Imposter Syndrome and depression: I feel pretty depressed that I am not as "qualified" as a close family member. In particular, this family member has undergraduate and graduate (PhD) degrees from Ivy League schools in mathematics. Whenever I try to solve a problem, this family member does it in half the time. Does this mean that I should try and find another field to specialize in?

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    Related: academia.stackexchange.com/q/2219/19607 and academia.stackexchange.com/q/11765/19607 (and many others)
    – Kimball
    Commented Apr 28, 2017 at 20:26
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    No way. Cedric Villani could solve any research problem I face in a fraction of the time - that doesn't mean I should give up a research career :-) I think as part of life, one has to accept that there are people better than you, but as you are doing research in mathematics you should realise you are one of the brightest set of people in the world Commented Apr 28, 2017 at 20:39
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    Two arguments against finding another field: 1. there are many math problems, so you won't necessarily be competing against people like your family member in everything you do, and 2. problem-finding is in some ways as valuable as problem-solving, and the people who are great at one are not necessarily great at the other.
    – Filigreen
    Commented Apr 28, 2017 at 21:03
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    Science and mathematics are not a competition. I actually get very excited and happy when I find other smart and capable people working in my field (and not just my field), or when I read about how someone else has solved some hard problem or done some great research. Commented Apr 28, 2017 at 21:11
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    "If you compare yourself to others you may become vain or bitter for always there will be greater and lesser persons than yourself" - Max Ehrmann
    – PCARR
    Commented Apr 29, 2017 at 9:55

15 Answers 15


Research in math (and I assume in general) is hard. It doesn't get better over time, but rather we seem to get used to the accompanying depression and angst.

When I feel down, I try to remind myself that I do math because I enjoy it, not because I want to be the best at it, and for some reason people continue to pay me money to do it. If they stop, I'll figure out something else. In the meantime, I get to think about problems that I love, even if the process of that thinking isn't always fun.

The above is also hard. There are still rough days. It helps me to know that other people, including really smart people doing great math, experience the same feelings.

If you want to switch fields, go ahead. But in general, any field will have someone (seemingly) faster than you - this is not personal, we all feel like this.

imposter syndrome

[Picture Credit: David Whittaker]

I would recommend reflecting upon why you are in mathematics in the first place. If you're in it because you love doing it, does it matter if someone else is a bit faster? There is plenty of mathematics to go around.

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    You single-handedly got my upvote with your convincing picture. Commented Apr 29, 2017 at 17:20
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    Disclaimer: I didn't make the picture. I saw it on Facebook at some point, and for this answer, found it here psychologytoday.com/blog/happy-trails/201511/feeling-fraud
    – Aru Ray
    Commented Apr 29, 2017 at 21:48
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    +1 for the answer, but I think the reference to the picture should be inside the post.
    – Earthliŋ
    Commented Apr 30, 2017 at 10:18
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    @SolarMike Well, most orchestras likely have an entire line of trombonists... might be more accurate to say "Only one plays the Bass Drum", or "Only one plays the Bassoon"... since that's more likely in practice... ;-P
    – SnakeDoc
    Commented Apr 30, 2017 at 21:54
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    This seems to be the real source: twitter.com/rundavidrun/status/587671657193455616
    – xehpuk
    Commented Apr 30, 2017 at 21:55

Even if other people have amazing lunches, you'd still want to have your own, even if less amazing, simply because you're hungry.


Do you love research and/or math itself? Do you love solving problems and learning about new things and finding out how things work? If not, then I'm afraid your motivation is misdirected.

As you progress through life, you will meet many more people that are much smarter than you. I teach students who are much smarter than me and I wish I had their brain. Some colleagues/peers are simply out of this world.

However, there is a place for you. There are many research areas and countless opportunities to contribute. If it's not in math, then it's in other areas; there are many areas/problems waiting for new tools and perspectives. This means it is all hands on deck. The scientific community is small relative to the world's population. We are motivated to generate and verify new knowledge. If not us, who else?

