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My PhD supervisor is indicating that I should leave my PhD due to health issues impacting my progress. What do you think?
I am a part-time psychology PhD student. In the first 12 months of my PhD, I have fully drafted a systematic review for publication and written my confirmation document, which is approximately 14k words. My confirmation is next week.
My health is pretty terrible and I have been honest with my supervisors about my health. When I was first set to begin my PhD, I was diagnosed with stage one cancer, so I had to be treated for that before I could continue. I also have an autoimmune disorder.
In January this year, I caught COVID and developed raised intracranial pressure as a consequence. I felt OK to continue once I had taken two weeks off, but they highly recommended a two-month intermission, so that's what I did. They said that this was their recommendation because sick leave doesn't "stop the clock" in regard to when my PhD is due.
I recommenced my PhD last week and had a meeting with my secondary supervisor. She said that my primary supervisor would be unable to continue to be my primary supervisor because she's finding working with me very "stop and start", and I'm working too slowly and inefficiently. She also said that she's finding my health problems a bit much to handle.
There were many suggestions that I should withdraw from my PhD. She said that I really need to think about whether I want to do the PhD because it's a long slog, and that it may just be better to work as a psychologist (I'm a registered psychologist and work part-time in private practice). I have obviously thought about this a lot and it's what I want to do.
She also said that I'm likely to struggle to find work after my PhD, and that if I do my PhD, it should be with the knowledge that is truly for the joy of the research and not employment opportunities.
She also said that she's not convinced that I didn't need to take intermission because of PhD-related stress. I said that COVID led directly to a neurological complication, and she said, "yes, but you know how the biopsychosocial model works..."
She said that at my confirmation I would need to explain my health issues to the examiners, and we will talk through it. I brought up discrimination and she stopped talking.
My previous primary supervisor, who is now my secondary supervisor, isn't going to talk to me about her decision, which is uncomfortable. She has told me in the past that she has 12 PhD students and she dedicates an hour long meeting once a month to her PhD students and she can't provide any support beyond that. She was recently promoted to Deputy Head of School.
I'm not listed as one of the students on the research lab's website. All the other students have also been given positions as research assistants, and I haven't.
My supervisor who is no longer my primary also developed the intervention that I will be adapting for my PhD. She is being very difficult and won't share the content with me, so that's going to look strange at confirmation.
Does anyone have any suggestions? There aren't any other academics in my field at this university.

Could you add a region tag? This sounds like a situation where you might benefit from additional resources at your university, the names and framework of which vary a lot across countries.

"I have obviously thought about this a lot and it's what I want to do." The "it" presumably refers to continuing your PhD, didn’t it?

Can you clarify that third paragraph?  I can't quite tell who was for and who was against the extended Covid-related break, and I can't tell what does and does not extend the timeline clock.

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"yes, but you know how the biopsychosocial model works..." What did the person mean by this? Could you explain?

@toby544 From google, "The biopsychosocial model is a general model that suggests that biological, psychological, and social factors all play a significant role in health and disease." In context, I believe what the advisor is implying is that the disease is all in the OP's head, at least symptoms bad enough that delay work.

@Andrew If that is what the advisor meant, this is one of the worst things said by an advisor that I have ever read on this site.

I did my PhD in a biology-related field, but I saw a few people have a similar situation to you where their advisor no longer wanted to be their advisor, suggested they leave, or straight up told them they would never finish their PhD in their lab. None of them ended up finishing.
So I know this seems drastic, but if your advisor no longer wants to work with you that's the end of working with them. It isn't going to be the effort and the end result will either be you burnt out or not finishing.
The best thing you can do is find a new advisor. Finding a good advisor is not just about finding one who does the same work as you, in fact, I'd say that is almost secondary, it is about finding one that will help you become the best scientist you can be and one that you get along with.
Go to your department head/student union head/any university person who is there to help you and get advice on what is possible in your university/region. But please, don't try working with people who don't want to work with you.

"never finish their PhD in their lab"... Do you mean that they were effectively shown the door, or that despite being given the chance they weren't up to the challenge?

@MarkMorganLloyd: It can be extremely difficult to judge the difference between these, without knowing the situation very closely.  Almost always in my experience, the supervisor will claim (and usually believe) they gave the student a fair chance — and conversely, whether the student believes they were given a fair chance is usually determined more by their general personality and self-esteem rather than a considered judgement of what happened.

It can, which is why I specifically asked @harper357 for clarification.

@MarkMorganLloyd I want to be careful with my wording here, a PhD advisor is supposed to be a mentor, someone who supports and helps you. They should not be an advisory. In my anecdote, the student took it as a "challenge", that they just had to prove something to this professor and they would change their mind. That was never a possibility. Their work styles were never going to fit. A PhD student has very little power in this dynamic. It is not worth the pain and headaches when the end result is already determined in their mind.

@harper357 Thanks for that, I think it's a useful clarification, as well as being a reminder that postgrads are fairly low in the pecking order.

First, people with health challenges can and do complete PhDs. Many of the PhD students I knew in my program, including myself, had a variety of both acute and chronic health issues.
However, it does require some introspection and potential behavioral changes on the student's part to work through this, which I'll highlight at the end.
Advisor / Supervisor Point of View
First I'll concede a few points that have been made to you. A PhD is a long slog (especially trying to do it part-time), and post-PhD employment is difficult to find.
But those items are true for all PhD students, regardless of health issues.
From your advisor's point of view, a PhD student typically represents two things:

A student to train in the ways of research in their field of expertise.
A resource that they are paying for, which enables them to make progress in their own research.

So from your advisor's point of view, the start/stop nature caused by your health challenges is a major obstacle to what they view as the focus of a PhD student.
And frankly, this is a valid perspective, even if we might judge it to be not particularly compassionate.
Your Point of View
The biggest question you have to ask is why you would want to continue with a PhD. Regardless of the valid perspectives of your advisor, no other opinion matters but this one.

You can find a new advisor more accommodating to your health challenges.
You can find a new research project.
You can even find a completely new program if you have to.

But if you're not fully committed to the "why" behind your PhD journey, the struggles that you are dealing with to work towards a PhD will be too much for your lack of motivation to overcome.
And again, this is true for all PhD students, regardless of health issues.
A Moment of Introspection
Finally, as with most internet questions, we're looking at this through a relatively specific lens that is presented. Another factor that often affects situations like this is quality and frequency of communication.
Regardless of what course of action you ultimately choose, you owe it to yourself to take an honest look at the way you've communicated about your work, and how your health challenges have affected it.
This single skill will have the biggest impact on your future both during and after your PhD program. (Again, this is true for all PhD students, regardless of health challenges)
As an example, let's say you tell your advisor you will have completed a task by Saturday evening. Some questions to ask yourself:

Knowing you have health challenges that could impact that deadline, do you consistently add that factor to your estimate of when you can have things done, or do you tend to over-promise in order to please?

If you were a deadline-motivated person prior to your health challenges, have you recognized the limits of that approach? Someone with no health challenges might be able to regularly put off a Saturday deadline until the end of the week and pull a couple of all nighters to get it done in time. Someone with intermittent health challenges needs to plan for the possibility that they will be incapacitated on Friday and likely start immediately and take full advantage of every moment of health.

If a deadline slips because of health challenges, do you communicate about this before the deadline, or do you typically communicate about it after the deadline has passed, perhaps days after it has passed, or only after your advisor has had to reach out to you about it?

I cannot stress enough the important of good, proactive communication in situations like this.
This factor alone can make the difference between an advisor who is willing to work with you despite your health challenges, and one who decides they can no longer deal with them.

My PhD was in a STEM field, so I know little about psychology departments, but I can tell you that an advisor with 12 Phd-students who picks up additional administrative duties and who has expressed a desire not to work with you will make for a very difficult slog through the program. Add this to your health issues and other responsibilities and I would run from this program as fast as I could unless your absolute heart's desire is a PhD from this exact department.
Two suggestions:
(1) Find a different faculty member in the department; one that you respect and seems like a reasonable person and with whom you have some rapport. Explain to them the situation and just hear what they have to say, whether explanatory or advisory.
(2) This one is difficult and I do not mean to suggest that I can detect any such thing, but there are reasons besides health and work output that can trigger/cause/incentivize faculty members to express an unwillingness or distaste for working with a student. One group of possibilities could be personality conflicts, personal conflicts, or things like political/religious conflicts. Have the faculty members in question ever just seemed consistently short with you for no apparent reason? A second group of possibilities revolve around your work style and even their perception of your abilities and aptitudes for PhD-level work. What did the faculty member say about your systematic review? The suggestion is to simply think carefully about these possibilities and perhaps sanity-check them with a fellow student or the respected faculty member mentioned above. Don't get imposter-syndrome based on anything a SE poster says! Just be clear-eyed about these things.
Most PhD-stints are difficult, at least some of the time, and some are horror shows. Faculty members can have their own personal problems, they can be under the gun for publications or stressed for other reasons. They don't always behave consistently with their best possible selves. Good luck sorting it out and making the decisions that are right for you at this time.

