounds too good to be true?
Because it seems we are going nowhere without radical change and external input, I thought I'd give it a shot here as there are people with much more experience than I have. Maybe someone who already completed a Ph.D., started working as a Developer, and now moved into Management. Please share your wisdom. Other institutes could clearly benefit from this, as I can imagine, we are definitely not the only ones struggling.
The best answer from the previous posts was purely from a management perspective: Start with a maximum effect thing and show how much time it saves. This is to convince other people by action and not by words. While that was certainly helpful, that was very unspecific. We need first-hand experiences from institutes that have been transforming and have been adapting to stay relevant to the industry. I promise you, many people will thank you for sharing how you transformed.
The worst answer sadly came from a purely academic perspective which might cost me a few sympathy points here but I tell you anyway. It said I should not care because "it is what it is" and "there are other people who should deal with this". I promise you, they won't be coming. Further, handling the industry transfer under these circumstances is already unbearable. The answer might be true if your scope is really limited to academia only and you solely care about publishing papers, but outside that world, things flow differently.

Very interesting question, but not sure we as Academia.SE are qualified to answer -- most of us are knowledgeable about research, not devops. At the risk of sending you to a fourth (!) stack, maybe try [pm.SE]?

Still, if I were to take a crack at an answer myself, my first question would be: how much authority do you have to enact change? Academics are generally rewarded for publishing, not producing nice code. If you can hire a team a team of developers and DevOps people to do some of the heavy lifting, then this might be tractable; if you can only "encourage" the academics to write better software, then I think you might be pushing the proverbial rock uphill.

Sounds like you're running into the situation where you can see a better world for your institute, but not getting traction. From what I've seen, the higher-ups nod kindly, but nothing happens. A few observations:

If you expect those same higher-ups to approve AND get things started, that's a mistake.  It's not from lack of interest. These folks are frequently presented with new ways to change the place or to invest money.
If you expect them to mandate use of source control systems, continuous integration, etc., forget it. I assume you don't have a CIO sort of person.
You have to start simply at the grass-roots level. If you're not getting traction there, well that's where you need to get it.

Your best hope is to demonstrate a competitive advantage, if any, modern IT practices might confer. Follow the $$$. From a different angle, figure out what potential penalties or problems or costs you might incur from staying Wild West. And another: Figure out the level of IT maturity peer organizations are at. You probably want to be ahead of the middle of the pack but not at the bleeding edge.

Make your own life easier, then help make the lives of others easier as well.  That's the crux of it.  It seems that there are several issues.  First, you appear to have problems with how your own work is organized and managed, and then second you appear to have issues with how work as a whole is organized and managed.  Particularly you seem to be concerned that a lack of organizational formality is causing serious problems during the knowledge (software) transfer phase.
I've found, especially in academia, that trying to cause big change is rarely the way to do it.  Blue-sky thinking about what this would look like is fun, and I'll bet a number of the researchers working there have a topical knowledge of various technologies and think they are cool, but it is unlikely to get much beyond the white paper phase.
Instead, focus on a single problem that is causing you, specifically, grief.  Ideally that will also be a problem that others face.  Solve that problem for yourself, for your specific projects, in a way that saves you time or pain at the transfer step.  Perhaps, for instance, you can become the Docker guru in the institute, but it may be something even smaller, like moving one function from Excel to a more useful online platform.  I don't know enough about what you do to make this clearer, but I'm sure there are tiny tasks that you do that are just pains.  Fix those.
Next, get others up to speed on these new ideas.  If you are going to be doing a PhD then it is reasonable to expect you will be supervising students.  As soon as they start just introduce them to these new procedures as though "this is how it's done here".  They will start with the understanding of how to do things, and as they become masters and PhD students suddenly they will just take up those ideas as well.
Once a few problems are solved you should have extra time to start thinking about re-organization of bigger things.  The key here is that you will also be known as the person who made those changes happen, so you may be given the responsibility to do more.
I've found that there are two major reasons that we as academics do not implement more industry-standard management techniques:

No one really knows about them - what this means is that we may have heard about various techniques or technologies, but at a very superficial level.  We have a solution in search of a problem, where we know that "Docker" is a thing that is used but we don't know enough about why and where it is used to really take advantage of it.  Once we do end up using these things it's usually at a superficial level or just plain wrong (for instance, using Excel for dev-ops...)

There are so many of these technologies/techniques that no one has a clue which is best.  This is usually from a lack of experience in situations where there is no choice.  For instance, if you work at Google, then there is a set of ways to do things.  You learn these from day 1.  In academia there is much more freedom, but as a result much more paralysis.

The solution to both is to start small, pick one thing, and get good at it.  Change happens when people's lives are made easier, not when meetings are held about making lives easier...

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How to point out a typo in an equation in an article?
In an article (from 2015) I came across a wrong equation with a sign error in one term. In the publicly available code, the correct sign is used, so the results of this particular paper are correct. However, several other papers have since copied and used this equation, and therefore likely have wrong results because of it. It won't change any conclusions I think, some results would change by a factor ~1.5. Should I just email the authors, or the journal? And what about the other papers that used the wrong equation?

Yes, you can email both the authors and the editor of the journal. A correction might be issued. But it is worth a bit of effort.
Of course, if it is obvious in the paper then it may be that it has been noticed by many and they have responded, or just ignored the error as obvious and moved on.
But it you have some evidence that the error has affected the results of newer papers then it might be especially important to reach out.

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Are academic papers required to have specific sections
I've seen that academic papers tend to have the sections Abstract, Introduction, Material and Methods, Results, Acknowledgements, and Literature Cited.  My question is if I wanted to publish an academic paper would it need to have these specific sections or could I have a different set of sections from the ones mentioned depending on the contents of my paper?

This is discipline specific.

Added here: https://academia.meta.stackexchange.com/a/4472/13240

In general, it is better to follow a 'common' or accepted structure.  This is because your community 'expects' a certain structure.  This in turn allows a reader to find the required info quickly.

Which one would you be skipping and why? Or do you want to add?

It is somewhat field (and even more so journal) specific.  You should have an idea the normal structure.  But then if you decide to separate Results and Discussion or combine them is a bit up to you.  (Or for long papers to use more topical subheadings.)
I recommend to take a look at '

Several papers in the journals you submit to (think of it as a biologist observing birds in the wild).

The specific journal's directions to authors (usually in January edition).

On Research by Wilson

Technical Writing (NASA pub) by Katzoff

After that, use best judgment as to what will help the customer (the reader best).  In my experience, after doing so, editors will leave your structure as is.

That depends on where you want to publish. Some journals are strict on requiring a specific structure, e.g. IMRAD, or on the naming of sections, while others are more freeform. As a general rule, read any "Guide to authors"/"Author information" or just try to follow the structure used in recent papers published in the venue of interest.

Have a look at a few papers in a few journals in your field. Probably will be illuminating.


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If I derive a formula for a paper do I need to put the derivation directly in a paper?
Let's say that I derived a formula that I am using in a paper, without any prior knowledge of the formula.  Do I need to then put my derivation directly in my paper, or could I submit a supplementary document containing the derivation, and then reference the supplementary document in my paper?

Perhaps write the derivations in your paper's appendix.

Is the formula a major or minor part of the overall paper? Does the derivation have any independent value beyond establishing the formula?

That depends on many things. What kind of formula? How important is the derivation? Is this a math paper or physics, engineering, economics etc? Pure math or applied math? There really isn’t a single answer that would be universally applicable, you’d better add more details if you want an answer that’s relevant to your particular situation.

This is what I would do: First write up the derivation of the formula (that way you make sure there are no mistakes). Then, usually I have a better sense whether it fits well or should be added to the appendix. If at the end of the day I choose to remove it, at least I know that I can add it if, say, a referee requests it. I know it is often tempting not to write the computation out of laziness, but I believe it is a bad practice.

In general, creating supplements for paper is not a good idea. I would have created a blog or something and posted the derivation and provide the link to the blogpost on my paper. In fact, this way you can make the derivation more fun, by adding things such as a brief motivation justifying why one should expect such a result to hold, etc..