Go back to basics, and follow your heart and interests. Keep moving and try to stop comparing; otherwise, it's like spending too much time in an art gallery and not doing any work :)


Math can be brutal to your self-esteem. If you are a poet of average skills you could (perhaps) convince yourself that you are an under-appreciated genius with as much raw talent as a winner of the Nobel Prize in literature. In mathematics, if you are mathematician of average talent, you can't plausibly convince yourself that you are even remotely as talented as a winner of the Fields Medal.

If you get to that stage you have to ask yourself what is more important -- your ego or your love of mathematics. If the former, by all means switch to another field, perhaps one with more subjective criteria where you can convince yourself that you are the best. If the latter -- keep with what you are doing.

Many mathematicians end up teaching undergraduates. If that is the career path you end up following, the knowledge that you are not a world-class research mathematician (if in fact you are not) can help give you the humility that you need to e.g. not lose patience with students who can't seem to understand the chain rule. What you are feeling now about your family member is similar to what some of your students will feel about you. This can help you empathize with such students. If you know what it is like to struggle with a concept that some people find obvious you will be in a better position to help others who are in a similar state.


No it does not. There will always be someone better than you and I in whatever we do, but that does not mean you should give up. Family issues are hard because it's so easy to compare yourself to a relative, especially a close one. However, that does not mean you should give up.

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    There are a handful of people who are actually the best in the world at something, such as the world chess champion. The remaining 7.5 billion of us just have to get used to other people being better than us in even our chosen field. Commented Apr 28, 2017 at 21:35
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    @Patricia: What you say is true, and as a logically minded person, I appreciate you pointing it out. However, from what I know about the psychology of "elite performance," the people who are in the running for being the world's best at X are most often hyper-aware of their competition and have an eye out at all times for how far they are ahead. Even being superior enough to only compete with yourself does not imply angst-free days: the struggle to exceed one's past accomplishments is overall very positive...but it's certainly not carefree and can lead to feelings of inferiority. Commented Apr 30, 2017 at 17:05

Although my field of study is not Math, I can relate to you because I had a experience that was very similar to yours. Just like you, I felt unqualified in my studies and just like you, I had thought about changing to another field and even giving up on trying hard. Eventually, I changed my field of study but not because I wanted to be perfect or better than others in it but because I came to the conclusion that if I want to spend my time and life on something, it should be something that I enjoy doing. I decided to focus on enjoying what I do and trying to improve myself over time rather than comparing myself to other people. For me, it is a fact that almost in any aspect of life, there are people that are better than me. As a matter of fact, there are people in my new field that are better than me (I have close interactions with some of them on a daily basis) and well, that's life.

Also, it is good to remember a well-known quote from Thomas Edison:

Genius is 1% inspiration and 99% perspiration

I have studied biographies of many prominent scientists and artists and two personality traits that I have found very common among them are that they enjoyed their work and they worked hard. In my opinion, these are the qualities that you should concentrate on. If you truly enjoy Mathematics, then just enjoy it. For a good biography, I encourage you to read the wonderful memoir of Issac Asimov, I, Asimov.

By the way, I hope that by 'feeling depressed', you do not mean that you are suffering from clinical depression (depression is always an alarming word for me). It is quite normal to feel disappointed about your qualities sometimes but, if you feel depressed about other significant aspects of your life too, please also consider seeking clinical help.

  • It is 99% hard work by EXPERIENCE. But it is not 99% hard work by FREQUENCY in the general population. Commented Apr 29, 2017 at 22:57

Does this mean that I should try and find another field to specialize in?

In any field you choose to specialize in you will encounter someone -- probably multiple people -- like your family member who have better training and probably more talent than you. That makes me wonder why you assume the premise that it is especially bad to have a family member who is that super-talented person? Won't it be just as frustrating to have such a person as your supervisor or your colleague? In which case, isn't the conclusion that your only hope is to retire to a desert island and not attempt to do anything meaningful with your life, so that you never have to compare yourself with someone who is better than you at what you do?