I Advise At Least Two Things
First, Talk To Someone Who Knows The Rules
I believe you.
I believe your supervisors said what you report.
But I question if what they said is accurate.

The part about PhD studies being a long, hard road:  Yeah that's true.  It's on you to make an informed decision.  It's on them to give you that information.  It's not on them to crush your spirit.

The part about the inflexibility of the schedules and the deadlines is, to me, highly suspect.  I am sure this varies by country and institution, but my institution (public R1 in the United states) considered it a matter ethics and basic human decency to work with students with documented medical issues, either emergent or chronic.

The part where they take it upon themselves to decide whether your health conditions are real is, at least here, entirely over the line.

The real complicating factor is that the current second supervisor is also moving up to something assistant chair of the department.  It's complicating because normally I would suggest you talk to the department chair about this to get clarity on how the university requires health issues to be dealt with.
If there is a separate Graduate College which administers the graduate degrees, I would start there.  Or an ombudsman, which many universities have.
Second, get new advisors
Like other responders, I am not in psychology, but twelve advisee sounds (your now secondary supervisor) like way too many, and then stepping up into major administrative duties makes that even worse.  It's rational, and probably even wise, to start stepping back from advising duties, but there are good ways and bad ways to do that.
Your primary supervisor, though... wow.  So many red flags.  A PhD supervisor-supervisee relationship should be a trusting one, and I'm just not sure how I could trust someone calling into question or outright disrespecting medical conditions.  (The rest of their behavior is bad, too.)
Once you have a firm grasp of the rules, start looking for another supervisor.

sick leave doesn't "stop the clock" in regard to when my PhD is due
Strange - this is certainly not how UK universities operate.
she's finding working with me very "stop and start", and I'm working too slowly and inefficiently. She also said that she's finding my health problems a bit much to handle.
I am sorry but that is both sickening and utterly unprofessional.
it may just be better to work as a psychologist (I'm a registered psychologist and work part-time in private practice)
I am glad you have a fall-back. Technically, this is sound advice (after all, it may be better) but it sounds a lot like pressure is being applied.
struggle to find work after my PhD, and that if I do my PhD, it should be with the knowledge that is truly for the joy of the research and not employment opportunities.
You already have a job as a psychologist! Does she mean post-doc type positions in particular? But look: you are already qualified and having the extra qualifications is not going to hurt.
"yes, but you know how the biopsychosocial model works..."
OK, I am sorry but this is hooey. She is just saying that you are being hysterical, although this is of course a word that would never pass her lips.
at my confirmation I would need to explain my health issues to the examiners
Yes, and...? Fair enough, right?
She has told me in the past that she has 12 PhD students and she dedicates an hour long meeting once a month to her PhD students and she can't provide any support beyond that. She was recently promoted to Deputy Head of School.
That is extremely minimal support for any PhD student.
I am so sorry, but you are up the plank and being prodded to jump. I honestly don't think there is any chance they are going to be decent about the whole matter.

I agree with much of this. The faculty involved seem immature.

My own experience is parallel but puzzling in comparison to yours. I agree-- sick leave does not stop the clock. It is also challenging to get, because the paperwork may or may not be available, and it may or may not be possible to document if diagnoses are in flux so that no specific doctor knows what's wrong or if one is sick enough that it is impossible to do the leg-work for the paperwork one's self.
Cancer is a heck of a problem. Wow. Autoimmune with Covid doesn't sound too great either. You really have been hit with a lot. My sympathies.
In my case, I was also in a position where my advisor was kind of downgrading me. I had been offered an opportunity to go to part time because of some low-grade health problems that were bothering my advisor. I was a bit puzzled by this because I had already published four papers in the research group in my 2.5 years there. However, he was right, there were recent health problems. I accepted the half time accommodation.
What shocked absolutely everybody is that immediately after I went to half time, my health problems spiraled out of control. Essentially the same week. I began having seizures every day all day. Eventually, medication treated this, but in the mean time, I lost my advisor and my funding in my fifth year in the program. This was at University of Minnesota in Fall 2010. I eventually earned an MS in July 2013. One might think that going to part time caused the health problems to spiral out of control but that doesn't necessarily seem to correlate with how the health problems actually work as observed today. It seems to have been a giant unfortunate coincidence, or maybe my advisor and I both had a sense something bad was coming, since I also had been diving deeply into neurology literature thinking something was wrong with me.
I don't particularly have any excellent suggestions. Your backup plan of working as a psychiatrist is a good one.
I didn't have a backup career. I moved in with my family, who paid for my living expenses. At the time, COBRAing was the best solution for health insurance if no other options were available. Now the Marketplace also exists. Some people with disabilities have Medicaire or Medicaid in the USA.
But if you are still coping with cancer and an autoimmune disorder, it may in fact be challenging to work some jobs. I currently am limited in what jobs I can take as well, due to the migraines and seizures that returned in 2016. I was able to finish my 3rd masters degree but I have not been able to take a full time job since. I work part time remotely. I don't recommend "part time remote" as plan A, but if your health is very limiting, it is much better than "totally disabled". I have a lot of sympathy for the situation you are in!!!
In the USA, employers are required to accommodate you, if you can perform the job function with accommodations, but if you can't, they are not required to  keep an employee who cannot perform the job function, I believe. I believe. So I'm not quite sure where you stand with regard to that. Research in academia can proceed at a slower pace, but if it is slowed down enough, then other people publish first, or studies that are time sensitive can't be finished and go to waste.
If they are able to freeze your PhD until you're past the cancer at least, that sounds like a great plan. Then you could focus on your health and recover until you're able to return to the time pressure of the PhD.
If it's fundamentally a long term disability, I have no specific suggestions...


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How to proceed if your post-doc advisor gives you terrible project ideas?
I'm currently doing research in computer science. It's been nearly a year since I began working on my project, as a postdoc, but we haven't achieved any tangible results yet. Initially, I was working intensely and implementing whatever my advisor suggested. I was truly believing that he may have some good reasons behind his ideas. However, we recently missed a paper deadline because our results didn't measure up to the baselines.
About a week after that, my advisor spoke to me for about an hour, expressing his dissatisfaction with my lack of organization compared to him. He went over all the mistakes he believed I had made during that period. Honestly, the lack of good results was due to his wrong understanding of the problem. Implementing all the ad hoc suggestions he made without a solid scientific basis was incredibly challenging. Whenever we get closer to the results and we can spend hours on few examples that our model fail, he come up with completely new ideas and implementations that can take up to weeks.
To be precise, leading up to the deadline, I was putting in twelve-hour days, from 7 am to 7 pm, for almost nine months. However, now I feel like he's not as intelligent as he wants to be perceived, and genuinely, I've come to the conclusion that I have more intelligence than him, which I'd rather not to talk about the details.
Overall, I find his ideas to be quite naive, and he lacks an analytical mind. He critiques everyone else's ideas while fully support all his own.
Do you think it's time for me to leave his lab? He is overall a good guy and answers all my technical questions. The center is one of the world's leading centers and a lot of famous senior people are around. So, I'm also concerned about how it might reflect on him in our center, as many advisors have their own labs, and gossips will spread all over. He's a perfectionist, a junior faculty, and doesn't publish as much as other faculty members, and I'm not convinced yet if I can develop a proper academic career with him.

Not addressing your specific question, but I don't see you acting as a postdoc - you don't do what your mentor tells you, you should be telling them what you are doing.

" The center is one of the world's leading centers" tangentially relevant: do not think/hope you will stay there for a more senior position. Consider yourself lucky to be there as a PostDoc and milk out as much as you can from them, but do not work for their prestige (you will do that anyway, even if you focus on your own only).

Irrespective of whether this is the right position for you (and it sounds like perhaps it's not), you should not think that you will be able to only work with people as or more intelligent than you. Part of being successful is working out how to work productively with people who are not as good/knowledgeable/skillful at you at something and still find that interaction useful

You seem to be forgetting that you have a link to your webpage on your profile. Probably best to remove this link.

In a comment you state:

It's the dynamic issue. At some points, I was proposing ideas, and he
started attacking them. After a few months, I stopped giving ideas and
"only" implemented his and found him happier. So every week, he lists
some ideas, wants, and asks me how they go. So the progress is not
about me that not working or not getting results

Yes, that is the issue, you are acting like a very competent PhD, not as a PostDoc. Unfortunately this will not bring you neither new contracts nor happiness. It does not matter how your supervisor is, you do not have control on them, but you have control on yourself.
Spend the rest of the contract building a network with other people (you are in a very good center, use that advantage!) and work on your own ideas.
Regarding the:

The center is one of the world's leading centers and a lot of famous
senior people are around. So, I'm also concerned about how it might
reflect on him in our center, as many advisors have their own labs,
and gossips will spread all over.