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What's the best way to tell the writers of an webpage that they made a mistake?
I was reading this webpage, not sure if webpage is the correct term, and saw that it has a minus sign for the potential 12 describing how the two electrons in a helium atom interact with each other.  Although this was opposite of what I would have expected I initially considered that if the writers of a webpage put something unexpected in an equation, then it is much more likely that it's because I have a blindspot in my understanding than that the writers actually made a mistake.
However the minus sign made me suspicious enough to look at other sites to see if they also had the minus sign, as I realized that if they made a mistake then the other sites would most likely have a plus sign in for the potential 12, while if having a minus sign being unexpected for me came from a blind spot in my understanding then they would most likely also have a minus sign for the potential for how the electrons interact with each other.
I found that this site, this site, this site, and this site all have a plus sign for the interaction potential describing the interaction between the electrons, and these are .edu sites, with some of them being pdfs so now it looks like the original site I looked at has something that contradicts multiple academic sites and so it's more likely that the writers of the site I originally looked at did make a careless mistake in the equation.  Note that one of the other sites initially looks like it has a minus sign for the potential I described, but that minus sign is canceled out by another minus sign.
The question now is what is the best way to let the writers of the webpage know that they made a mistake?  I saw the contact information, so I know how to contact them, but I don't know the best way to tell them that they made a careless mistake.

When I saw the original version of this answer, I realized it could be just a typo, so I left a comment for the answerer. A few days later, the answerer got the message, correct the message and thanked me.

What is nice about @scaaahu's example is that it phrases the comment as a question, which is much less confrontational than saying "Hey, I spotted a mistake here". That's a good way to do it.

@scaaahu thanks for the advice!


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Advice on unintentional academic misconduct
I took an online exam a month ago and ran into some technical issues which caused me to do it on another device. I realize now that this can be seen as academic misconduct since it shows me leaving the test page quite a few times near the end and going on the LMS. A month has already passed after the exam and my final grade is out. Should I still contact the instructor in the circumstance that they look back on completed courses to spot for signs of cheating, or is this just overthinking on my end? This has been on my mind a lot and I would like some advice as to whether I am overthinking this one issue. I’ve been reading about Some people getting accused months later have been giving me anxiety since I do not want to be falsely accused, and I would like to know how often this happens and whether I should reach out to the prof, or is this unnecessary for my case since all I struggled with were technical problems.

As you describe it, it wasn't actually misconduct.

They operate in balance of probabilities, but I decided to just leave this problem as it is because it seems like no one has emailed me yet and likelihood of them emailing me in the future after final grades are slim

Teachers usually understand that technical issues come up, and yours probably already saw what happened and figured that it wasn’t a big deal. Especially if your test wasn’t proctored or recorded I would think that leaving the test browser is one of the lesser signs of cheating they would be looking for.
As for people being accused months after finishing their class, I’ve personally never heard of it and would imagine that your justification will be just as reasonable if you do end up in such a situation sometime down the line.

Definitely agree that a complaint after the course ends is very unlikely.

I think that you have nothing to worry about, just make sure you inform them of so just in case.

I don’t think anyone will look after final grades are out, maybe everything I read was just fear mongering and those cases after final grades only happen due to someone reporting the student after the fact or some plagiarism checker picks up something. Since everything is online now, schools will give the benefit of the doubt for technical issues during exams when investigating academic misconduct?


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Are tutorial type articles their own distinct category? (in physics)
In 2021, PRX Quantum released a new type of publication distinct from articles and reviews known as the tutorial. This is described as:

PRX Quantum began publishing Tutorials to help the quantum community educate the next generation of quantum scientists. Rather than provide a comprehensive overview of the field, as is typically found in a Review paper, Tutorials are hands-on guides written by experts invited by the editorial leadership of the journal. Tutorials focus on the essential knowledge and relevant references that will allow newcomers to a research field, approach, or methodology efficiently move forward with their work. For example, they should ideally help researchers migrate to a new field, bridge knowledge gaps for interdisciplinary collaborators, and contribute to the education and development of PhD students and postdocs. They focus on explaining well-established milestone concepts, the latest techniques, and developments in the field, providing a flavor of current research.

I've noticed these hand hold the reader very closely and are in its own distinct category from review articles as mentioned in the quote. Where can I find a repository of other such journals and what exactly am I looking for in terms of search words when it comes to this looking for journals that will publish this type of article? Also, do the somewhat more vanilla journals such as "PRB" or "EJP" accept these kinds of tutorial articles?

It feels to me like this recent PRX Quantum approach is fairly novel, and I'm fairly jealous that I haven't seen anything like that in areas that I'm responsible for teaching.
If I were looking for resources like this, there are a number of approaches I would try.  Since the publication class you're describing looks like just another type of publication in a journal, I would try to search for people who have cited publications of this type, and hope to hit some article on education that compares the efficacy of works of this type to more traditional methods.  If such papers exist, they may well point you to other similar resources.
A second approach would be to try to find journals that specialize in education in the areas you're interested in.  This, of course, would cast a wider net than what you're looking for, but the advantage is that you may find a bigger picture that brings you even more tools.  As an example of such a journal, I'll point you to Advances in Physiology Education
Lastly, a chat with a good university librarian when you're looking for resources is never a bad idea.
Good Luck!  If you do find such resources, it would be fantastic if you can post them as an answer to your own question!

One way journals compete is by offering different content types and filling different niches. Tutorials is a fairly unique type that, as far as I know, is only offered by two APS journals: PRX Quantum and PRX Energy. Traditionally in physics, guides and hands-on material have commonly been written up as lecture notes. Especially summer school lecture notes can have a similar nature. A fairly recent avenue that may be of interest is the journal SciPost Physics Lecture Notes. Otherwise, lecture notes have often ended up being published in various forms, including book volumes, review articles, or just PDFs. Finally, as Scott Seidman writes, some pedagogical material is published by the more education-focused American Journal of Physics.


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Is the Math GRE Subject test still important to US grad schools post-COVID? And can it actually help math grad school apps?
I'm taking a gap year and I plan on applying to grad schools again this fall. I'm wondering if the GRE Math subject test is helpful/required anymore?
Personally, I have very low grades in some important math courses (imagine like C+'s/B-'s in algebra/analysis because I could never force myself to study for them) and I haven't taken anything like topology/geometry either. I want to go to grad school for applied math, but I do think proving that you are capable of understanding these fields is somewhat necessary?
But, does the math GRE actually show that? Most of it is calculus based, so does it actually help? And does anyone know if grad schools in general still care for it? Most waived requirements during covid, but since we're in a post-covid(-ish) time, would anyone happen to know if it still matters?
Edit: adding some more details.
I plan on applying for both masters and PhD applications (I'd prefer a PhD but I don't have too much research experience). Since I messed up my GPA a bit (~3.25), I know that top ranked programs are probably out of reach so I'm mostly planning on applying to mid-high ranked programs (imagine ranked top 30-100 in the US.) I have done a senior year research project but it didn't lead to a thesis/report and we were only required to do a presentation. But it was using a niche-ish topic that isn't taught at the undergrad level mostly. I've taken majorly graduate level math courses, and I do have at least 2 good recommendation letters, and possibly a third from the instructor who taught my C+ (grad only) course. I've also been a head Teaching Assistant for a calculus course this past semester, and I'm trying to get a TA-ship for a differential equations course this summer. But yeah, pure math course grades are still pretty low so I wanted to see if there's anything that can prove I can still work on those subjects.

Masters or Ph.D.? What type of programs -- highly ranked, mid-ranked, low ranked? Do you have anything particularly distinguishing to offer as evidence of your potential (e.g. publications, summer research work, strongly excelling in some difficult applied math courses, top 100 Putnam exam score, etc.)?

Thanks, @DaveLRenfro! I've added this stuff as an edit. Forgot to mention that, yes, I've done pretty well in some difficult applied math courses (numerical linear algebra for example was a graduate course co-offered to undergrads, and I got an A-, so I think that counts? And there are others as well, but this one was quite difficult, especially with the way the instructor grades.)

