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Imposter Syndrome in Mathematics

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I dropped out of a PhD program because of funding cuts and, after a few twists and turns, got a job in a research division of IBM.  I was 1 million percent certain I was in the wrong place -- these were really smart people who were very seasoned software developers -- people who had invented programming languages and operating systems.  

But I felt the same in grad school, and, to a certain extent, as an undergrad.

I got a really good yearly review, a pay raise, and more responsibility and thought, "My boss is just being nice.  If he really knew .."

Yeah, they promoted me out of ignorance -- that MUST be it.

Decades later I realize I will never be done with that sense that I am in over my head, it is always tapping me on the shoulder and reminding me that what we do is hard and someone is better at it than me.  But I've done ok and I keep coming back to the question of "why do I do this at all?"  Because so many people get their pride caught up in the profession like I do and feel a certain sting when things change -- be it more or less responsibility.  

I've come to the conclusion that there is a certain craving at the bottom of my impostor syndrome, a craving for validation that both motivates me and criticizes me.  That group at IBM was slowly dismantled and I was shown the door like everyone else.  It was crushing, I still mourn that loss, and I still feel that sing of doubt.  If my craving for validation was amenable to reason, this would have passed long ago -- so it is unreasonable and is no longer helpful so the best I can do is recognize it and talk back to it.  

I had a psychotherapist (old school Freudian talk therapy, great stuff) who had a quaint office filled with books and a funny little stitch pillow that said, "If all else fails, lower your standards".  On our first meeting he pointed to the pillow and asked "What do you make of my little stitch pillow?"  I laughed and he smiled and explained there are only ever two reactions to the words -- laughter and fear.  The pillow is something of a litmus test. People seeking therapy are all working out how adjust their standards and if they will be swept away by unseen forces if they can't be flexible.  But I believe everyone is working that out -- how to be flexible so they don't get swept away by rigid standards -- especially the standards they have adopted to help motivate them in the first place.
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>How do you cope with these feelings of inadequacy or unbelonging?

Poorly lol. It's not a healthy answer but I kind of just repress those feelings until I hit something that enables me to reason them away but they always come back eventually.

When I was in my undergrad for comp sci, it would be from other students knowing how to make GUIs and build things that people outside of the field could recognize as something substantial. This got better when I started looking for jobs and got one almost immediately.

In industry, it's that someone else always seems to have an answer to every problem while my skills start to feel useless. For this I just have to remind myself that it's never one person that has all of the answers, but I tend to think of colleagues in this regard as a single unit so it seems like if 6 solutions are accepted then I should feel bad about just 1 instead of 5 despite the team being 6 people.

In my first attempt at a master's, I couldn't keep up at all and failed out after one semester. This bothers me much less now as I've realized that CS is not the path for me and that I had undiagnosed and untreated ADHD.

Now finishing up my undergrad for applied math, it's back again because I'm simultaneously in upper division classes despite having gotten a D in ODE originally and having forgotten A LOT of calculus. But at the same time, when I really apply myself I can get through it, I notice things and ask questions that don't occur to others, and my professors all seem genuinely happy to have me around.

Then there's the ones that are currently looming over me. I just got let go and even though I had been contemplating leaving, it was a huge blow to my confidence.

And of course there's the continuous one that is ever present. As a trans woman, I regularly feel this way about my own existence. I'm not sure if that one will ever go away.

I wrote more here than I had intended but hey, maybe it'll help someone as a show of solidarity.
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I personally stopped worrying about this when I started thinking that I'm probably not a mathematician. I do math because there are some things I like to know, some contributions that I'd like to make, but that's really it. I started thinking about who really has the authority to deem my work worthy of the "mathematician" label, and there's really only a few people in my life who I'd respect enough to confer that title on me, and then I decided it wasn't exactly worth putting that much work in, and so why worry about it after that point?
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Yes, the "applied mathematics is bad mathematics" canard is extremely prevalent in US mathematics departments, which tend to be overwhelmingly "pure." I've had colleagues write anonymously in my promotion votes that I practice "mindless productivity." I still struggle with these issues to this day, and I definitely feel far more acceptance and appreciation for my expertise from my science and engineering colleagues. The hiring practices also mean that the people I want to interact with researchwise are almost always outside the mathematics department.
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To play Devil’s advocate here for a bit, how can one be sure that they really do belong and are just suffering from imposter syndrome?
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Currently working towards my PhD in Astrophysics, 7 months in to my first year (in the UK, where a typical PhD takes 3.5 years).