It will reflect on the center and on your advisor X reputation as "advisor X has now a PostDoc vacancy to fill". You are peanuts to the centre reputation and to your advisor reputation.

Thank you. This was a really good analysis of what's going on. It's also a matter of different "gradient" issue. My goal is to build my career, and hopefully his goal is to be a good/famous advisor. The only intersection in our goals could be the number of publications which is low in my point of view.

Careful - there are many different roles that come under the heading "postdoc". Some are independant researchers doing their own thing. Others are employed specifically to work on somebody else's project. This does not sound like a good supervisor - and certainly not a good supervisor/supervisee relationship - but that doesn't mean that the OP can necessarily just do their own thing

@Flyto - Indeed, looking at where the OP works and I mean the country, rather than the institution), I can tell that nearly all postdoctoral staff are hired to work on projects preagreed between the funder and the PI. Its very rare for postdocs to be able to be hired to just "do there own thing" - advisors may give employees more or less leeway in how to conduct the preagreed project, but research should be making progress in those specific areas. In my case I also encourage advisees to follow their won projects, but only after they've done the work I have promised to the funder.

I am not suggestig doing things behind one advisor's back, but if a postdoc does not start thinking about their own projects/ideas from day 1, by the time the advisor give the postdoc some time to follow them, the postdoc will end their contract before anything can be done.

Is your advisor forcing you to work on their ideas? Or are they graciously offering you their ideas since you couldn't come up with any on your own?
In the former case, then you probably do want to find another position if possible. In some fields and settings, it is normal to hire a post-doc to work on a particular project, so "forcing you to work on their ideas" is not necessarily a red flag. But from what you describe, this is not working out: you do not respect your advisor's ideas and they are not happy with your progress. And it seems that you agree the progress is not good, so keeping things as they are is not good for your career either.
In the latter case, it is perhaps not fair to blame your advisor, nor necessary to find a new advisor. If your advisor graciously offered you an idea and you accepted it since you couldn't think of anything better, it's not really fair to blame your performance on your advisor's bad idea. True, a new supervisor might have better ideas that they could give you -- but there is no rule that you can only get ideas from your supervisor; any senior collaborator probably has lots of ideas and would jump at the chance to have a competent post-doc work on them.

I think the former is slightly more relevant to this situation. It's really not a matter of not having an idea. I have a PhD, and he was too just 4 years before me. It's the dynamic issue. At some points, I was proposing ideas, and he started attacking them. After a few months, I stopped giving ideas and "only" implemented his and found him happier. So every week, he lists some ideas, wants, and asks me how they go. So the progress is not about me that not working or not getting results. It's more about him not listening to people. He has one point in his mind and waits for you to finish.

@jda Sounds like it's time to apply for a different post doc.

@jda "he was a PhD just 4 years before". It does not matter. He could even have been a PhD after you, if now they are a professor, they are above you. Please aff the comment " It's the dynamic issue. At some points, I was proposing ideas, and he started attacking them. After a few months, I stopped giving ideas and "only" implemented his and found him happier. So every week, he lists some ideas, wants, and asks me how they go. So the progress is not about me that not working or not getting results." to the question, instead of the deadline issue. It is very relevant

I understand it can be difficult but, for your career, the ideal path could be to keep things cool and publish with this PI one or two papers, and then move on to the next (postdoc) position.

Considering that you are smarter than a young PI at a top research center is rather bold. I know it can be tempting but usually it is wrong.
I don't agree with some other answers claiming you're not acting as a postdoc - it really depends on the field and often the expectation from a postdoc is ineed to do what is being asked.
That being said science is often about trying many ad hoc solutions. The fact that you spent a lot of time on it doesn't necessarily mean that you did it in an optimal
way.
But all this aside if you feel that things don't work well and you have a possibility to try another PI or lab - why not? Postdocs shouldn't be slaves and it is also PI's job to make a postdoc want to work for them. It sounds like yours is not great at it. There's always a lot of trade offs about such decisions though. Jumping between postdocs is pretty hard

I used to think I was smarter than my postdoctoral advisor. Every award imaginable, Nobel shortlist, member of the National Academy, and countless accolades later (for him), I can assure you that I am not/was not and likely will not ever be smarter than him. BUT I damn-well knew my specific project better than he did, so I will maintain my ego boost from that.

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Should I wait to apply for Ph.D in Machine Learning - US/Canada
I'm a 4th year CS and Stats student with a 3.86/4.00 GPA in the US and about to graduate soon. I want to apply to top-35 ML Ph.D. program in the US. As we all know, ML Ph.D. has become insanely competitive, and especially with the economy, it gets more competitive every year.
I'm debating if I should apply in December 2024, December 2025, or both. I'm doing research with 2 different professors and they are happy to write me a letter of recommendation, but I only have two papers in prep. So, I'm not sure if my application will be strong enough for December 2024 and I should just try and have more publications and apply in December 2025. This will be a conversation that I will ask both professors, but I'd also love to hear more input.

For your very last sentence, this may be helpful. Your overall question may be closed as "strongly depending on individual factors", but it may attract answers to "what to keep in mind in thinking about delaying an application to a Ph.D. program".

Frankly, I don't see how your application will get particularly 'stronger' the longer you wait. Did you apply for admission this fall? Why or why not?

@StephanKolassa Thank you so much!

@JonCuster My reasoning is to work on more publications before applying (stronger application). I didn't apply 2023 fall since I knew my application wasn't strong enough. Stephan did provide a really interesting post about delaying applications that I will read.

Your only disadvantage for every application season where you're qualified is the time investment and the application fees. You miss 100% of the shots you don't take.

Your question had accumulated some close votes, so I suggested some edits. We are not career counselors, and future readers will not have your exact statistics, so we frown on including too many details. But the underlying question is probably “on topic” here.

Yes, you should apply, and if you're worried about getting in, apply on multiple cycles. It will not take much of your time to apply in December of 2024, and it seems to me that your file is strong. I push back slightly against the "As we all know, ML Ph.D. has become insanely competitive." At my university, we send plenty of students into PhD programs for machine learning, stats, data science, and computer science. Just last year, a student graduated with a record weaker than the one you are describing, and got into a PhD program. I think the landscape is less competitive than you are afraid of. That said, it's wise to apply to a range of programs, and include some "safety schools." I encourage our students to apply for around 10 programs. Some of our students get a master's degree and then go on to a PhD, but ones with a strong record like yours are usually fine going directly into a PhD.
One last thing. Currently, someone with expertise in machine learning, even at the undergrad level, can get a good quality and high-paying job right out of undergrad. For this reason, fewer go into PhD programs, compared to fields like math. Similarly, for the student's entire time in grad school, they will be tempted to leave and go make lots of money at a company. Lastly, when they finish their PhD, they will be tempted to leave academia. For this reason, there are not enough professors with expertise in machine learning, and that's creating a bottleneck where students who want to learn this topic are unable to get into courses on it. It's essential to the success of the machine learning community that we reserve slots in PhD programs for people who want to go into a career as a professor. The same situation in CS is described in the wonderful article Conserving the Seed Corn.
If you would like to be a college professor, I'd mention that strongly in your application.

I don't want to "out" my former student so I will mention that the PhD program he got accepted to (after 4 years of undergrad) was ranked in the top 50 but not the top 30.

I see no reason to wait and lots of reasons not to. Next year will be just as competitive, and you are probably a decent candidate having some papers in their final stages. This assumes your professor(s) will comment on their value.
However, don't restrict your applications to just the top 35. Make it a bit broader to (greatly) increase your chances. You can get a fine education at any R1 institution in the US and similar places abroad. Waiting has few upsides and you are just guessing about where you sit now and will then.

Note that delaying your career probably isn't optimal. Also, think of the issues at the other end of your doctoral study. Do you expect the job market to be better if you wait. I was late in finishing and the job market (math) completely fell apart in the interim.

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How to do a systematic literature review in countries without access to databases like WoS and Scopus?
I need to make a PRISMA systematic literature review on a sociological topic. To do this, I need to systematically search the major databases, arriving at a list of metadata of the academic papers (articles, book chapters) that fit the search terms. For now, the important thing is finding this metadata in a systematic way (i.e., not just cobbling together references from whatever sources I happen to think of). Finding the full-text of the papers is not (yet) the issue.
The problem is that I am in Russia, and we do not have access to Web of Science and Scopus even via my university. For example, WoS search by documents is prohibited even with VPN.
Given this, how can academics in countries like Russia complete a systematic literature review? Are there known strategies for overcoming this problem?

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Talk to your local friendly research librarians.

:))))), man, you, clearly, have no clue what Russia is @JonCuster

Use another database? Google Scholar springs to mind, or Semantic Scholar, etc.

They provide poor search options (e.g. Google Scholar gives only two options - title/all fields). I have a long and specific search term so they do not work well. @Allure

I haven't encountered this exact scenario. But I've done a few systematic reviews where I have needed access to a particular database I didn't get through my institution. I have solved this through collaborations with other researchers who do have access, or by maintaining affiliations with institutions that give me access (in addition to my primary affiliation). Basically I think that you have 3 options.