The actual grade of A- is not really relevant, but how you did relative to others in the class (best in class, only others better are going to top 10 Ph.D. programs, etc.) and whether your performance could be something the teacher of that class could base a letter of recommendation on. Also very important is the baseline competence required in pure math courses/qualifying exams for the program you're applying to.

Ah yes, fair point. We're graded on a curve in most of our courses, including this one, and the average score usually gets around a B, so I was well above that? And in another class with this instructor, I was ranked 3rd out of the students as well (incl. grads). I have heard that she thinks highly of me from another instructor, and she did agree to write me a letter, so I'm hoping that it'll turn out well. Your second point is really important too, tbh. Some programs I applied to last year required all students to take some pure math courses, so I'd probably have to do well in those too.

While the GRE is required less frequently than in the past, the advanced (subject) tests can measure your overall understanding of a subject. But, unless things have radically changed in the last half century, the math test is very hard. I was a top student and did well on the test, but there were quite a lot of questions that I had no basis to answer, as it is very broad. I don't recall applied math being part of it then, but that may well have changed.
But you need a reality check. Analysis, Algebra, and Topology are core subjects in most math programs and if you did poorly in some and missed others you are in a poor place to do well on the math GRE since it reflects that core. It is possible that you learned a lot outside class, of course, as some do.
I recommend that you take the exam without sending your scores anywhere and see how you do. If you get great scores then send them everywhere that it is possible. If you get mediocre scores then send them only to places that require them.
But, expect a very hard test. Expect to feel disappointed when you leave the test (as I did), though you may do well in spite of that feeling of dread. The exam is very broad and the undergraduate curriculum can hardly capture the breadth of mathematics. And, repeating, it is very hard.

Thank you for the response! I do understand that it's quite difficult. I have improved my knowledge in algebra quite a bit, and I plan on revising analysis and self studying topology over the summer so that I'm able to prepare by Sept/Oct. I'll take a practice test to see where I stand though. I don't think applied math is part of it, but I do believe the math itself is probably going to be quite difficult. I'll follow your advice and only send my scores if they turn out good enough. Would you have any tips on how to do well? (Other than to just study a LOT)

The standard advice on taking such exams is to so a quick pass over all the questions answering only the ones you find easy. Then do a second and third... pass for the harder ones. Don't get bogged down since time is a factor.

Ahh yes, understood. Thanks!!!

You used to be able to buy study guides for all the exams with advice and typical questions. I used them for several standardized tests as well as general study.

Ahh okay, yesss, I'll see if I can find some where I am (not in the US so might be difficult if it's not online, but I'll look online as well). Thanks again!! Really appreciate the responses!

This question should go to some of the universities that you are applying to. The program determines what is required and what can be provided. There are admission directors of graduate programs and admission office people who will be able to answer your question. They will also tell you if they would look at secondary data such as the scores of the GRE subject test if they do not require it.
Since you are applying to a Mathematics program, it makes sense to invest into taking the GRE subject test as well. You can show that you understand the basics of an important subject. Calculus is pretty fundamental in applied Mathematics, and showing that you master it despite having gotten a so-so grade in Analysis would be information that I would like to see if I sit on the admissions committee. More important would be of course a good recommendation letter that has some information on your thesis.

Hmmm. The math subject test doesn't really focus on Calculus but on things far more advanced than that.

Thanks for responding! I agree with you that it would be better to ask each school I plan on applying to. I was just wondering if the general policy was being modified post covid (as it was for all the UC's I believe, along with quite a few other institutions). Calc is like ~50%, while there's a lot of other stuff as well, but yeah, I do think it's quite important. Will definitely be taking the test then!

@Buffy I'm not sure I agree - I recently took the subject test, and even if you don't want to count diffeq stuff as Calculus, a good 1/3-1/2 of the test are questions well within the realm of a Calculus I/II class.


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Is it a good idea to add a cover letter to a scholarship application when a cover letter is not specifically required?
My scholarship application was denied yesterday. Fortunately, I can still request the scholarship committee to reconsider my application, provided that I have new credentials to present in my curriculum vitae. The scholarship application portal asks only for an updated curriculum vitae. But would it be a good idea to add a cover letter to my curriculum vitae that explains why a need the scholarship?

If you have been already denied, then it would be good to explain how the current application differs from the application that was denied. If I were on the committee, that would be the first thing I am looking for. The best medium for this explanation depends. As a committee member, I am not likely to spend a lot of time reading long explanations. As the portal asks for an updated CV and as the request has to be based on a change in qualifications, it seems that a cover letter is usually not the best medium. However, make sure that the change in your qualification is not hidden in your CV. If it might get lost, then yes, put in a very short cover letter.


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Should I look for a job in a foreign country before I get there to pursue my Ph.D.?
I got accepted to a Ph.D. program in New Zealand. For now, I have enough funding to cover only my first year of study, which is why I plan to work in that country while I study. Is it advisable to look and apply for a job there now? Or should I look for a job when I get there?

Two important points to consider:
First, a PhD is a full-time job. Most PhD positions come with a side-job that provides funding and, importantly, some sort of tuition forgiveness. Sometimes that side-job is fully overlapping with your research work, sometimes it's a separate task (like teaching), but in either case it's a position designed for someone doing work towards a PhD, with full expectance that their time will be split between those tasks.
I would highly recommend against taking any PhD offer that requires you to pay tuition and expenses. Universities may make these offers, but really they should only ever be taken by people who are already so wealthy that the cost doesn't matter. Consider them like a bribe or donation to let a rich family send their kid to a prestigious place. You really don't want to be in the financial position of paying a bribe meant for oligarchs and kleptocrats.
Most other jobs, besides hourly work, will expect your full attention. You should not expect to be able to hold a job and make satisfactory progress towards your PhD at the same time. Rarely, some people may work on "part-time" PhDs, but they should expect to take much longer to graduate and need to arrange this with their institution as a specific plan to move slower than normal, not just show up to do half the effort.
Second, if you're studying in a foreign country, you'll need to comply with their immigration policies. I do not know any specifics about New Zealand, but you should certainly not assume that whatever immigration policy allows you to be there as a student allows you to hold a job. It seems most likely you will (see https://www.immigration.govt.nz/new-zealand-visas/options/study/working-during-after-your-study/working-on-a-student-visa per comment by Allure), but you'll have to ensure that applies to you and doesn't conflict with any rules for being a student at your institution.

The last point is very important and is very easy to overlook. When I was at Waterloo as an international (US) student, I was not able to work off campus as it was against my student visa restrictions as I was already being paid TA/RA money by the university. I could only work on campus through the university for some extra money (and did so as a tutor through a program aimed at students with learning disabilities). You could of course do some stuff under the table like tutoring for cash only (no paper trail), but I don't suggest playing those kinds of games in a foreign country.

You are allowed to work full time as a PhD student in New Zealand. https://www.immigration.govt.nz/new-zealand-visas/already-have-a-visa/my-situation-has-changed/study/can-i-stop-studying-to-work-full-time-if-im-a-phd-student

@Allure "usually" - I have no idea how much work that word is doing (for example, if it applies to work done as a PhD student rather than outside employment unrelated to the degree).

I am certain PhD students can work in New Zealand, in fact you can work as much as you want. https://www.immigration.govt.nz/new-zealand-visas/options/study/working-during-after-your-study/working-on-a-student-visa If you are enrolled in Masters by research or doctoral degree programme awarded by a New Zealand tertiary institution, your visa conditions will not have any restrictions on the hours you can work.

First thing you should do is discuss with your supervisor, because you can't really do anything without his or her approval anyway. Getting a job will not be easy - it's not that you don't have permission from the New Zealand government to work, you do, but rather that it is very time-consuming and that will detract from your PhD (which is also a full-time job). There's a good chance you'll get some supplementary income as a teaching assistant at your university, but it's not likely to be sufficient to live on.
So ultimately you will need to find funding somewhere, and whatever you decide on you will need your supervisor's agreement. Therefore discussing with them is the first step. You can decide afterwards if you want to, e.g., convert to a part-time PhD and spend the rest of your time working.


