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I am currently a PhD student advised by a new (and awesome, in my opinion) theoretical computer scientist in the field of optimization. This was my dream ever since I took a class on convex optimization a few years ago during my MS.

However, I don’t have a math or CS background. My master’s and industry experience have both been in applied signal processing. When I recently looked at the kind of grad students who work in my current choice of research area, I realized the level of competition I am up against.

These are all from amazing institutes around the world and had been the brightest kids in their colleges, the ones with medals in olympiads, top Putnam scores, etc. I am from a mid-tier college in my country and never won an award for excelling in math/algorithms.

How do you come to terms with the fact that you might be doing research in what you love with an amazing mentor, but you’ll just never be the best in even your research community? How's that not discouraging?

  • Comments are not for extended discussion; this conversation has been moved to chat. – ff524 Apr 9 '17 at 2:28
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    The Delphic Oracle said that Socrates was the wisest person in Athens. Not because he knew everything, but because he alone was prepared to admit his own ignorance rather than pretend to know something he did not. – ctrl-alt-delor Apr 9 '17 at 11:37
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    Watch this: ted.com/speakers/carol_dweck – ctrl-alt-delor Apr 9 '17 at 11:38
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    Can't imagine why one may want to be "the best" in one particular thing instead of being good or reasonably good in many things. So I'm not the best to answer such a question. – roetnig Apr 10 '17 at 14:10

21 Answers 21

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If every swimmer were to compete with the latest 20 year old Olympic gold medalist, they would soon give up. That's why we have different leagues. They provide more relevant frames of reference to compare different athletes. Thus you need to:

Shift the frame.

Adjusting a bad frame:

You are a PhD student who completed some regular college and an outsider to your field. But you are comparing yourself with your supervisor and with "the brightest kids" in the world and, what is more, with scientist who specialized in your field from the get-go. How can that not be disappointing?

What about: You are an up-and-coming young researcher with real-world experience and a background that is not the usual run-of-the-mill in the field you are working in. You have an amazing supervisor who trusts your work and you are at least as successful as the other PhD students in your cohort. Perhaps you are the only one from your college who made it to graduate school in the last couple of years. You still have plenty of time as a researcher to develop your own profile according to your interests. Don't be fooled by the impostor syndrome.

Dropping a bad frame:

Never mind what I said in the beginning. Science is not a competition -- at least it shouldn't be.

If you're doing research mainly to outcompete your colleagues, to improve your social status, to feel pleased with yourself: you're doing it wrong. Then you are extrinsically motivated, and this is neither sustainable nor does it make you happy. Have you ever delved into a problem and forgotten to drink or eat until the sun went down? Have you ever felt deeply frustrated because you just couldn't wrap your head around some strange finding, only to realize later that it completely makes sense when you look at it from a different angle? Experienced the enthusiasm that came with that discovery? Do you deeply feel that you have to understand this? Then you know the feeling of flow that really only comes from intrinsic motivation. Forget the competition; enjoy the game.

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    @astronat Yup, Jackson and Csikszentmihalyi even describe how focusing too much on their competitors, athletes risk to impede flow and thereby impair their performance (Flow in Sports, Champaign, 1999, p. 115). – henning -- reinstate Monica Apr 6 '17 at 8:07
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    +1 for flow and Have you ever delved into a problem and forgotten to drink or eat until the sun went down? Actually, I forgot to sleep until the sunrise. – scaaahu Apr 6 '17 at 9:25
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    This is an awesome answer, but I just wanted to add one more point. Remember that contributing to a great team is also important. You have different skills and a different perspective, never underestimate the power of thinking in a different way when everyone else is too similar to each other to make progress. – JenB Apr 9 '17 at 13:37
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    I would add one more comment about group think. Innovation is often born from differences in opinion which leads to more research. When we all believe the same things because we were all trained the same way, we often stifle innovation. Embrace the differences you have as they allow you to adjust the frame; considering things others may not. You may still be wrong, but sometimes questioning the status quo leads to greater leaps in progress. – xQbert Apr 10 '17 at 18:49
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    I loved your response. I recently got a book written by my favourite YouTuber who, through seven years of hard, has now attained a lot of success, and one of my favourite quotes in it was (paraphrasing): "Be the best version of yourself". Your answer explains this philosophy very well. Thanks! – user42273 Apr 11 '17 at 0:14
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The vast majority of people working in academia are not the best. That is just a logical consequence of the fact that only one person can be the best and all others are not. Even if you relax the definitions by subdividing all fields and defining "the best" to be a group of individuals in a very specific sub-sub-sub-field rather than one individual, the group who is not the best must be significantly larger than the group who is the best in order for the concept of being the best to be meaningful.