You could identify other databases that are not restricted. I'm not in social sciences so I don't know of any specifically but it may be worth investigating.
You could try to start a collaboration with someone from an institution that is not in a banned country and have them run the searches. I don't know how feasible this is for you, but it would probably be the smoothest option. Honestly, if you have a search term developed and ready to go, I have to imagine that someone in your field would be willing to just run the search, export the results, and send them to you.
You can try to circumvent the block. This one is tricky and may not actually be all that realistic. Scopus and WoS both require paid institutional subscriptions to access their databases. So it isn't so much an issue of just getting to the sites and logging in (which any decent VPN should let you do). I would have to imagine that any russian emails (institutional or private) or russian payment methods, or accounts linked to russian institutions would be blocked, regardless of the current location of the user. So you would need to use a VPN to hide your country of origin AND have access to an account managed by an institution not in a banned country. The only legal way I can think of to get around this is to get your own account through institution that is not in a banned country and then use that account via a VPN.

I hope this helps.

Thank you! This definitely helps a lot and brings more clarity about the given situation.


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My paper is still with editor for about two months. Should I email the journal about that?
My paper is still with editor for about two months. My field is engineering. the paper is not controversial. It is a review article. However, the IF of the journal is high (6.7). Is it normal, or should I email the journal about that?

Did you get any feedback from the journal yet?

Yes. An email that the paper has been received by the journal, and another email that Dr "...." from editorial board is now handling the paper. Since then, I've got no emails and the article status did not change.

I assume you are not the only author? What do the other, senior collleagues say?

The same thing happened to me. The status had not changed since the submission date. After about two months, I wrote to the editor and asked him politely to tell me if there is something wrong with my paper. Then, he responded. But, the response was nothing but just "I apologise for the delay to your paper. I have sent a reminder to the Editor to progress your paper." After three days, the paper was rejected.
So, I think: it is better to send an email to the editor and ask him to tell you the status of the manuscript. Otherwise, the status will not change (at least in the near future). Be prepared to see what I saw.

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


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Does the year of publishing for corrected proofs change in the final version?
I have an accepted manuscript published in an Elsevier engineering journal. The status of the article on its sciencedirect page is "In press, corrected proof". For now the article can be cited using its DOI and year of publication (2017). However, the journal is now working on two volumes: the December volume of 2017 and the January volume of 2018. I have noticed that some articles accepted after mine have been assigned to the January 2018 volume, while my article and some other articles accepted within the same week (1-7 July) are still in the corrected proof status.
So I have two question:
1- Can the article get assigned to the January 2018 volume considering that it is now cited as an 2017 article?
2- Is their any priority criterion for publishing? Topic? First submission date? ... etc?

I'd argue that, at least for the purpose of references, the doi is more important than the year.

@Dirk possibly, but both matter a lot, if you have another paper in the other year that could be confused. However - for Elsevier journals, I think the DOI includes the year, so it probably can't change :-)

Re. 1 - Yes. I have a paper that was published "epub ahead of print" in one year, and later published normally the next year. Both versions have different year numbers when cited.
Re. 2 - I would expect they do it in chronological order normally, but sometimes journals publish "special issues" on a specific topic that result in postponed or quicker printed versions. Also comments/replies to specific papers often get published in the same issue, suggesting that those ended up in print version quicker.

I don't think there is a uniform consensus on it - academic publishing has a long and rooted traditions on what is "right", but they do not explain what to do in the Internet era, when almost every result is first available as a preprint online.
However, I believe, we normally don't put a year on a paper unless it is published. I've seen something like:

A. Author. The greatest paper. In preparation.
A. Author. The greatest paper. Submitted to J. Cool Research. Available at ArXiV:1709.XXXX.
A. Author. A nice paper. Under review in J. Cool Research.  Available at ArXiV:1709.XXXXv2.
A. Author. Another paper on cool topic. Accepted in J. Cool Research.  Available at ArXiV:1709.XXXXv3.
A. Author. Another paper on cool topic. J. Cool Research (in press). doi:1701.10/xxxxx.xxxxx.  Available at ArXiV:1709.XXXXv3.
A. Author. Another paper on cool topic. J. Cool Research vol X, pp. yy-zz (2018). doi:1701.10/xxxxx.xxxxx.

At least in my experience, putting provisional years is not unusual, e.g. “A. Author, Some facts about stuff (preprint, 2015, available at arXiv:1509.XXXX)”.  The advantage of this is that until the paper is published, it’s more informative (and in some areas of maths, some valuable + influential papers never do get published but remain forever preprints).  The disadvantage is of course that when/if the paper does get published, the original date will probably end up mismatched with the official publishing date.

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


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When should someone be a coauthor instead of being in the acknowledgements?
We had a master's student working on our project.  He set up a database for us, and wrote some of the initial code with me in a pair programming session.  At one point, he had more commits to the repository than any of the other students working on the project.  Then he went to do an internship for the summer, and after that my advisor did not want to keep him on the project for some reason, even though I thought he was friendly and easy to work with.
My advisor chose not to list him as a coauthor, and put him in the acknowledgements section instead.  However, there was another guy (a professor) who didn't write any code at all, and wasn't there throughout most of the project, but he wrote the introduction and related work sections for us, and he got listed as a coauthor, even though he probably did a day's worth of work on the project (maybe two).  In fact, my advisor gave him the coveted last author position, even though my advisor came up with the idea and directed the whole project.
What determines who gets put as a coauthor, and who gets put in the acknowledgement sections?

You meant to say first author is coveted, not last, correct? The first author is considered to be the person who drove the project.

@Joe the last author is also coveted since it sometimes indicates you were the Principle Investigator on the project.  For instance, my advisor, who was the PI on all grants I was under, was always listed as last author.

@farrenthorpe Only some fields give first or last authorship special importance, and only some fields consider being a PI sufficient for coauthorship. (My field does none of these things.)

I think a research contribution to a paper is necessary to be listed as a co-author. It is unclear (from the post) whether coding constitutes such a contribution.

Usually, the key indicator for co-authorship is the contribution of creative content. Did the student have own ideas that improved the paper? Was the program/database he wrote just a technical thing, or did it contribute scientifically? These are some questions that can help make/understand the decision.
There is a fine line to walk sometimes. Especially between different subject areas, there can be discrepancies who gets to be co-author. Sometimes everybody is counted, sometimes only the first author and his advisor(s) without any students.

It's complicated.
The norms for co-authorship are across the board and highly field dependent. Generally two big ones seem to be pretty consistent though:

Wrote or edited the manuscript that is submitted.
Made a significant creative contribution as noted by ian_itor.

The idea of if software development is a creative contribution is still hotly contested. One norm that seems to be developing is that developers are typically only credited as a co-author if software development is a significant aspect of the publication. For example, chemistry papers may mention an "internally developed tool" used for analysis and may only credit the developer in the acknowledgements.
Personally I belong to the school of thought that software development is at least in part a creative endeavor. As such, I would suggest the following:

If the software is the point of the manuscript, the person should be included as a co-author or as part of a development team.
If they software is not the point of the manuscript, but the research is dependent upon the software, they should be included if they were involved in design and architecture.
If the research could not have been completed with out the assistance of the person (ex. they optimized an algorithm to run on a distributed cluster) they should be included as a co-author.
If the software is incidental to the research (ex. chemistry paper, but a tool was written for analysis) then the development team should be individually recognized in the acknowledgements.

Generally I feel it is also rude of the manuscript authors if developer contributions are not acknowledged at all.

As a side-note with regards to item number three: when it comes to optimizing research algorithms, it really should be a non-question for these people to get a co-author credit. This can be extremely complicated work that in and of itself could justify a manuscript in some journals.

I've worked with people on projects that I thought should've been coauthors, but was told not to include them.  Part of the reason was that they were not one of the official collaborators on the project.  They helped, but in no way contributed to the actual manuscript.
In general, if someone is a co-author, they will be given the opportunity to make revisions on the manuscript as it goes through the peer-review process.  It is advisable to keep this list to a minimum, so that only the core group of contributors are listed as authors.  Otherwise, the revision process can take too much time and publishing the manuscript gets difficult.
If someone helped to write the grant proposal that funded the project, they will almost certainly be listed as a co-author.  Another thing to keep in mind is that a co-author will be a representative for your manuscript, so it is advisable that they completely understand the scope of the project and research material.  And, sometimes its just good to have someone well-respected in the field as a co-author, even if all they did was "write the introduction", because they have experienced insight.  So, if they can get involved after most of the research work is done, they can contribute to the manuscript nicely in just a few hours.  This is in contrast to a student who did weeks of coding on the project, but may not be able to contribute any real substance to the manuscript.