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Is it possible to switch from applied maths to pure maths?
I've found a couple of questions of the type "is it possible to go from pure to applied" so I was wondering if anyone knows for the opposite direction.
Say you are an applied mathematician with an applied math's masters (say, a total of 6-7 years of applied maths in total, including undergrad: you'd know functional analysis (as well as convex analysis, Fourier analysis, complex analysis, etc),  general topology, the very basics of abstract algebra, a lot of optimization, probability (markov, etc) and PDE). Is it possible to then switch to pure mathematics? Can you get into a masters program on pure math's? Do you have to take a masters on pure mathematics before going for a PhD in this case? How likely is it for one such person to get accepted on a grad school program for pure maths?

As always, the correct answer depends on the country you are in. In the US, for example, Mathematics Ph.D. programs would accept someone with a background from an area that uses Mathematics such as Engineering. Also, many programs do not make a difference between applied and pure mathematics. In India, you might have more problems because career paths are less permeable.
If you already have an MS in Applied Mathematics, and want to get into an MS in Pure Mathematics, most programs (in the US) would not hesitate to take you provided you can provide letter of references. It is your money that you are going to spend on a somewhat useless degree. ("Useless" because I cannot think of examples for jobs that you can do only with an MS in pure Mathematics.)
Chances for admittance will depend on finances (if you are a foreign student, tuition at state universities will be higher, and any support would be more expensive; the availability of support), your test scores, your prior research experiences, how your interests match up with the departments, your references, ... In general, pure Mathematics is not the most-sought out Ph.D. program.

I cannot think of examples for jobs that you can do only with an MS in pure Mathematics --- In the U.S. this is a fairly standard requirement for a community college teacher of mathematics (sometimes just 18 semesters of graduate math, and a masters degree in anything), although for this career path the OP already has an appropriate degree, since "pure mathematics" and "applied mathematics" are probably not going to differ for the requirement. Incidentally, other than possibly algebra, the OP probably already has more background than most U.S. "pure math" masters-only degree holders.


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Credit as Undergraduate Researcher PI
(PI: Project Initiator, I get this term from proposal-writing) I am an undergraduate student (and have been off and on over the last 7 [now almost 8] years). I went to a professor at my university with a novel idea. I was able to provide good answers to their questions and they are willing to conduct the experiment with me. This would likely take the form of a "Research Problems" 1 to 3 credit course this semester, and next semester, and a few grants, including possibly a grant to work over the summer on the project (they would be listed as a sponsor).
I am wondering about credit, I came up with the idea, and I would mostly be focusing on this (and maybe one other project at a time) for the next year (I am planning to take less classes to focus on it, and even graduate even later). It would probably be less of an "assistant" role. I am wondering about how credit would be shared or what my professor might expect. I know often the first name on the paper matters a lot, would the professor expect to put their name first? If so, if I take on the role I expect too, would it be interpreted that I was an undergraduate assistant of some sort that sort of helped? I just don't want to lose credit/recognition for the idea and be recognized for the work I am planning to do (as a foundation on which to submit future articles -- possibly without an institution or company attached).
I am hoping to maybe become an independent researcher, and I want to start building my reputation with this.
Thank you
EDIT:
I think I may have misunderstood the term "PI" a bit. I just basically meant the person who came up with the idea and got the project started/organized (but not necessarily remaining in a managing role or providing oversight). Perhaps I was a little "overzealous" in saying it.

I think it would be good if you could mention the field you are working in. My feeling is that it might depend a lot on that.

PI is not "project initiator" its "principle investigator", and generally refers to the individual who has legal responsibility for an externally funded project.

@IanSudbery Thank you for the clarification, that is a good thing for me to know. When you say "externally funded project" could you clarify, the context in which I learned this term could imply that, but was also used for projects internal too an organization.

@SeverinSchraven Quantum communications/physics

The term PI may be used internally for the person who is officially responsible a project
Again, it would be the person accountable, even via non-legal means, for the spending of the budget. Its highly unlikely that an institution would ever consider an undergrad a PI in this situation, as it has no way to enforce that accountability on a non-employee. Now, PI is also often used, informally to mean "the boss". If someone refers to "my PI" they probably mean their boss.

If you enter into a project with another person, you should set the expectations of everyone at the beginning. You need to discuss this with the advisor, If you tell them that you are hoping to be first (or sole) author on the work when done, then that has implications about how much they need to guide you and participate.
If you make it clear that you want the "credit", then you are also making it clear that you want to do the intellectual work to make it happen. Another person could still advise you with feedback, but if they contribute intellectual content to the work then they are an author also.
Since the original idea is yours, you probably have a claim, at the moment, on first (or sole) authorship, but that can change depending on the participation of the other person.
But don't make up titles for your role, such as PI.

I think misunderstood the term, I recently took a course on writing proposals (NASA L'Space NWPEE Academy). Perhaps I was a little overzealous with term. Good thing for me to know before I would use it in this context haha.
Not looking for sole authorship, but am looking to put the majority of the work in or at least about 50%.
Didn't know if it would be appropriate to ask for primary authorship (given that that comes to fruition).

Primary authorship is a whole other thing. Most subject areas have their own principles for establishing that, being the project PI is sometimes one of them, but is my least favorite. There are whole threads here on that.

For funded work where money is coming from your school or a government agency the Principal Investigator is the person responsible to the grantor for prompt reporting and correct use of the money according to the applicable regulations.
Government agencies typically have long documents that explain how proposals are to be prepared in response to their Requests for Proposals or similarly titled things. Your university probably has a department for grant handling called something like the Office of Sponsored Projects or similar who actually legally sends the proposal from PIs to the agencies and handles the bureaucratic issues (depending on US state and agency). Each entity will have rules on both sides for who is PI eligible mostly depending on position and educational background. Both ends must agree. Exceptions are possible, but I’ve never heard of one being granted to an undergraduate researcher. Position permanence is also part of the formula and undergrads tend to graduate before projects complete. Professorships are generally more permanent, and those kinds of personnel tend to stick around long enough to not worry about them leaving the project midstream. If you’re not at a university, then you’d have to learn all those regulations yourself or hire a specialist company to do it for you. Each agency’s programs will say if who is eligible and if companies can apply.

Thank you, I just took L'Space Academy, the PI basically was the person on the team who came up with the idea (and wound up leading the team). I think I was a little overzealous with the term, I will update the question. Thank you for the info.
But PI != first author necessarily right?

That's right. I have a first-author paper from an unfunded project that I would not call myself the PI on. It's not really even project, just something sorta theoretical that I noodled about on dry-erase boards, chalkboards, and paper until it came together. A friend checked the equations for me before I wrote it up, and I sent it in as a solo-author journal paper. Several similar papers have come out since which I think are better, but I don't have time to pick them up and implement them in my code to or time to analyze them side-by-side. Wouldn't count myself as PI on this "project".

thank you, I appreciate the detail and completeness of what you are saying.


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Can you apply to scholarships during a gap year?
I've decided to take a gap year because I cannot afford school. I'm going into my Junior year of undergrad after my gap. I plan on graduate school and want to be debt free. I've recently taken it upon myself to apply to a scholarship every week of this year. However, I'm starting to notice that they require students to be enrolled full-time. Does anyone have any insights on this? Will they just ignore it?

What sort of graduate degree are you seeking?  Possible duplicate of https://academia.stackexchange.com/questions/29504/is-it-worth-self-funding-a-phd-to-attend-a-top-10-university

Typically scholarships require students to be full time while they are getting the money not when they are applying, but it could vary.

It will depend on the scholarship. There are many different patterns and rules. It ranges from automatic application by the school when you apply to the school up to requiring somebody in some council etc. to submit your name for consideration. Check with the admins of the scholarships you are concerned with, and the admins of the schools you are considering applying to.