My impostor syndrome grows in strength with each passing day.

Admittedly I do have some mental health and sleep issues that reduce my work ethic somewhat, but I'm still putting in tons of time and effort and feel like I'm just not equipped to do this - while I'm certain that everyone else around me is way better than I could ever be.

Thanks for sharing your experiences as someone with much more academic experience than I have. It's comforting to know that I'm not alone, but also worrying that I might feel like this long in to the future.
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I believe it comes under the heading of "intrusive thought". Like many intrusive thoughts, there is probably an aspect of truth to it for most people. I think the naive instinct is to deal with it by pushing back against it fully: "I \*do\* belong, I \*am\* good enough". Personally I don't find that to be useful. I think a better approach (this comes from cbt btw) is to consider the evidence for and against the statement, and devise a more balanced statement that is closer to the truth. It is true that there are some gaps in my mathematical knowledge that other similar-stage researchers seem to know, but I have been given a PhD, I have published papers in international journals, I am clearly capable of research. I haven't published in as strong venues as I'd like, but my strength is maybe breadth rather than depth, etc etc. The truth is, there are areas I can work on, and I am never going to be a superstar but I am clearly capable of a career in mathematics (even if the reality of the situation is that the academic job market is terrible).
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So i am a PhD student in particle physics so it may be a bit different to math circles, but i think its mostly the same.

What i have come to realize is that imposter syndrome is a good thing. It means that you embraced your critical side of yourself and are ready to admit that you are not sure about something, that you dont know something.   


I will trust a person with imposter syndrome way more than a confident "i know it all" person.

Think about it. What they teach us in Math and Physics is to be critical, to think about the problem, to think about what you know, why you know it and how you know it. To me, imposter syndrome is just a stage in life where you finally achieve that. The next step is to overcome it by realizing that nobody knows everything, and its just a bunch of people who know small part of math/physics and not having a clue about anything else.  


The fact that you feel like an imposter is what makes you belong in this group of people.
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Hi,

 

Maybe in some cases, for American or Australian mathematicians, some imposter syndrome (i.e. modesty) could be a good thing. A lot of mathematicians commit some accidental malpractise, over-estimating their ability to find good thesis problems or exam problems because of being in a little complacent cul-de-sac.  

 

I remember once disrespecting a guy who sat in the common room, and later out to dinner with people, talking about a raft of bad student evaluations and trying to understand, what on earth is going on? Later, I realized that that complete openness was a really important aspect of that department. I think the same is true in medical departments, when people openly and un-ashamedly question themselves.

 

A second comment is, if a person has a little unexplained warning from their own mind about setting projects for students, if they might be trivial or uninsightful, that could be something like:  how you are supposed to listen to dreams. Brushing it under the carpet like a little spark in front of a fire would be the wrong thing.

 

I also wanted to check, who is posting this? Someone in a limited subject area somehow?   Seeing this, you have some intense and insightful videos about function spaces and seem to be a self-learner who gets very far, rather than someone who is riding on the back of being at a previous school of thought. Also you look really stressed-out and over-worked. It's good to care about students, but this is ridiculous.

 

Also, isn't the role of students to learn/read some new things and explain them to you so you won't have to. So you can structure your exams to see if they can read a definition from a paper they claim to be interested in.
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I had this too.

I love math and did a MSc in Medical Statistics after a BSc in Biology. Because of my non-math background I allways felt that imposter syndrome, especially when dealing with math Professors.

But eventually it forced me to develop and improve my self-learning strategy. I learned how to use it to my advantage.

I think one must know that everybody is learning (or had to) at some point and this syndrome actually can be dealt with to improve skills and drive commitment.

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