If someone helped to write the grant proposal that funded the project, they will almost certainly be listed as a co-author... sometimes its just good to have someone well-respected in the field as a co-author --- No, no, a thousand times no. Coauthorship requires direct intellectual contribution to the paper.

What is an "official collaborator on [a] project"?

An official collaborator is someone listed on the grant proposal but not part of the funded research team.

@JeffE In my field of work we have community computer models that have had hundreds of people contribute either monetarily, intellectually, or through coding.  It requires that you pick and choose who will be an author on the paper and who has time to go through the peer-review process.  In my experience, the students and post-docs do all the heavy lifting for the specific paper and then the professors/collaborators that are connected to the grant proposal get involved with the manuscript.  And yes, sometimes someone can get involved for a short while and contribute intellectually.


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When should one invite co-authors?
To my understanding, there are pros and cons to inviting (well respected) researchers to co-author a paper.
Pros: Being a co-author with well-respected researchers puts one in a good light. They can make valuable contributions. You improve your chance of being invited to work on projects with them in future. All these points can advance one's academic career.
Cons: Too many cooks spoil the broth. There is more chance of conflicting idea and styles, which might lead to frustration and delayed publication. They might not contribute as much as you hoped. More authors means less credit for the work per author.
I would like to hear your views on this.

Sorry, i should have clarified the particular situation: I have started the project with one other author, but we are considering whether to invite one or two other researchers we have in mind.

@GavinRens Do you really need invite someone? Is it the case that if they are not involved, your project would not be completed?

@Coder We could complete the project on our own, but there are Pros in bringing in one or two other people we have in mind. If we don't bring them in, we lose the Pros.

When you "invite" co-authors is when the project is still in the formation phase - as early as possible. Authors are people who contributed to the project, not people whose names might power a paper past reviewers. And the reasons for their invitation should be substantial and scientifically valid reasons.
One thing to note is that after the project starts is potentially a bad time, as presumably you don't necessarily have the budget to pay them, the potential for them to be genuinely engaged in a question they're interested in is a bit of luck, and you've lost out on the chance for their expertise to to actually influence the formation of the project (where it's probably most helpful).
It's absolutely not appropriate to invite them at the paper stage.
For reviews or commentaries, it might be acceptable to do this before the paper begins to be written, but for other papers, co-authors should not simply be added to a project at the writing stage. Indeed, doing so violates a large number of authorship guidelines.
I'd also like to contest one of your cons: "More authors means less credit for the work per author." This is highly field dependent. In my own, noone cares, or tries to divide credit by number of authors.

I think OP meant "when" in the sense of "in which cases? under what conditions?" rather than "at what time?"

@NateEldredge I'll expand a bit. My issue is that "co-author" tends to imply at the paper stage.

I think it's not too uncommon to start a project, work for a while, and then realize that you need expertise that none of the original authors has.  Surely it is better to invite additional co-authors at that stage, rather than abandon the project altogether, or take a long delay as the existing authors learn a new area?  Of course, in an ideal world, the need for the extra co-authors would have been foreseen, but often that doesn't actually happen.

@NateEldredge The question was "should" not "is it possible". I've found that trying to add experts midstream has a much lower success and engagement rate. This is certainly my feeling when I'm added midstream.

Fair enough.  My experience has been the opposite - I've been in projects that were completely stalled until a co-author was added, which revitalized things and led to successful completion as well as further collaborations.

@NateEldredge My experience is that, doing mostly modeling or statistics work, a "mid-stream" project is likely to have already collected the data and then found themselves in an analysis quagmire without the budget to collect the data to get them out.

Ok.  My experience is from pure math where there isn't any such thing as "collecting data".  But anyway, it appears our experiences differ and there is nothing wrong with that.  Maybe I'll add another answer at some point.

@DVSA The question is about inviting particularly well-known researchers notable for their stature. That's well beyond "Oops, we realized we need someone who does X". Also, the question is should. You should have someone who knows what they're doing well before you're writing a paper.

I find this answer overly restrictive. Suppose, for example, Alice and Bob are working together on some project. After six months, they realise that the project actually requires considerable knowledge of widget theory, which they do not have. That would be an ideal time to invite Chris the widget theorist to join the project.

@DavidRicherby I don't see how this contradicts the answer in the first sentence "As early as possible". Sure, when you realize you need a Widgetist is an acceptable time. But it would probably have been better if one had realized this need at the outset, no? And it will be harder to get your Widgetist onboard if the budget is committed, you're not really focusing on an interesting aspect of modern Widget Theory, etc.

If one could foresee everything in advance, life would be much easier. So many fruitless avenues could be avoided!

@DavidRicherby Indeed, but this is more a suggestion that there is never a good case for waiting. The ideal stage for "Should" is the earliest possible, and the later you get, you head asymptotically toward "Useless".


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Tutoring is depressing because my students are struggling too much with my exercises. What do I do?
I am a tutor for first year math majors at a European university. By "tutor," I mean that I have office hours that all math students can attend. I am paid by the university.
I recently changed universities. At my previous university, where I also tutored, the exercises were very demanding for the students; the problems were interesting and not easy. So I was really glad to be able to help.
Now, this is not the case anymore. Exercises consist simply of paraphrasing the definitions, and almost all the students are struggling pretty hard on these very simple exercises. Typically, they think that solving Ax = 0 when A is a 3×3 matrix is too hard. They have very little intuition about what is going on, especially in algebra. When they ask me questions, I try to answer so they see a way of thinking that can be generalized. But sometimes they just look at me as if I was an alien.
I am not here to complain, but to ask for advice. What should I do? Should I simply answer their questions as simply as possible? What I really want is to push them to work harder and become more familiar with mathematics. On the other hand, I am probably doing this already a bit and I don't want them to be disgusted by mathematics. I really don't know what to do.

When I read your question first I missed the point that you are actually tutoring math majors (I thought you are tutoring students of other subjects in math). Why would students who know so little and find it difficult to understand general explanations and paraphrase definitions choose to become math majors? What is it they try to achieve? Even if they somehow obtain a degree, what is their idea of a job they'd do? And after these questions the third: Shouldn't the university actively discourage students who only waste their time from continuing?

@Peter-ReinstateMonica: Haven't you heard of this and this and ... [too many more to count] ...

@user21820 I'm not quite sure what cheating has to do with selecting a math major while untalented. Sure, the weeding out may fail, but the core question remains.

@Peter-ReinstateMonica: When cheating is as endemic and popular as the links demonstrate, it no longer matters to the cheaters what degree they get, as long as they get it from some 'reputable' university. When people have simply no interest in working hard, it doesn't matter to them at all what subject they attempt because their underlying motivation is neither to learn nor to acquire useful skills and knowledge.

What you're experiencing is pretty much what all college teachers are wrestling with all the time everywhere.
Allow me to point out that the abyss of need can go much, much deeper than what you're currently dealing with. In the U.S., most college students are attending a community college. And most students entering U.S. community colleges do not have 8th grade algebra skills, nor even 6th grade arithmetic skills (e.g., fractions, proportions, negatives, estimations, times tables). I've had a good chunk of a college math lecturer career at this point and I've never taught anything as high level as matrices.
Here's how I've been able to jiu-jitsu it in my own mind. Think of it like a diagnostician. Doctors have to find it fascinating to track down hideous diseases. Detectives have to find it compelling to decipher ostensibly horrible crime cases. So too: I find it endlessly fascinating to diagnose what exactly is the block or problem in students' heads, or to track down the place where their reasoning first went off the rails. Ask questions to try and find where their reasoning starts and where it stops. Do something of a binary search to try to narrow down the problem spot. I'm continually discovering new gaps in people's knowledge that I never would have expected. It's surprising and amazing every day.
Usually I do find that students simply cannot remember starting definitions. If they've come up through a system that depends on raw faith and memory (and not mathematical reasoning), they don't get how important that axiomatic basis is. Many also clearly have learning disabilities that make this difficult for them. "All your answers are back in the definitions", I say several dozen times per semester. Have the book handy so you can turn back to the starting definitions at any time, and see if they recall or can see how their reasoning got off track that way. In fact -- this explains why at your current school they're asking students to reiterate definitions; whereas for us that's natural and obvious, for some it's an overwhelmingly difficult blind spot to fill in.

Thanks, I like your answer, especially second paragraph.

" I've never taught anything as high level as matrices" wow

@Rüdiger yeah, it's positively-definitely frightening...

"I'm continually discovering new gaps in people's knowledge that I never would have expected. It's surprising and amazing every day." You should do a study on this. Or at least write a book or something based on your experience.

"Doctors have to find it fascinating to track down hideous diseases." A friend of mine was studying medecine. During a hands-on lesson at the hospital, going from patients to patients, the professor saw a tomography and told the students, right in front of the patient "Look at this wonderful brain tumour. How big and well defined it is!"

reminds me of my military service as a medic. We had a soldier with a severe head wound and the Lt. called us that he will send a vehicle to drop that soldier so we can take care of it. After half an hour or so, they arrived and entered the door and the physician simply said "Fine, there is finally my head."