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How can a developer of fundamental software components best get the credit they deserve?
Developing useful software products is becoming an increasingly important research activity in many fields.
However, it seems the proper credit/incentive system has not been fully worked out.
The situation becomes particularly problematic when large and complicated software products depends on many individual components developed by different research teams.
Consider a situation in which a researcher spend years of effort to develop a software component C that solves a very specific but very difficult fundamental problem. This researcher then publishes a paper on C.
Another group then develops a more general software B in a few weeks, which is a thin wrapper for C.  It basically reduces a more general class of problems to specialized problems that C can solve and then feed to C.  With everything being open source, B can directly incorporate C into itself in various ways.  Let's  assume this is done legally, and the README file in B contains flattering acknowledgement to C. This group then publishes a paper on B, which properly cites the original paper on C. (Best possible situation)
Fast forward a few years. Since C solves only very specific problems, no one uses it directly (other than B). The more general class of problems that B can solve (thanks to C) happened to become a hot topic. And the citation tally is now:

C: 1 citation (just the paper on B);
B: 1200 citations.

This seems like a terrible situation for the author of C. And this is not purely hypothetical. I have seen this happen to several people already.
More broadly, this credit/incentive structure may be bad for a field.  In particular, any one in tenure track position probably shouldn't be developing software for solving specific but fundamental problem (even though they are likely in a career stage in which they are most capable of doing exactly that).
My question is, taking what I described as given (I know it happens, so there's no point explaining why such situation does not exist), how original developer of fundamental software components could position themselves (other than keeping things closed) to get proper credit?
More broadly, how can a field setup proper structure to incentivize the development of such software?

Why is recognition in the form of citations important to you? Why don't you write B1, B2, ... BN yourself? Lots of papers only have one citation. Write more software. People who only write one paper don't normally get a lot of citations.

Maybe the insight that this software can be used generally is actually worth more than the software itself. But if that is not the case here: fortunately there are more and more scientists who can judge these situations correctly instead of only counting citations.

"The whole thing that makes a mathematician’s life worthwhile is that he gets the grudging admiration of three or four colleagues." -- Donald Knuth, Computer Scientist

People who usually contributed to significant frameworks and components have pretty solid standing in the field and are highly regarded by community. People who volunteer their time to develop software are usually motivated by addressing certain problem. Success is measured in adoption of solution and that often results in commercial opportunities. A lot of papers on R-relate topics will be concerned with specific models, etc. but no one would question the role that R Core Team has in creating the language and making it available.

One idea is to develop a measure, similar to Google's PageRank algorithm, that measures papers not only by their direct citation count, but also by indirect count. So if C is cited by a highly-cited paper, the rank of C will increase too.

@Buffy, Yes, ideally the natural follow up work from the author of C should be B1, B2, ....   But there may be many obstacles, e.g., the lack of a broader understanding of the problems or lack of time.  Just generally speaking, it is possible that developing a tool for solving a single problem (C) and the higher level understanding of which tools can to solve what problems (B) require different skill set.

@usr1234567, Knuth neglected to say that a mathematician's life probably won't exist without getting the recognition from a hiring committee.

If B was so important, and follows immediately from C, then the researcher should have made B themselves. I'm sure you're familiar with the concept of low hanging fruit. Do you expect some kind of reward for neglecting to pick it? On the other hand, if perhaps B was not obvious, or B was more work than you imply, why should C get the credit for that work?

@ErelSegal-Halevi But how can you tell the importance to a paper for each of its references? Paper B references paper C, but it references many other things also. Maybe it references stuff that doesn't work, as an example for how badly paper B is needed. Why should that stuff get credit for B's usefulness?

@CrisLuengo you are right. Counting citations is too crude a measure.

Create a culture where evaluation of researchers is done by expert judgement rather than crude benchmarks.

Sorry, I don't follow. Say more?

The experts in the field know that C is more important than B - so if evaluation is done by expert judgement than C gets more credit than B.

Yes, if everyone did the right thing then the world would be a better place. However, ...

@Buffy I agree, that’s why I upvoted this answer for proposing that people (and universities) should do the right thing, and for explaining what “the right thing” is.

Well, as far as I understand we had that. It had good outcomes as well as bad. The big danger is cronyism.

Well, as much as I think that this is how it should be, this does not address the question, namely how the "original developer of fundamental software components could position themselves (other than keeping things closed) to get proper credit". This is something that the community should be doing. The developer with the 1 citation probably doesn't enough influence to make a noticeable difference. Also, it is reasonable to assume that these pea-counting habits will remain while hiring committees do not have the time to evaluate candidates extremely carefully...but will this ever change?

Once a metric becomes a target, it ceases to be a good metric

@Persistence: That is a (paraphrased) quote. What is the source?

Quoted in the 2021-11-29 Stack Overflow blog post The four engineering metrics that will streamline your software delivery - Goodhart's law (1975): "When a measure becomes a target, it ceases to be a good measure."

One thing is getting journals (and referees) better at referencing software dependencies. I've seen similar situations where large code B depends on some code C, everyone cites B but forgets to cite C. The only way is start yourself, making sure sure to cite everything, then when you referee papers, if they only cite B then request they cite C as well.
At the end of the day people should be citing the relevant literature, when they don't then your job as a referee is to request they do. Also when giving talks make sure to be more explicit that while you used B, that it is based on C to remind people about the link.

Isn't this a chicken-and-egg problem?  Most people will know the existence of C.  That's the problem.  If C is already well known, then of course there is no reason to count citations.

how original developer of fundamental software components could position themselves (other than keeping things closed) to get proper credit?

This is a very subjective question, since "proper" will be defined differently by different people. In the original Q OP mentions citations.
But citations are not even a measure of how useful something is. It is a combo of visibility of the original paper, PR campaign, having friends in the field, and how useful is the final product. That is not bad, because awesome but invisible or unusable software should not be rewarded.
So, the original developer should realize that current scientific system rewards very specific behaviors, where generating valuable products is only part of the equation.
If the want to develop fundamental components, they should:

integrate their work into larger eco-system through collaborations
spend time not only coding, but building community around their solutions or ideas
they should not ship just the bare-bones solution, but a valuable toolkit that can be applied, or at least a protocol that will help others develop applications.

Perhaps you should look at your software license.  Why shouldn't it have a clause requiring that software that is using it require that papers that cite that (using) software also cite it?
If there was sufficient interest in a project group, or the community at whole, an open source software promoting organization, or a university, could task lawyers with creating such a license and the whole community would benefit.
(It would be not much different than, say, current BSD, which requires all using software, when distributed, to properly cite the copyrights of all BSD-licensed software it depends on, directly or indirectly.)

Is there any example of license?  I cannot think of any.  Also, if people don't even know about C, they certainly won't know what its license says.

If people are using C in their work sufficiently to cite it they will also know what its license says.  If not, that implies a great deal of disrespect of software and licenses in the academic research world which does not occur in the commercial world, where this is taken seriously.   And would be surprising, to me, because the academic world is itself very concerned with plagiarism.

I don’t think you understand how academic citations work. Authors cannot be legally mandated through a software license to cite someone’s work that they do not wish to cite. Such a requirement would be seen as blatantly unethical and would be completely unacceptable to both paper authors and journal editors. Personally if I ever ran across any software trying to impose such a requirement it’ll go straight into my trash bin, never to be looked at again.

@DanRomik - I do understand how academic citations work.  And your choice to not use software that carries such a license is indeed your choice.  Just as it is for the many commercial companies who also choose to use or not use software depending on (among other things) its license.  In this particular case, it would mean you couldn't use derived software B.  And since B's own creators accepted foundation layer C's license before building on it - that would be fine with them too.  And since it is fine with you: no problem.  If you choose to use it and NOT cite it: whose ethics is implicated?

@davidbak a citation is a specific kind of signal that an author sends to her readers (with the implicit approval of the journal). The convention is that if author X cites work Y, then X believes work Y deserves to be cited and that the citation serves the needs of the readers and is not added gratuitously to serve someone’s ulterior motive. But now you are suggesting to create a legal framework whereby if author X cites work Z, they will also be legally required to cite work Y regardless of whether they believe adding such a citation is warranted and respects that convention. …

… This places on X a requirement that they cannot ethically and conscionably comply with. Nor can the journal publishing the work conscionably give its approval to this state of affairs. So, in such a situation X is forced to either not publish their work, not cite either Z or Y (which violates their ethical duty to cite Z), or cite Z but not Y (which violates their legal mandate to cite Y). All of these options hurt science (the last one doing so the least, hence it’s the one I would likely choose if forced to). Therefore the original requirement is unethical.