A lot of work that needs to be done to move a field forward is just checking and re-checking, applying a result to different contexts, etc., etc. That does not require super intelligence, but is still vital. Identifying with my sub-field, and doing vital work to move that field forward is what motivates me.

Also remember that as you move up, you are entering an increasingly selective group: There is no shame in not being the most intelligent person of the world.

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    This answer perpetuates the mythological notion of "best." Even within very specific subfields, a linear ordering is not usually possible. Denounce the myth! – Kimball Apr 6 '17 at 20:26
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    I generally agree, but would like to disagree with this: "the group who is not the best must be significantly larger than the group who is the best in order for the concept of being the best to be meaningful." The whole point of a PhD is to become the very best in some very specific sub-field or problem or question. In fact, it does not take much research before you are the premier expert in the very particular question that you are considering. For any paper, the writers of that paper are the best people in the world in terms of understanding the material of that paper. – 6005 Apr 7 '17 at 9:14
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    So I think fundamentally the OP misunderstands what it means to be the best. It certainly isn't a matter of intelligence. Rather, it's about specialization. Perhaps the OP's real worry is that they will not have much of a practical impact or influence on fellow researchers (hopefully, with a good mentor, this should not be a concern). – 6005 Apr 7 '17 at 9:31
  • @6005, I would vote for something like this statement as an answer. – Dawn Apr 7 '17 at 17:53
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How do you come to terms with the fact that you might be doing research in what you love with an amazing mentor, but you’ll just never be the best in even your research community? How's that not discouraging?

The same way that a police officer comes to terms with the fact that they'll just never be the best police officer. Or a doctor. The same way that a business owner comes to terms with the fact that they'll just never be the richest person on the planet.

There's nothing to come to terms with, because "being the best" isn't the goal and "the best" isn't even a meaningful concept. People enter academia to study the subject that they love and to share their knowledge with others who want to know about it. None of that has anything to do with being "the best" because it's not a competitive pursuit. Sure, there are competitive aspects, such as getting jobs or studentships or funding, but job applications are competitive in any walk of life. And even if you ask ultra-competitive people, like athletes, they'll say that they're motivated by loving their job and wanting to be the best they can be. Almost nobody says, "I play sport X because I want to be world champion."

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    'I play sport X because I want to be a world champion' -- Tyson or Bolt or Federer or Phelps would disagree. Then again, you said 'almost nobody'. Perhaps the last sentence should be 'Almost nobody says, "... world champion", except world champions'. – Prof. Santa Claus Apr 7 '17 at 4:30
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    +1 because I like the sentiment. But: "People enter academia to study the subject that they love and to share their knowledge with others who want to know about it." A few years back, I went around and did a bunch of personal interviews across departments and locations to determine why people went into academia and down their various paths. There was less commonality than I'd initially expected; love of their field was perhaps one of the more common reasons, but no single reason seemed to be shared by a majority. – Nat Apr 7 '17 at 9:42
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    @OldGuy But "almost nobody except world champions" is still "almost nobody". Even within the realms of professional sport, most people don't get close to being world champion. Anyway, I don't want to make a big deal of this: it was just the impression I've got from listening to interviews with athletes and certainly isn't based on any scholarship. As long as you don't think it's wildly inaccurate, I'll just leave it or maybe add a few more weasel words. – David Richerby Apr 7 '17 at 10:06
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    @Prof.SantaClaus: actually, from what I know about Federer you are wrong in his case: he says he plays because he enjoys it. Of course he enjoys playing great, but it is a commonly held opinion among Tennis commenters that the longevity of Federer has much to do with his focus on the game rather than on the competition. It probably helped him through his less dominating periods (which now lasts for 7 years). – Benoît Kloeckner Apr 10 '17 at 10:21
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I've upvoted both the answers by Maarten Buis and henning, but I want to highlight and make even more clear and blunt a principle that one of the answers touches on and I personally adhere to:

Stop trying to keep up with the Joneses and start keeping up with the @convexityftws.