The answer of course is that the premise is incorrect. You should aspire to choose a profession that brings you the highest level of personal satisfaction. If math is that area, it would be a shame to choose a different area for the sole purpose of avoiding professional jealousy between you and a family member, when in all likelihood you will encounter many other people likely to arouse similar feelings of jealousy in you. Better to learn to deal with the jealousy, accept that you are not the smartest person on earth, and find joy and meaning in your ability to make humble but useful contributions to mathematical knowledge. Good luck!


you don't say how far along you are. If you haven't finished a first degree in maths and he has a PhD from a good university then he ought be at least twice as fast as you. In fact, if he is only twice as fast as you, you are doing rather well.

A more interesting question to ask, is how is his career going? I have seen plenty of people with PhDs from top name institutions have trouble making a career in maths. If you really truly believe that you have less talent and he is having trouble in the job market, it's probably a sign that you should specialize in something more employable.

  • My experience contradicts the first sentence. When I was in my first two years of undergrad I was besting the tenured faculty at my university; these weren't Harvard PhDs but they weren't exactly slouches. Commented May 6, 2017 at 23:54
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    That's just ridiculous. How can an undergraduate beat a tenured professor? I'm sure he's not competing with you in any sense.
    – Shake Baby
    Commented May 28, 2017 at 0:38

Whenever I try to solve a problem, this family member does it in half the time. Does this mean that I should try and find another field to specialize in?

If you and this relative are unable to put a bit of academic distance between yourselves, for example by refraining from tackling the same math problem (and then comparing your results and your speed), then I imagine you would probably be happier not studying in the same field. It sounds as though you may be setting yourself up repeatedly for this type of comparison, which you then get discouraged about.


In a way I can relate to this experience. My siblings are both in your situation. I am and have been the "smart" guy in my family. My siblings were very often compared to me by teachers, friends and family members and used to be asked why they can't be as "good" as I was. That got them depressed and made them give up on things they wanted to achieve because they believed what they were told, that they "have no talent". If I ever regret something in life, is that I didn't pay attention to that and didn't as much as tell them what exactly talent was.

Because, here is the thing. I have no particular talent in anything. I only know that if I work hard enough, smart enough, and I keep myself healthy, I can acquire many talents. How to learn something is a whole science, and I don't plan to discuss it here. All I'm saying, you can get a PhD, a successful career, even if you seem much less competent at the beginning than your peers. In fact, I was surprised myself how many of my PhD colleagues who seemed to struggle with just about everything, ended up making important contributions to the research fields they happened to specialize in.

I also think I should mention that even if you don't know whether you'd like or not a certain research field, the beginning is not the moment to decide on that. It's as if you'd decide not to marry someone because you don't like their nose. But, if you stay long enough to know them and you realize they treat you well and have many qualities, I doubt you'd care so much about the nose. Same with the research. Once you reach a certain level of understanding, you begin to like the field.

If I were to do a PhD again, I'd choose a field that gives me enough job opportunities, enough challenge, and problems worth solving. I'd not factor other's talents in this decision.


Einstein struggled a lot more with mathematics than a whole lot of his contemporaries, particularly mathematicians. David Hilbert was able to retrace (and do the finishing touches Einstein was still working on) a significant amount of Einstein's General Relativity work in a small fraction of the time Einstein needed and made a paper which he later retracted since he saw it as credit-stealing.

Einstein needed a lot of time to get where he wanted to but he had the advantage of knowing for sure where he wanted to get. That produced more tangible results than brilliant minds without his aim.

So no, the mere speed and skill with which one of your relatives (what does it matter that he is a relative anyway?) works with mathematics does not tell much about what mathematics can do with and in your life.

I mean, if he is a relative, that should be a good omen, shouldn't it? That makes it likely that your genes are not entirely remote from your interests.