It sounds to me that the course itself is designed to be a gentler introduction to some of the mathematics they will be encountering in their future careers.  If the goal of the course is supposed to be difficult and demanding, but it is not being taught that way, that's a different question.  However, it sounds instead that the actual course itself is not designed to be at that high a level.
Think about the learning process that everyone goes through.  I can use the exact same token to say that a grade 1 math class isn't "rigorous" enough and that the students are not gaining the intuition I want them to.  In this case, it's not appropriate to make the course more difficult since the children are gaining that intuition through repetition, simple problems, and exposure to the concepts.
In your case, I would think about the learning objectives of the course, and the level of the students, and their eventual careers.  Then, I would try to figure out how I can get them to learn as much as they can against those learning objectives, without necessarily turning them into mathematicians if that isn't what they're there for.

I am teaching introductory linear algebra at my institution right now and am experiencing this at some level. This is the version that is designed for non-math majors (same classes with more advanced treatment is also offered here), so most students have not seen proof before. Even seemingly bright students struggle a lot and I have come to the conclusion they struggle at such a simple math mostly because they are not spending necessary amount of time on the class.
What I am trying to say is that someone who never dealt with an abstract math concepts do not realize that they need to do extra reading, spend extra time working on problems while getting lost. Most students think they need outside help the moment they get stuck and simply stop working.
Simply put, they got used to thinking that math is all about plugging numbers to formulae so they get lost when they take any math class beyond calculus/differential equation. Like the other answers mentioned, this must be a serious problem among the math educators at high school level.

The course is too easy, many students are not so motivated, many of them see your math TA class as the ideal time to relax. You can deal with that by announcing in class that in two weeks time there will be a take home test that they must submit within a day. So, if they haven't mastered solving systems of linear equation by that time (something that ten year old primary school children can learn to do), they're going to be in deep trouble.  Also tell them that you're available for questions, extra exercise problems via email and on some hours of some days in your office that suits you best.
You should propose this to the instructor of the course, just tell him/her that most of your students are at F-level and they're not making progress and you see doing an intermediary test as a possible way out.

Completely aside from how bad this idea might be in the first place, the OP says that they're a tutor, not a TA or someone with a class of their own, therefore, probably not even doable.

This has all the signs of someone who has never taught.

@DanielR.Collins I've taught many courses, but solving systems of linear equations is a high school level subject here, so we don't have students who struggle with this as they would never have passed their high school math exam.

This is sadly not true, students are definitely not relaxing but almost about to cry, after spending 30 minutes for every exercise and finally ask someone the solution. I agree the classes are too easy but I won't imagine make it harder since this is difficult enough for them. For the test, I already has this idea and I talked about the teacher but he told me this is too late for change the system. Anyway a test would be a butchery. Also I'm not available for anything outside these tutoring hours since I am currently finishing my master degree and have lot of work by my own.


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Postdoc reco as PI won't even co-sign undergrads who aren't co-authors
My whole summer I worked meticulously in a REU for the PI to tell he never writes or signs letters of recommendation for interns. I need a third recommender; my first two are great profs.
Will the postdoc who mentored me closely be a good option or should I take one from a professor who doesn't know me but I have taken the class. I am really frantic I can use examples of people who got in with 1/3 reco from a postdoc of a completely different lab.

A postdoc who knows you well would be a good letter of reference.
And, in general, a strong letter from someone who knows you (your research or academics) well is better than a letter from a more famous/prestigious/important person.
For example, a supervisor at a relevant job (e.g., summer internship in a relevant field), a postdoc, lab manager, or similar position would be okay,especially, if you have strong letters from professors.

+1. I would just add that if the post-doc can write in their letter that the prof has a firm policy of never writing LoRs for interns, that would probably be a good idea.

@cag51, indeed, although "protesting too much" would not be good. Simply something succinct, like "By the way, Prof X has a firm policy of not writing letters for interns, so I'm writing the relevant letter for Y."

This is a good idea I will let him know


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Private sector professional being screened out of PhD program
A little background:

I'm a data scientist and machine learning entrepreneur. I co-founded a sorta successful company in the AI space that got top-tier VC investment. Certainly not a unicorn or household name but a solid business that has been going for over 6 years and has a realistic shot of getting acquired by an industry player at some point. After many years, I've stepped down from my operational role and I'm working on other stuff.

I have an MS, I didn't get anything published, but I worked on computational biology, heavy on statistical methods. I found the atmosphere focused on lab seniority which emphasized pursuing publications to set up future positions in academia sort of empty, so I graduated and started doing my own thing. While I felt disappointed in myself at the time, it ended up being a great decision that resulted in developing a love for building businesses.

The Problem:

I want to go back to my local University and get a math PhD. There are professors there who have great expertise in fields adjacent to my research interests (theories of statistical learning).

I got denied last year and I want to apply again, but I will likely get rejected again. The feedback that I'm getting is (1) that I don't have relevant letters of recommendation from academics (they are colleagues I have worked with), and (2) the lack of any substantial math focus in my undergraduate degree.

I can see where they are coming from -- because I didn't publish, they aren't really aware of my statistical work. It wasn't a class on a transcript, it was doing work for my PI. My undergrad was in biochem, at that time I wasn't even really into math, I took the classes I had to take. Grad school was over 13 years ago; people who knew me well are unreachable or dead. People who didn't work with me that closely aren't even sure we worked in the same lab.
Outreach to professors is understandably not very effective. Even though they think my background is great and my research interests are on point, they don't feel comfortable writing a Rec for someone they don't even know. I don't blame them.
But now I'm "locked" out of academia. I know some great young students who got accepted -- they are really just starting out! They are training and building models for the first time ever. They are outstanding young researchers, but they are just really getting their sea legs. They were shocked to find out I can't even get into the program as a PhD candidate, knowing that some graduates have interviewed at my company!
So, for the next application, I'm going to take the Math Subject GRE. The GRE is waived because I have an "advanced degree" but I think it will go a long way. Letters of Rec are trickier - I have been using professional references. Beyond that: what else can professionals like me do to avoid being sidelined for PhD admissions?

Have you disclosed your role as the co-founder of your company?  This seems like it should count for something.

I know you have already accepted an answer, but I have to chime in with what other people are saying. You are having trouble getting into a PhD position in mathematics because you aren't a mathematician. (This is in addition to the fact that you have narrowed your search to a single location, which is normally not likely to result in success.) So, Step 1 is to do something about your lack of mathematics undergraduate, not jump ahead to a PhD.

Just echoing what @DavidA.Craven has said - a math PhD requires more math background than just statistics. Something adjacent to look at is measure theory for the real analysis background.

What sorts of math PhD have you / do you want to apply to? A supervisor who has previously worked interdisciplinary and whos research is related to computational statistics would probably look more favourably than say someone whos speciality is "further away".

This is somewhat jurisdiction dependent but in your case it may be more feasible to aim for a PhD with a particular professor at the university without being enrolled in their classic graduate program. You do want a professor who is willing to supervise you as a PhD student but you don't necessarily need a graduate student stipend (which according to your background I would assume would be financial peanuts for you).
I know that in the German system getting a PhD advisor and getting money for your salary/stipend are two separate questions (although you often get both in a package). Having only a PhD advisor would also give you a lot more freedom in terms of the typical hours/ week commitment to a PhD and allow you to continue working (the total amount of time needed for a PhD doesn't change, so the PhD will take a lot longer if you do that).
I don't know how common this setup is in your jurisdiction but it might be worth looking into.

I really appreciate this thought. I think partnering with a professor is the right option for me.

This is exactly what my brother-in-law did (and successfully got his PhD) . He was in an almost identical situation as @lunchball.

My gut instinct is that your application may also particularly suffer from focusing on math departments, based on the nicely concise but necessarily limited information in your question. In short: I suspect you're quantitatively very fluent and there's little question that you have the work ethic to see a PhD through. But you may be missing a lot of prerequisites I'd want for a math PhD.
We typically spend a good amount of time teaching math majors to write rigorous formal proofs in undergrad. PhD programs then continue this with additional years of higher level proof-based coursework. For example, at least a year or more of abstract algebra (groups, rings, fields) is a common core requirement, often with a prerequisite of an undergraduate version of the course.
Between being out of school for awhile and probably not having taken prerequisites, I'd be pretty concerned about how you'd do with these kinds of courses. Maybe you'd be able to pull out all the stops and develop a proof-writing skill set very quickly, but that's a risky bet to make when more straightforward ones could be available.
I hesitate to advise you either way on putting energy into the math subject GRE, but I feel compelled at least to warn you that a good score may not help as much as you'd guess. Many math departments are phasing the test out or already have as an application requirement. The test is in a very unusual format for undergraduate mathematics and doesn't necessarily say much about a student's ability to do research or write proofs.
That all isn't to put you off doing a math degree, but rather just to give some thought on why your application packet may stall. If math's what your heart's set on, fair enough. You may, as others have suggested, need some strategy to do interstitial academic work like a math masters or some postbac undergraduate courses to generate clear evidence of sufficient preparation. If you're a bit more flexible, other quantitative departments are often more flexible than math for PhD work: Computer science, biology/computational biology (or a bio adviser who doesn't need you do wet lab work), and applied math/statistics come to mind as departments where you can do a similar PhD to a computationally-focused math PhD without routing through proofs.