@DanRomik -  But if authors of the derivative software B accepted the license of C, THEY were saying that C was critical to their software B, and is deserving of recognition.  Whatever.  The OPs question was how to arrange that C got credit.  This is a way to arrange it.  Anyone who doesn't like it doesn't have to use C.  This doesn't hurt "science" any more than if C didn't exist in the first place.  If it didn't exist, B would have had to create it - maybe they wouldn't have done the work and then B wouldn't exist either.  Now, that would hurt science.  Do what you want. Be moral for sure.

@davidbak interesting opinions, thanks for the discussion.

The NIH asks applicants to fill out a "Biosketch" that is used to assess the qualifications of the PI (and other key members) of the proposal.
It asks for up to five "Contributions to Science", each of consists of a half-page of text and up to four references to "research products", which need not be publications or even your own work. This would be an ideal place for the authors of C to explain how their work underpins the more popular package B. Indeed, I've heard that people have had success doing something similar with data resources: "I collected/curated data set X, which others have used to do impactful things Y and Z." The one important caveat is that NIH does not allow hyperlinks in grants, so you can't directly link to the README, but I imagine you can allude to it.
Here's the Biosketch Instructions, which include a sample.

I support the answer of Alexander Woo, but would like to elaborate on "expert judgement rather than crude benchmarks". In my opinion the benchmarks will always be there, whether we want it or not. This is simply not practical to pull experts from their main jobs to do evaluation of other scientists.
Benchmarks deserve their existence. However, it is up to experts to devise clear criteria for the evaluations. One such criterion could be to exclude engineering and software engineering from the academic evaluations. We should evaluate academicians according to academic criteria, scientific programers according to 0.5 x software engineering + 0.5 x academic criteria, and programers according to industrial standards.
The problem is in the self-perception of scientific programmers. Very often they position themselves both in academic field and industry to maximize their chances of finding a job. Pure mathematicians, string theorists, philosophers, or social scientists do not have such an escape.


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Precedents of student affair/DEI providing input in faculty hiring, promotion, and evaluation?
Has there been any examples of office of student affairs or office of Diversity Equity and Inclusion (DEI) or equivalent offices in university administrations providing (direct and nontrivial) input in the hiring, evaluation, and promotion of (academic) faculty?

Hard to prove that there never has been. One can easily imagine the office of student affairs bringing up cases where a promotion candidate has not followed university policy, particularly if they were found in the wrong and punished in some way.

Probably not in individual cases. But they might be involved in setting policy.

I agree with @Buffy. In the University of California system for example, contributions to diversity are taken into account (at least to some extent) in promotion and hiring decisions in all cases following standard university policy. That policy was no doubt conceived with assistance from the types of offices you’re asking about. But I’m not aware of a more direct type of influence.

I meant to type precedents. I'm not aware of any current examples, so it's mainly a question of existence of such practice. Prevalence would work too.

Search in U. California system, specifically, UC Berkeley,UCLA,  Cal State Universities. If there were examples, there were in CA.

There are usually rare cases of just about everything. However:
An office of diversity would most likely be involved in setting policy that other parts of the university must adhere to. But, in the US, at least, those are unlikely to affect individual cases other than at the margin. Diversity is still a difficult problem that has few answers, partly because it is contentious. (I have no experience outside the US.)
The office of student affairs will often collect complaints from students. Those that can't be handled immediately will probably be passed on to other administrators that have direct responsibility for faculty. So, enough complaints, forwarded to the department chair might well have an effect on tenure or promotion, but it would be more likely to be other than direct involvement by student affairs.

While the above is a view of what happens officially, who can say what goes on in private meetings. A faculty member with a sufficiently bad reputation that reflects badly on the university, might be handled sub-rosa.

Policy has some influence. We also have to go through a DEI training to be on a search committee. I have definitely seen committee members incorporate what they learned into their hiring.

@Dawn. one would hope that policy has some influence.

Having an affair with a student likely will impact promotion in many places...


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Do universities generally allow faculty members to teach while getting NSF summer salary?
What is the general practice for universities in USA in deciding if there any conflict between receiving 2 month salary funded by an NSF grant (the maximum) and teaching a Summer course (which produces additional salary)?
It is possible very short Summer course may be an exception. I’m mainly interested in longer Summer courses that will definitely overlap with the 2 month research that we generally have to claim 100% effort.

My university has the policy that one can't be paid for more than 12 months per year.

It might be possible to take 2 months of summer salary from an NSF grant (or a grant from some other agency) and also teach a summer school course for another month of summer salary.  This assumes that your academic year contract is for 9 months.  For example, our institution pays one month of summer salary for teaching an 8 week summer school course with one hour of lecture per day.  That's reasonably 50% effort during that time.  This could be combined with one month of full time effort before/after the summer session and two months of 50% research effort during the summer session.

US granting agencies operate salary splits on an "% effort" basis. See for example https://www.nsf.gov/bfa/dias/caar/time.jsp which stipulates that your effort must:

Reasonably reflect the total activity for which the employee is compensating across all grant-related and non-grant related activities (100% effort)

Support the distribution of employee salary across multiple activities or cost objectives (for example, effort spent on multiple federal awards, spent on general/or administrative activities, vacation, sick leave, leave without pay, etc.)

...etc.
You can't be paid twice for the same time, the government doesn't recognize 'overtime' (the same is true for most salaried positions in the private sector), so while you could potentially work part time on a NSF (or other federal) grant and part time teaching, you can't have over 100% effort (post-game sports interviews notwithstanding).
I'm not as familiar with summer NSF grants as others are here, since my field is mostly NIH-funded and year-round, but my understanding that these are typically meant to fund someone full-time over the duration of the grant, so you would be expected to put 100% of your effort towards the work that grant funds during that time. You would not be able to teach while certifying that you've put 100% effort towards the grant paying your salary.
Ask your administration, though, if there is any way to manage things differently.

My office of sponsored research, shockingly, does not know.

@Bilbo They should probably figure it out one way or another.

In my observation, in the U.S., in math, at big state univs, your own research office and other admins would not allow this.
This does not entirely make sense, indeed, in the traditional context that academic salaries are "nine-month" salaries (though may be paid out in 12), and the NSF (traditionally, anyway) would pay at most two months' summer salary (so 2/9 of one's salary), leaving a month in which one was not officially being paid for any particular obligation.
However, it seems that both NSF and many univ admins do not allow anything further after that 9-months + 2-months.
... not to mention, as @Buffy commented, that the double-time summer school teaching takes a lot of energy...

My big state university has no problem with people getting paid for all three summer months, through some combination of grants, teaching, and occasionally other sources.

@Buzz, interesting!

@Buzz, in those cases, could there be overlap between the months one has to teach, and the months one claim 100% effort for NSF report?  If teaching only occupy 1 or the 3 months, I can see that will not be a problem. But what if there is overlap?

@Bilbo You cannot be paid a salary twice over for the same time.  I suppose that if you had only half (or whatever fraction) salary support during some period, you might be able to supplement it with partial support from another source, although I have never encountered that, and it seems like it would a logistical nightmare, to say nothing of convincing the funders to accept such an arrangement.  In practice, it doesn’t matter much which dates are specified as being funded by which sources, but the total has to come out right at the end of the summer.

While I doubt that this is possible, the way to be certain is to ask at the grants/funding office at the university or the NSF program office.
Don't attempt it without notifying everyone involved of the entire situation.
The compressed schedule of a summer course implies significant attention be paid. The research (I assume) that the NSF is sponsoring likewise. It would be hard to do a decent job of both.


text:
Colleague stops replying emails about project, and later publishes the project with other colleagues?
I met a Chinese colleague in a conference, where we identified a research topic of common interest. So, we agreed on collaborating on a project and started exchanging some emails about the project, where we came up with a clearly defined project and preliminary results (including R codes and statistical models). This happened in the course of around 3 months after he went back to his country.
Then, he started taking long time to reply to my emails, claiming he had internet access issues until one day (at around 6 months after we met) he stopped replying. So, I just thought he was not interested in the paper anymore. However, around 2 years later, I saw the paper published in a top biostatistical journal. At first, I was dumbfounded to see it was exactly the same idea, same formulation, just with the remaining bits and pieces completed. Two more authors were included in that paper. I emailed my colleague to "check if he wanted to continue our collaboration" but got no reply anymore.
I went on a rollercoaster of emotions, thinking of emailing the Editors (I have emails and drafts and code), but then I decided to leave it to Higher Powers in Life.
My question is, in general, what is the Ethical thing to do when you find your colleague publishes a paper on something you contributed, not only to formulate, but also to develop.