All kidding aside:

Be your best self.

~Rose Voisk, 1948 Olympian

The idea is that yes, we may be in competition with others, but at the same time, we must be even more in competition with ourselves.

The principle is competing against yourself. It's about self-improvement, about being better than you were the day before.

~Steve Young, Former NFL Quarterback

It's the secret of great athletes such as those above, but as Ms. Voisk affirms, it can also be applied to "every field, not just in sport but in everything we do."

And if you feel like these people are out of your league, then how about out of the mouth of a Paralympian with muscular dystrophy?

I am my biggest competitor.

~Yip Pin Xiu, Three-time Paralympic Gold Medalist and One-time IPC Gold Medalist

And wait until you really get the hang of it and you can start getting into some friendly cooperative competition, co-opetition.

Then you'll really be on the ball, and then, who knows. Perhaps "being among the best in your research community" won't be so far out of reach after all.

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    Can you explain "start keeping up with the convexityftws"? You imply it's a joke but I don't get it. Or is it just a typo? – user2390246 Apr 6 '17 at 10:01
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    @user2390246, heh, the joke is that the OP, convexityftws, should only compete with the OP-self, convexityftws, instead of trying to compete with the Joneses. – Teacher KSHuang Apr 6 '17 at 10:05
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    Ah, right, I'd not spotted OP's username. Thanks! – user2390246 Apr 6 '17 at 10:15
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    OPs doubts come from his desires to be the best self. My gf is the same, she'd get depressed over every other weirdo that's slightly ahead of her. They just want to be the best, better than themselves, and to be the best, even better than yourself you have to defeat the best. But that's not always possible. – Иво Недев Apr 7 '17 at 7:51
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    “There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self.” - Hemingway – rhombidodecahedron Apr 11 '17 at 17:31
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TL;DR It really isn't important to be the best, as most people in the world aren't the best at their jobs, and yet many of them can choose to be happy about it.

My story

I empathize with you because when I was a PhD student, just as you did, I had dreams of grandeur. I would publish amazing papers, get a job in one of the best universities, give amazing talks, etc.

Unfortunately, my dreams didn't come true. My PhD research projects did not go as smoothly as I wished, and I graduated one year later than I had planned. Nevertheless, I did graduate and find a tenure track job.

Along the way, I got married and had kids. Being a father has changed my priorities, and I would say that I realized that contentment is much more important than achievement. What do I mean? A billionaire could still feel unhappy because he/she wants more, on the other hand a homeless person could be full of joy because he/she is grateful for what he/she has.

Why am I content? I am content because:

  • I enjoy my research
  • I am reasonably good at my research
  • I and some other people find my research meaningful
  • I am paid reasonably well for research and teaching

My advice for the OP

Paraphrasing what you wrote:

The grad students who work in my current choice of research area... are all from amazing institutes around the world and had been the brightest kids in their colleges, the ones with medals in olympiads, top Putnam scores, etc. I am from a mid-tier college in my country and never won an award for excelling in math/algorithms.

In my opinion, you shouldn't be too hard on yourself that you didn't take part in olympiads. I say this as someone who did get a medal in an olympiad (the IMO). In fact, someone who got a PhD from the same institution as myself is a much more successful in math-related research than I am, even though he did not take part in any olympiads. (I suspect he probably would have been good at the olympiads, but he just never knew he was good at math until he got into university.)

I would say that to succeed at olympiads, you need to be smart and work hard, but you also need to grow up in an environment where you are exposed to information about olympiads and you need to have the opportunity to train for them.

I would use the analogy that earning a medal at an olympiad is like being certified to have a high IQ score --- it suggests that you could do high-quality math/CS research, but it definitely does not guarantee that you will do high-quality math/CS research.

In short, my advice is: Don't look at your competition, how many awards they are winning, how many papers they are writing, just do your best to work with your awesome advisor, and to do the best research and write the best papers that you can!