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    "Einstein struggled a lot more with mathematics than a whole lot of his contemporaries, particularly mathematicians." Einstein was a physicist, so yes, some mathematicians were better at math. The idea that he "struggled" with math -- more so than anyone who does advanced math struggles with it, I mean -- seems to have no factual basis: see e.g. content.time.com/time/specials/packages/article/…, in which we learn Einstein had mastered calculus by 15. Hilbert was by the way the most brilliant mathematical mind of the time. Commented May 1, 2017 at 18:56
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    Einstein's IQ was reckoned around 160 -- in other words, probably not the very highest among physicists (having a high IQ can help you in academia, but only up to a certain threshold, and Einstein's IQ was well above that threshold) but surely enough to make him quick-witted among any reasonable cohort. "Einstein needed a lot of time to get where he wanted to" Again, not really -- he is famous for his annus mirabilis, in which he wrote four amazing papers. He was 26 at the time. For what it's worth, I agree with the last two paragraphs much more. Commented May 1, 2017 at 19:01
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    @PeteL.Clark the sentence "Einstein needed a lot of time to get where he wanted to" seems to refer to the period 1908-1915 during which Einstein was working on developing general relativity, so I think user72889 has a valid point here. With that said, I agree with you that it's misleading to claim Einstein "struggled" with math - rather, he "struggled" to develop a revolutionary new theory of gravity that made use of sophisticated mathematical tools that were understood by only a handful of mathematicians at the time. Not quite a great basis for comparing OP's situation to Einstein's.
    – Dan Romik
    Commented May 1, 2017 at 19:44
  • @PeteL.Clark It is hard to say IQ does not help above the threshold. For instance, Von Neumann obviously benefited from his remarkable abilities. Even though he was perhaps not the best mathematician of all. Commented May 2, 2017 at 19:16

On the contrary this should encourage you to go into the same field as your family member. The best way to improve at something is to surround yourself with people who are more talented than you are.

When you have a problem that you are working on (or even better after you have solved it) you can discuss the problem with your family member about how they would have solved and how you could solve it better in the future. You also have the benefit of having casual conversations about things tangentially related to your professional interests.

I think that key thing here is that you already have a network of highly skilled people in your field. This is an extraordinary advantage and you should harness it.

  • There is a problem with this answer: It does not take into account the personality of OP and the interpersonal skills of the family member (which are both not stated in the question). For (an extreme) example, if the family member was Sherlock Holmes who would always tell me (directly or indirectly) how stupid I am, then I would not be comfortable working with him. Unfortunately, I met many people who have a Holmes-like attitude.
    – yupsi
    Commented Nov 28, 2017 at 13:37

This may be a cause to move into a different sub-field than him... Many people want the glory and to feel they have done something. There is no reason to think this cannot be done within mathematics.

But on the thing of comparision, do you have better questions than him? Do you have novel approaches? These are the things that matter. Also when you talk of his ability to solve problems more quickly, are you talking about elementary problems that take mere minutes? Does he betray a deeper understanding than you?

  • +1 for sub-field. There must be an area within math that doesn't interest him/her but could be loved by you. Something special. Some niche.
    – leymannx
    Commented May 1, 2017 at 8:39

Absolutely not!

You should only consider a change in a specialisation if you choose to, not due to a feeling of being forced - the latter, in all likelihood, would not be sustainable. Explore your specialisation to see if you can identify and capture a niche area that grabs your interest.

When I feel a similar feeling, I look at a list I prepared of what I have accomplished within the topic, what I have going at the moment and the exciting prospects that I have planned. Doesn't always work, but does help most times - there is no magic solution though.

One thing to consider is engaging your family member in a collaborative project, work together and even learn from them. Good chances are that he'll learn off you at the same time.

Perhaps, there is an opportunity to be mentored by your family member - benefit from his knowledge and skills.

As a saying goes "chase the dream, not the opposition" - but without the opposition, as you are not in competition with your family member.


I think that mathematics research is about being more creative than being fast. Being faster is more likely to help you in math competitions, examinations. But you will need different qualities for mathematical research.

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