If you do want to go into a "traditional" math program, you might see if you can arrange to take a proof-intensive undergraduate math course or two.  Look for Real Analysis and/or Abstract Algebra classes at your local institution. A letter of rec from the professor(s) in such a course would help even more.

I'm a math professor.
Echoing what @user176372 has to say, a math program seems like an odd match for your stated background and interests. Have you studied abstract algebra, real analysis, or partial differential equations? If not, do you want to spend most of the next two years mastering these subjects?
Programs in data science or statistics (among other possible options) seem like better matches, and I can imagine that your background might carry much more weight in graduate admissions there.
This would involve applying to a variety of programs, and presumably moving.
If it is important to you to stay local, then ask yourself this question: what are your long-term goals with a PhD? The academic job market is difficult and getting worse. (I believe it may be better in statistics and data science than in math; conversely, it is horrifying in the humanities.) Moreover, due to the upcoming "demographic cliff", things are likely to get worse.
If you want a job in academia, you may eventually get one if you are lucky -- but you will certainly not be able to find one locally. More common is that you have to move at least once for a postdoc, and then move again for a tenure-track job (if you are lucky enough to find one).
If you want a job outside academia, then a PhD can help you get a foot in the door. But, it sounds like you have a Goliath-sized foot in the door already! There are some more research-oriented positions in government, industry, and nonprofits which you might be competitive for with your existing background.
Why do you want to get a PhD in math? My impression, without knowing you and only judging based on what you wrote, is that your interests would be much better served going in a different direction. If you really do want to get a PhD in math, then imagine that I'm the one reading your cover letter when you apply, and convince me that you are prepared for it and that it lines up with your long-term goals.

This is an important question I have meditated on for some time. Thank you, your answer is helpful in clarifying my thinking. I am pursuing a math PhD because I am convinced there are particular disciplines within Theories of Learning that I would like to study, and after lots of learning, become an expert in. My weakness is in formal mathematical research methods, and that's what I would like to strengthen. I have followed a particular lineage of research that I think is promising, but I don't have the credentials or affiliation to extend that knowledge.

@lunchball: The problem is that formal mathematical methods are something you learn in mathematics as an undergrad, not as a grad student.  Realistically, you need to be able to understand and validate mathematical proofs and come up with simpler proofs before you start graduate school in mathematics, not as part of graduate school.  Proofs are at the core of mathematics, not some optional add-on to empirical observations.

@lunchball: I'm glad you're thinking about this here. Re: "disciplines within Theories of Learning" sounds very much like a non sequitor to a math PhD, I actually can't see any connection at all. Maybe a math education PhD would be more appropriate?

@DanielR.Collins I think OP Is talking about the mathematical theory behind machine learning or statistical methods

You have an extremely narrow application focus (1 university). It isn't surprising that you aren't sufficiently high on the "likelihood of success" scale if they have competitive admissions. Entrepreneurship isn't the same as research. Creating products isn't the same as extending knowledge. Valuable, but not the same.
One option is just to expand your search to other universities. That will increase your chances of admission, but no guarantees. The other option is to find a way to fill the gaps. Perhaps the math requirements are most important to form a basis for research in your field. You aren't locked out, but you may be knocking on the wrong door.
You can probably go talk to one or more people at that local university to form a direct path to a better outcome.

Thanks, this is helpful -- the option of forming a direct path is the most likely.
In this case, I need to stay local. As far as I can tell, there aren't "real" PhD math programs which can be taken online, I have an infant and the whole family is here, additionally my business activites are here.

Lots of great answers already, I upvoted them all.
I very much agree that a focus on math after doing data science will look... strange. I am a math Ph.D. and have worked as a data scientist for almost 20 years now. While my grounding in a "mathematical way of thinking" was invaluable for my career, I have a very hard time picturing starting out in data science and then pivoting into doing classical proof based mathematics. And make no mistake: someone who is doing statistical learning theory in a math department is doing math and proofs, not data science. (They may be branding their work as "data science" because there is much more money for that than for measure theory. Don't be fooled by branding.)
So I would absolutely recommend you dig into formal maths first, just to you are certain you know what you are getting yourself into. Get a couple of undergraduate textbooks, e.g., those from Springer. Read the first couple of chapters. Then think seriously about whether you want to do this for the next five years. This earlier answer of mine might be helpful.
If you are still set on doing this, here are two things I would recommend:

Talk to those professors whose research you are interested in. Just cold email them with a short mail and invite them for a cup of coffee. (Not everyone will accept, or even reply.) Find out what they think of your CV and portfolio, and whether they think you stand a chance - both of getting accepted, and of being successful and getting a Ph.D. Ask them what they would like to see you do to improve your chances.
This shades into "figuring out whether you really want to do this" as described above. But beyond this, this may also get you a foot in the door. (Which is why you should not go beyond an invitation to a cup of coffee, to avoid bad optics.)
Of course, do your homework beforehand. Read their last couple of publications. Find out what courses they offer. Look at their current and recent grad students and their research projects.

Another, possibly longer-term method to improve your chances: you note that you haven't published anything, but have been doing scientific work. If there is anything at all out of that work you might be able to publish, then try to do so. You don't need a Ph.D. or an academic affiliation to publish (although the latter helps).
Yes, getting a publication accepted can be a long slog. But if you do manage to do this, this can be quite impressive.
In figuring out where to submit, that part about reading those professors' recent research will be very helpful. If you can place something in a conference or journal where one of them also publishes, this will provide instant name recognition. And conversely, if you find out (possibly the hard way, unfortunately) that your work is not appropriate for any of those particular venues, that gives you another important piece of information about the match between your interest and that of the people you are looking to work with.

Good luck!

Your skill set seems more like the competency that you'd need for a physics or computer science PhD than a maths PhD. The way you describe your goals, "I am convinced there are particular disciplines within Theories of Learning that I would like to study, and after lots of learning, become an expert in", sounds quite vague. This might be okay if you can back up your skills with an undergraduate degree in maths, but probably won't carry you if you can't demonstrate evidence of skill. I also get the feeling you view maths as a tool, closer to a physicist mindset (or possibly computer scientist) than a mathematician's mindset. Its also hard to judge if your statistical work is relevant, without training in the field you may think you did something difficult while in actuality to a mathematician its like a script kiddy saying what they do makes them a brilliant programmer. The other thing to be aware of is that master's level research generally just teaches you tools and skills that are used in research, but not actually how to do academic-level research itself (that is what PhD is for).
From this I don't think you are being screened out because you were a private sector professional, but probably because you don't demonstrate (yet) sufficient competency/mindset for a maths PhD.
I'm also not sure if a maths PhD best aligns with your goals. Why do you want to learn about theories of statistical learning? Are you trying to provide deeper understanding of the models that are taking over the world so they are less of a black box? Are you wanting to improve your models so that your business is stronger? Are you wanting to gain deeper insight into human intelligence by learning about artificial intelligence? Do you just want to know the maths behind the models?

In what follows I'll assume you are financially independent/don't need to worry about money and can dedicate at least 2 or 3 full working days a week to studying without distractions.
If you want to learn the maths, enroll in a undergraduate or master level maths degree. This will teach you how to think formally as a mathematician does and provide you with a grounding if you decide to go into a maths PhD. You can then also begin to read reviews and books on your subject, for example https://www.cs.huji.ac.il/~shais/UnderstandingMachineLearning/ might be relevant, though it is a relatively simple introduction to a mathematical view of machine learning.
If you want to do research, you may need to do the previous suggestion first. But you should also look at the webpage of the researchers and groups who look interesting to you, see if they have a colloquium or talk series and try to go along to one of them. At the colloquium you can try to talk to some of the researchers, ask them about their research and try to understand the big picture/their motivations. Focus on listening and asking them what they think you'd need to know/do to contribute to similar kinds of research if it interests you. They would be able to judge your level of compentence better than anyone over the internet can. Doing this for a while, you can get a better feel of the landscape and raise the idea of collaborating on some research, be aware that you are essentially asking them to take on another PhD student without recognition but if they think you are competent and have the potential they might be willing to guide you.
If you really want the maths PhD (either to move into academia or just for the title) you probably need to do a combination of 1 and 2 if you are restricting yourself only to the local university. You need to demonstrate that you are worth their time, since even if you are self funded, this is time that they could dedicate to another student who has a safer background and may promote their name/work if they go into academia.