I feel very sorry for you and admire your open mind. I don't have enough knowledge to answer your question, but I can add a little background for this kind of issue. It really depends on whether this colleague belongs to a Chinese research institution or not. Based on my humble experience, the Chinese government generally ignores and even encourages academic misconduct. This is to say, he could have done similar things multiple times without taking charges from his own institution. I don't know about the US but I highly doubt he could do the same thing there.

Wow, not nice. Unless you have proof of misconduct that would be accepted by a journal, you have little to resort to. Strike them off as a bad investment. Who knows, karma will strike at some point.

Thanks everyone for your comments. It seems like it is better to leave things where they are and learn a positive lesson from it.

Send an account of the incident (without any judgement and accusation, like the one you has written here) to the head of his department.

I admire your attitude. However, by not doing anything, you allow (and a bit encourage) this behaviour. From the community's point of view, it would be better to report so this behaviours stops. I do understand, though, that for you it may be much better not fight and leave it be.

Please don’t write answers in comments. It bypasses our quality measures by not having voting (both up and down) available on comments, as well as having other problems detailed on meta. Comments are for clarifying and improving the question; please don’t use them for other purposes. If you have an answer in the comments, please consider moving it to the answer box; otherwise it may be moved to chat or deleted.

You are facing two different possibilities.
One option is where you put the incident aside and move on.
The other option is relevant when you have evidence that your work was used to generate the publication without an appropriate acknowledgement. The three legal levels of proof of misconduct are presented at this link. Start at the lowest level (preponderance of evidence). You might for example be able to determine, on hand your previous notes, that preliminary results or source code from your email exchanges appear in the publication. If so, you can decide to prepare to contact the journal editor and make your case to be included in an errata, listed for example as co-author. If you take this choice, you may want to present your case first fully to a trusted colleague at a higher (more senior) level to assure that you remain objective in your statements and that your arguments are logically sound, doing so before you write to the editor of the journal.
Whichever path you choose, you may take an underlying lesson: When you put forward an idea and, for whatever reason, do not lead it diligently to its end, you may loose it. Your final response has to be divorced from the emotions of the loss, even though emotions are appropriate from this incident. I too would feel rather betrayed either by my own inherent trust in the good-will of others and/or by the behind-the-back stab of a clever thief.
In summary, by taking the second approach, you will pursue a somewhat legal path when you can find evidence (and self-confidence) to support it. By taking the first first approach, the words of a friend of mine might strike home ... "Oh well. It seems I lost that one. Next!"

You can report this problem to the editor of the journal, and send the relevant email with the corresponding information.


text:
Should I delete statement from my thesis?
On my bachelor's thesis' frontpage, I wrote this sentence: "submitted by [my name] in partial fulﬁlment of the requirements for the degree of Bachelor in Computer Technology".
I had someone review my thesis and they told me that they never saw that. My thesis is worth 30 ECTS credits and I have to get 180 ECTS credits for my bachelor. They made mistakes with my thesis' contents (or my sources are wrong) so I'm wondering whether or not they're right. Is this sentence wrong and should I erase it and why?
Thanks in advance

No one here can answer this. It depends entirely on your university. Every university has different requirements for formatting and what is required. Check with your university

Ask your advisor or look at a previous thesis. It might be standard some places. For publication, it is up to you to include it (perhaps as a footnote) or not.

My university doesn't have any guidelines about this. Their guidelines are less formal. I was wondering whether or not it was factually acceptable. Without this (i.e. with only "submitted by [my name] in fulﬁlment of the requirements for the degree of Bachelor in Computer Technology"), would it mean "complete fullfillment"?

Are you asking about the word "partial" (as your last comment suggests) or the sentence as a whole (as the question itself suggests)? In the former case, yes, keeping the sentence but omitting the word "partial" would imply that the thesis itself is the only requirement for your degree, which is factually incorrect. But deleting the sentence entirely is a different matter.

I wanted to know if I should delete the word "formal", the whole sentence or nothing.

the original sentence does not contain the word "formal"....

My university doesn't have any guidelines about this. Their guidelines are less formal.

Then it doesn't matter too much.  It's a matter of personal preference.  Include it if you want, or omit it.

I was wondering whether or not it was factually acceptable.

Well, yes, it is factually correct.  But if you leave it out, no one will assume it means complete fullfillment, simply because the vast majority of all degrees require both coursework and thesis.

I assumed it. I asked this question because the proofreader said that I should avoid it.


text:
I am doing a PhD and I want to start a BA on the side, not sure how to approach this with my supervisor
I am close to the end of my second of five years of funded PhD in philosophy. Because of personal interest, I would like to start a part-time BA in Law on the side, which is tailored to people who have a job, thus it only has non-mandatory evening classes. I want to talk about this with my supervisor because I don't want to hide this from him, but at the same time I fear he might think that I don't take the PhD seriously or that I am a fool for trying to do to much.
Long story short, I would like to be honest without giving him the impression that I don't know what I am doing with myself. Any suggestions on how to approach this? Any similar experiences?

Why do you want a BA when a few courses might be enough. If this is the US, there are a lot of other non-law courses you would need for a degree.

If I was the PI, I would not be concerned that you're not taking your PhD serious or that you're a fool. I would be concerned that you underestimate the effort and how much focus an additional BSc would take away from your thesis. Many people struggle with completing just their PhD, and a BSc on top seems a huge additional workload.

Perhaps you should say which country. Undergrad degrees differ quite a lot from place to place.

I am in Belgium

You only comment about the class commitment in your question. Law degrees have huge reading requirements. As a philosopher, you are used to reading, synthesising and arguing so it is likely that your workload requirements would be lower than the average hours quoted by the university, but it's important to understand that the research and writing times are considerable.

Not enough reputation to comment, so have to paste this as an answer. I did actually start an Open University (part time, evening classes) BSc alongside my PhD. I didn't tell a soul. Well I guess I just did! There was no problem. That said, it was masses of work but I considered the OU degree was giving me skills complementary to my PhD.
So my short answer: if you feel you must confess... can you sell it as complementary? Will it boost your skills for the current PhD and bring skills and knowledge to the PI's group?

Thank you so much for this reply. I do not know anyone else who is doing the same so it feels a bit strange, but I am really committed to doing this. Can I ask you in which country was this? I think it can be seen as complimentary indeed.

OU normally implies UK. It is a very high quality distance learning university. I don't believe it is open to everyone world wide, though. They tried and failed to establish a base in US. I don't know the EU status. And a UK degree is quite different from a US one.

Do the skis taste better after you brine them?  :)  (Please edit your post for typos!)

Sorry about typos, on my iPAD in a busy environment, but no excuse.  I think some kind soul has already corrected them?  This was UK.  I wasn't suggesting the OP enrol in OU, but just giving an example that I did do this. I hope it wasn't naughty. Genuinely felt the need for more training! ...and it has served me well.


text:
My fears and resentment about my supervisor
I have now submitted my thesis. My advisor didn't help me at all during this 3 and half years time. My thesis hasn't been read properly and I fear about the outcome. Unfortunately the culture of my school is not something where you can change things but nothing I can do except getting on with it.
I will feel burdened If I see my supervisor's name with my papers the ones I will get out of this PhD. She hasn't contributed anything than only accepting me to do this project. I also worry she has hand on my data and she can use it for her own publication once I get out of the University.
So I would like to ask, Are these just my own fears or is it something I really deal with it? Has it happened with someone else too? What are the strategies I should adopt?
Thanks for help!

If your supervisor publishes your results, then that's plagiarism.