Related: In a separate answer, I explain how you do learn some problem solving skills in your preparation for the IMO, however, real academic research in math or theoretical computer science is quite different from olympiad math.

10

Being the best researcher isn't about having gone to the best school, having won the best prizes at Olympiads, or being the most intelligent. Sure, they are factors (intelligence is useful, and success before the PhD correlates somewhat to success during the PhD), but they are not the only factor at all. There are lots of other factors that matter:

  • Motivation: lots of smart kids do a PhD by default, and then don't do well, because they don't like research, or they don't like what they are doing, and all the intelligence in the world will not make a PhD write itself. You say that you love your research and that it was your dream to work on what you work on: I think this is a great sign, as not many PhD students would say that.
  • Tenacity: being intelligent and being hardworking do not correlate so much. Further, Olympiads-type exercises that you do before the PhD are like sprints, whereas research is like a marathon. If you work very hard and reliably, you may end up achieving more than some smart people who are just goofing off most of the time.
  • Adequate supervision, an extrinsic which you say you have, and which is very helpful and motivating, but that not everybody manages to get.
  • Writing skills: if you like to write stuff and are good at it, it will help you a lot to write papers, whereas again there are smart people who don't express themselves clearly or don't like to write, so they have lots of ideas but never get around to writing them up.
  • Social skills, to some extent: someone with very high intelligence but zero charisma (or who is socially unpleasant) may miss a lot of opportunities that would be afforded to someone who is charismatic even if less intelligent.

See also a better written post about the qualities that matter in PhD students: http://matt.might.net/articles/successful-phd-students/

So I don't think that your comparison to other students is fair, if it is just based on the criteria that you gave. I have no idea how well you perform of course, but I would say, just try your best. :)

[I would worry more about the fact that people from top schools may get better opportunities later for the same PhD research. As research is very competitive, coming from a less prestigious background before the PhD may be a slight handicap for later. However, good research should quickly make up for it: once you can compare people based on their track record as researchers, you usually stop caring about where they come from.]

So I think the reasonable question is, "how to deal with the fact that you are not currently the best in your research community, and probably never will be?". Not "... that you never will be", because usually it's hard to tell.

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〈HUMOR〉 It is discouraging. You are a loser. Go sell ice-cream instead. 〈/HUMOR〉

Now more seriously. You are in a great place with the folks who are better than you. This is the best situation you can find yourself in. If feeling inferior bothers you so much, you could try to overcome such thoughts by trying to be the best in a nearby field. E.g., you will create or contribute to a phenomenal, usable, and useful implementation of an algorithm which folks would be really eager to use. Or you will be giving excellent, 1-alpha-class talks on well-known material. Or you will be great at acquiring research funds. Or something else. Be the best in some area in which you have a chance to win. Don't compete in areas in which you have no chance to win — there, simply learn from the winners.

  • Anybody can be best in a narrow field .I have an overachieving brother who was /is overall better .But I stuck to my Knitting and can be best in some things . – Autistic Apr 8 '17 at 0:39
  • It is not "the best situation" to constantly be the weakest, least intelligent, least accomplished, and to some extent looked down on. For many (most) people, peer recognition of ability and worth is a significant factor of emotional well-being. – einpoklum - reinstate Monica Jan 31 '18 at 12:53
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I have come to a similar thought as you have mentioned. The feeling of perceived inferiority can be very strong and somewhat academically-debilitating (sometimes leading to counter-productive thoughts as 'why am I even bothering').

I am PhD graduate from mid-tier rural university in Australia, the first experience I had in my research area was through my MSc and then the PhD. I am self taught in the programming part - I have never achieved any awards and in terms of employment I have just achieved an Adjunct position from one university and a part time (1 day per week) research fellowship.

Time has eluded me, as I have to do 2 more jobs to pay the bills etc. So I have only 2 dozen publications to my name over 4 years.

All this working with remarkable academics with dozens (and even hundreds) of papers... but:

  • a couple of the papers of mine are considered to be cornerstone papers (dozens of citations each).
  • Recently, I am being approached by many academics who wish to collaborate on similar projects.

One of the academics I work with, someone with almost 300 publications (including books) summed it up for me when I asked a similar question to him - perseverance is key

Give it time, keep persevering and chase the dream, not the competition.