Two more thoughts:

Start a masters program for math. There you will learn math, get in touch with professors, and maybe create some attention. This will help with your application, publications, and letters of recommendation. And it helps you to re-evaluate, if you really want to do Maths.
Have you enough money to pay for your own project? If you can provide enough money to cover your salary for four to five years plus the expenses of the university, you might be able to fund your own PhD position. Might be unorthodox, but why not profit from your success as a startup founder?

An additional idea: You could absolve the admission exams (having the subjects "math" and "probability theory") for an actuary certification path. Doing this might show the university that you have a working knowledge of probability theory at a high level and are fast at solving mathematical problems in this area such that your knowledge is applicable.
Note that to be successful the university should know what an actuary is. Example exams à la "I have  solved a difficult exam like this one under high time pressure" may be helpful.


text:
dealing with the feeling after rejection
I interviewed at one of the good universities in the Netherlands as a lecturer two days ago, and I was informed today that I was not selected (five did the interview, and two were selected). I am really feeling sad. I don’t feel guilty now as I prepared for three weeks, and I felt I did well in the interview. It was strange because the interview was supposed to last 45 minutes, but it ended in nearly 30 minutes. I’m trying to reflect on this now, especially since I was really interested in that job. Yet, I feel like it might be time to move on and forget about searching for a career in academia as it is the second time rejection after one for a PhD two months ago. I would appreciate any recommendations about how to deal with such a situation, maybe it helps to go over this sad time:) I yet believe life will work out
How can I deal with the rejection, personally and professionally?

Did you get feedback like reasons for not being chosen? If not you can ask for it.

Others are not chosen dozens, even hundreds of times. What would you tell them to do?

It is part of your job search, and you will find a good position, trust me. It was hard for me too when getting rejections when looking for faculty, especially later I felt I was much better the candidate selected by search committee. But the more you try, the more you will handle this negative feeling.

Do you have someone who loves you? If so, you have everything you need. Everything else, like a job, is just something you want.

Failure is part of life. You can try reading CV/record of failure of some very successful people in your field. They also have a lot of failures. This makes me feel better at that time. More in the following link:
https://www.sciencealert.com/why-creating-a-cv-of-failures-is-good-Princeton-professor-viral
I also want to add one more point: if you do not have failure, it is likely that you undersell yourself, or you do not try hard enough.
E.g. I can also submit my paper to tier 3 journal and get accepted easily to avoid failure, but we can be sure that we don't want to do that.

Keep trying. There seem to be more seekers than jobs in many fields at the moment making competition fierce.
Talk your qualifications and approach over with a trusted colleague, especially a professor who has some experience.
Talk to a professional about your mental state if you seem to get too low for too long. Good luck.

And talk with folks in your network.

And if you don't have a network, at least you may talk to your (past) teachers.

… @hym3242, and start building one.

(This answer isn't specific to academia; I think the important points apply to all job interviews, house-hunting, and many other situations in life.)
As the question already implies, this is a numbers game.  You didn't fail because they hated you; you didn't fail because you weren't any good.  It may well be that they liked you, that they were impressed by your skills and/or attitude, even that they would have offered you the job if there hadn't been other applicants that they liked even more.  And (much as the interview process aims to find the best people) chance is bound to be a factor.
Rejection will always be hard to take.  But it's only a temporary setback.  Ultimately, it won't matter whether you were rejected once, or a hundred times — in the long run, only the acceptances will matter.
And, since this is a numbers game, you can simply maximise your chances by making more applications.  (Doing that will also give you more experience of the whole process, which may help too.)  Yes, it can be hard to find the energy/will to go through it all again — but it will get easier.  And if you keep at it, sooner or later you're bound to succeed.
So maybe the answer to dealing with rejection is: try to take the long view.  Try not to take it personally, nor to dwell on what might have been — instead, learn what you can from it, and then forget it and move on to the next.  Because when you look back, you won't remember the rejections, only the ones that worked out.

I suggest that you reframe this event that you're calling a "rejection." All large goals take many steps and attempts to achieve them. Think of these as stepping stones. You go from one to the next until you reach your end goal. Each stone is a positive step forward. If it takes 25 tries to get a job in the Netherlands, you started out at zero and completed two out of 25 required attempts. You are now at #3 with 23 attempts remaining. There is reason to celebrate each interview regardless of the outcome, because you're one step closer to your goal. Reframed like this, every interview is a success!
It's arbitrary to think of an interview as a failure. You can just as well think of it as a step forward. Both could be true in some way. In that case, don't invest in negative framing, because that will lower your energy and decrease your chances of success. Invest in positive reframing, not because you "hope" it's true, but because it "is" true.
If you want to drive from Rotterdam to Amsterdam, that's 78 km. After 1 km you don't say, "Zut, that didn't work." You say, "Yay, only 77 more km to go!" ;-)
Much of life can be viewed in more than one way. Choose the way that benefits you the most and makes you feel uplifted and energized. Generate positive counterthoughts to neutralize negative thoughts. Not "I failed this interview," but "Wow, I got an interview!"

This is my favourite answer. Such an inspiring and motivational way to face adversity in all aspects of life. Thank you :-)

Two other people were in the same situation as you, and more people who interviewed for that job were rejected than were accepted. And you got one of only five interviews so clearly your CV did it’s job and you were deemed a strong candidate. Even though you weren’t ultimately selected, by any reasonable assessment in the sum this reflects well on you not poorly.
In general rejection is the norm in hiring in general, and my guess is that academia is more competitive than industry given the huge number of PhDs and the tiny number of professor positions. Interviewing sucks and can be super stressful, but if you don’t give up then as long as you're qualified (it sounds like you are) and you’re not making self-defeating mistakes*, you should eventually succeed at landing a job. It may not be where you originally planned (or it might), but the key is to be strategic, try a whole lot, and focus on the eventual success not on the many failures that preceded it.
That’s not to say you shouldn’t leave academia, or that you should. But I wouldn’t base that decision on one interview that didn’t go your way unless you’ve been searching for a job without success for so long that your chances of success are rapidly approaching zero (this doesn’t seem to be the case since you got a coveted interview at a good university).
*It may be worth deliberately working on your interview skills if you aren’t already doing this. Doing well in an interview is an art form and most people aren’t naturally good at it. Learning how to ace an interview could give you an important leg up in your job hunt.

There is nothing further that I can contribute to the discussion. Just that maybe it would be beneficial for you to read Karen Kelsky's "The Professor is in" book during this phase. It's an excellent resource.


text:
How can I talk to the professor who has accused me of cheating?
My professor gave me a course incomplete because my lab3 homework on GitHub is very similar to someone else’s work. I would admit that I did asked former students from this course to send me the lab3 answer but I just used it to learn the course material, I never submit it for any grading. One month later after I understood the correct logic of this lab3, I pushed my slightly modified version to GitHub so that I can review for final exam. The professor is asking me the source of my code for lab3 and I am afraid that he might accuse me of academic misconduct.
BTW, he did emphasize more than once that we should not look or copy other people’s code. Even though I did somehow broke the rule, I did not submit lab3 for grading. I only used it to help me learn faster because I encountered a mental crisis this semester due to my brother’s death and so I missed a lot of school work. I looked at other’s code only to help me learn faster. What should I do about it? And how should I explain it to my professor.

so you received a completed homework assignment from another student, did not actually submit any work for that assignment, and then uploaded (a slightly modified version of) the other student's work to your GitHub account? And part of the rules for this course were that, not only can you not copy another student's code, but you also can't look at it?

The post is significantly improved after your edit. But, I'm still not entirely sure what question you would like us to answer. If it is the title question, that may be a duplicate of: How should I phrase an important question that I need to ask a professor?

To answer Esther's question: YES. I have again looked at the class policy and it say clearly we are not allowed to look at other people's code before or when we are writing our own code. Otherwise, it is deemed as cheating. However, I did not obtain any benefit for my self even though I looked at other's code.

To answer cag51's question: I wonder how I can communicate to the professor so that he could actually believe that I never had the intention of cheating in this course and how I can convenience that I looked at other people's code only for learning purposes and should not be deemed as cheating.

@Leeee Why would you describe it to the professor any differently than you're describing it to us? If you're looking for a code phrase, that doesn't exist for this situation any more than it does for asking Helen Mirren on a date; however creative you are she doesn't have to say yes. Whatever you say to your professor they don't have to believe you if you've run afoul of rules.

I don’t quite understand the situation. The title says the professor accused you, the body says you are afraid they might accuse you. Those are quite different situations to be in.

Professors are humans, so you talk to them like you would talk to other humans. Depending on the local culture, you need to take more or less care of the difference in status. Like all other humans it is unknown how they will respond.

I actually felt very sorry for what I did even though I did not really cheat in this course. To be honest, I would say learning faster by looking at other's code indeed violates the class policy although it did not help me earn better grade for my assignment. I think I would just be as candid as possible with the professor and if there is still any consequence, I will accept it.