So you were not financially supported, never met with them, never discussed anything, never used any equipment, never benefited from introductions to others?

@JonCuster: What do you want to imply with this? Should a student be happy if he/she gets financial support but no support for the actual research? I know that there is no use in complaining about unfair supervisors - you need to be pragmatic about that. But there is also no need to thank them for their effort.

@J.FabianMeier - the implication is that we have one side of the story. The OP declares that their advisor "didn't help me at all" - well, is that really true? It is possible that this conclusion is colored by personal perceptions.. A neutral observer might have a different conclusion. While the feelings of the OP are not changed, the path forward is different.

@JonCuster  I think it easy to generalise a phd story. But we should know that there are students who are doing self-funded PhD, I am one them. I have paid £21,000 in three years to pursue a PhD. Yes I met them (not often and they stated they are extremely busy), I had a desk and I haven't been introduced to any well known scholar in my field. My perceptions are ultimate result of my experience. I approached the management for this matter but it appeared that they are all part of a gang. If I had some help I would have appreciated it. Unfortunately I am not the only one in my school with this.

I understand your bitterness.  What you might want to do to protect yourself is to make sure your self-documentation of your research is well organized so you can refer to it if it ever becomes necessary.  Collect the key bits and email them to a reliable person.  That can help you substantiate your original work.  Once you've done that, you can rest easy and move on with your life, leaving your bitter experience behind you.

@aparente001 cheers thats what I would do.

I had exactly the same situation. My supervisor has 2 students (including me) and in the 4 years she was in the department (she joined the same time as me) she didn't publish a single paper with either of us.
Initially I tried to be very involved, deliberately going to see her at least twice a week to discuss things, going through my workings, asking for advice on what literature to read etc. I realised within 3 months she wasn't really engaging in anything and her other student said the same to me. The supervisor published 2 papers in her first year there, both jointly with people she knew from other universities. As I became more involved in collaborating with them I realised she didn't actually contribute anything to the work beyond the most superficial (largely thanks to how her English was better than the collaborators so she always did the writing up...). In one instance she presented "her research" to the group in one of our weekly internal presentations and at the end I leant over to her other student and whispered "Every single result in that presentation [Collaborator 1] sent me 3 months ago, she didn't do any of that!".
To make matters worse she was away the entirity of my 2nd year due to having a child (and when she returned she'd mentally 'checked out'). I felt completely lost and without direction, due to the fact all the other people in my domain were elsewhere in Europe or in the US. Eventually I managed to give myself some drive in the area AND I picked up a 2nd supervisor on a different topic. By the end of my PhD I'd published a paper with the 2nd supervisor, one with the collaborator and one entirely on my own, without her even reading it. I'm also certain she didn't read my draft thesis. She didn't read any of my paper drafts. I once asked her "Have you seen anyone do this sort of approach before" and she said "No", only for the External Examiner of my thesis, whom she picked, to say "I did a similar approach in my last paper". To find that out during a viva was a hell of a shock! I managed to defend my thesis though, my approach and ideas were different but I'd definitely have benefited if she'd informed me correctly.
Her other student wasn't so lucky. Our supervisor actively blocked her taking up a 2nd supervisor. She'd also done enough with the student that the student couldn't publish the work herself without breaking rules. The supervisor sat on a final draft of the student's paper for 9 months! Eventually the other student had to take her to the Head of Department to force her to either sign off on it or fully bin it because the student was approaching the 4 year deadline.
We both managed to get our PhDs and I think I came out of it stronger but it's not something I'd like to repeat. I couldn't say "**** you to Dr [Supervisor] for being useless" in my thesis but all I did was acknowledge her existence. I didn't mention her in any of my papers at all, which might be considered the height of rudeness usually but that was kinda the point... I think the department realised it was something problematic too because she didn't publish another paper and ended up leaving Academia 6 months after I finished.
In terms of ways of dealing with it I found that picking up a 2nd supervisor really helped. Collaborating by email is okay but it doesn't replace a face-to-face discussion in front of a blackboard. Ideally it's in an area with a lot of overlap with your own, it'll make it easier to hit the ground running. By making progress with this second strand of work it reduces the stress of working on your original problem and often that's enough for you to start making headway on your own.
You definitely need to be regimented with your time (though you could say this about doing a PhD in general). With no one looking over your shoulder it can be easy to just become apathetic. Keeping a schedule and daily routine helps to avoid that. If you're stuck on something then don't just stay at home that day, find a paper in your area and try to rederive the results (I was in theoretical physics so lots of maths workings) or work through the details the paper might have glossed over. That way you're keeping the subject active in your mind and who knows, maybe you'll think "Hey, I can do this a much better way!" and there's the spark of a paper all of your own.
At the very least, talk to people. Don't shut yourself off from other PhD students in your group, either socially or professionally. The occasional rant or indepth discussion about some aspect of research can be mentally uplifting.

It wasn't an easy journey and but some friends really helped to get on with the research. I don't know how a supervisor can be so lazy. I mean once they were a PhD student too and they should know the importance of this relationship. But its just so frustrating when they become selfish and lazy. I am glad I am almost done with my supervisor.

The ratio of rant to information in this answer seems a bit high; could it be edited to preserve the salient points and advice, while toning down the chatty stuff?

Many supervisors do not help their PhD students (I do not have statistics, obviously, but experience from different universities and research areas). These students often feel lost and also unsure about their PhD thesis. At least in Germany it is not uncommon that PhD students who have these kinds of supervisors drop out or take exceptionally long for their PhD.
I think the best you can do in such a situation is to get help from other sides (often difficult), and if this does not work out you should finish as quick (and as good) as possible and leave that particular environment.
It is unlikely that you'll fail if you submitted a proper PhD thesis. It is also unlikely that your supervisor will directly use your data or results if she is not really involved in your research. She might give them to the next PhD student, but you (as a postdoc) will probably be much more experienced so that it is unlikely that this PhD student publishes something you also tried to do.
So, I would not worry too much but look for a better place for your future research.

Also, not every negative supervising experience is bad. For example, I know a guy who had a bad supervisor which didn't help him at all. Although it was tough at the start, he managed to publish only sole author papers and to finish the PhD without any help. He now works as a researcher for an institution, and have a very good publication record, being one of the best researchers in this institute. I gave you this example to show that in certain conditions some "negative" experiences   turn into very positive ones.

I don't share @MikeyMike's optimism — I think those "advisers" do not usually create strong researchers but put lots of potential in a meat grinder. But I agree that a bad start does not have to be the end of your career. So yeah, get that bad experience behind you and concentrate on your career (i.e., publications). As for "fearing the defense", ask whether anyone did fail. Usually that's rare because it always falls back badly on the adviser.

@MikeyMike agree!! After submission I can say that the journey was definitely very difficult but the self learning experience is something I would cherish. I might sound bitter with today's question but I am learning everyday through these experiences.

I disagree with your sentiment Mike, that a brilliant researcher is only brilliant because they went through an abusive relationship for X years. Sometimes there isn't a silver lining. Sometimes bad people in high positions just hurt science as a whole. Discoveries go undiscovered for another 5 or 10 years. We should not consider it acceptable to ignore a PhD student for any reason. It's like saying "Sure rape sucks, but on the plus side it makes you better at sex."

(At least in the UK) a PhD student is required to have more than a single supervisor.  In other words, here exists a figure of a secondary supervisor with whom you can discuss problems that you may have about your main supervisor and general topics about your research when the main supervisor is not available.
This approach mitigates issues where a person is unavailable too often or not interested in the research of his/her PhD students (which I find strange since that should be a good source of ideas for his/her own research).  Moreover, it is not uncommon to see papers including the names of the PhD student and the second supervisor (main supervisor not included).
Even more, just the fact that someone is working inside a university allows him to interact with other PhD students and often exchange ideas.  I believe that, on at least a single paper, you may have included (possibly not in the authors but maybe acknowledgments) some of your colleagues.  That must be worth something.
Nevertheless, you managed to complete a thesis (you submitted it), congratulations!  You can argue that it was a difficult journey without the help of your supervisor, but you made it.  (Well, almost, but if you submitted the thesis you're a good way towards the completion of the road.)

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