5

Academia is just means to an end, not an end by itself. As we study to learn the basics, to learn how to learn, to do research, etc., we have a system of incentives like a teacher's praise, a good grade, a citation of our publication by a peer, and ultimately a prestigious prize or reward. None of those things are real goals, they are just incentives to help us get through. Once you have learned enough, you go on and try to fix the world's problems. When you work improves the lives of people just a tiny bit, that will feel like a reward greater than any of the incentives your received throughout your academic development.

5

Keep in mind that there's virtually always someone "better" no matter who you are. Are the "best" people in your community better than, for example, Alan Turing or Albert Einstein?

It was a huge deal when Roger Bannister broke the 4-minute mile, but other people have done a mile faster since then. Does that mean that Roger Bannister should drive himself nuts until he does better than the people who beat his record?

In fact, a lot of world records have eventually been broken, so you could ask the same about them.

The best thing to do is to let go of comparison. To learn more about that, I suggest reading The Gifts of Imperfection by Brene Brown, who's one of the better authors on the topic.

You may also want to look into the idea of Unconditional Self-Acceptance, which implies that you don't really need to be "the best" or to hold a particular position in the "pecking order" in order to be able to accept yourself. This is particularly important given that your position in the "pecking order" will likely be changing constantly.

Besides, as others have indicated, the concept of "the best" in this kind of work is remarkably amorphous anyway, so it's not a reasonable standard to judge yourself against. Who's a "better" scientist - Isaac Newton or Albert Einstein? How would you even define or measure that?

4

There will be a day when you don't have a teacher or a professor. This is important to prepare some students for as they otherwise risk getting rather lost when they finally graduate and realize there is no list of correct answers, no grades and no golden stars on their papers any longer. Many a student have had a tough time after graduation because they were not prepared for this fact.


Try and find happiness in the work itself and not so much through validation. Most researchers will at some point reach a level of specialization where they don't have a teacher who can teach them more, because there is no one who has worked that much on the same things as they have.

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    find happiness in the work itself - something I consider of the most important and understated virtues in research. – user70612 Apr 10 '17 at 10:36
3

You're never going to be good enough

If you're struggling with feelings like falling short of being a leader in a competitive field, you're probably already a fairly competitive individual. If anything, that feeling of inadequacy is evidence of your drive to push forward and do better.

But, you're never going to win. Never.

Sure, perhaps one day you might discover some world-shaking truth. Maybe the Nobel committee will grovel for the privilege of throwing medals at your feet, and the world might come to celebrate your name and deeds. But no matter what, no matter what you achieve, you will never be good enough. You will always stand in the shadow of what you dream of becoming.

Your "betters" are figureheads. You're not envious of them; there're merely symbolic of the ideal that you chase. And if you come to stand in their shoes, you'll find them inadequate. If you surpass them, you'll forget that they ever meant anything. Just like that A+ you got on that spelling test in 1st grade; remember being proud of that? 'course not.

It's fine...

Not posting this answer to provide you with any personal comfort or reassurance. That isn't even a particularly enviable thing to seek.

Keep seeing yourself as imperfect; keep striving. In the end, as you find yourself a failure for all of your mistakes and shortcomings, the world'll be better off for the shining star that you actually were.

...maybe

Unless it's really bugging you. Obviously I like the hardcore critical approach to things, but it's probably not for everyone.

3

I will add to all the answers by saying that the fact that you consider yourself to be unlike the people you consider 'wiz-kids' can actually be a positive thing. There's a lot of discoveries that could be considered to be 'low-hanging fruit' but are actually extremely important, and would have been completely overlooked by the 'wiz-kids' for looking 'not-complicated-enough', or for not following the usual expected recipes.

There is enough high-level incremental obfuscated research already. Science is in dire need of fresh, unusual, simple approaches. Here's where you might come in, especially given your more diverse experience. Don't be fooled into thinking simple isn't groundbreaking; if anything, most often the opposite applies. Just dare to follow your ideas in your own individual style, and only good can come of it.

2

Maybe flip the question over? Why would it matter if you are or aren't, and why do you feel being "best" is important?

One way to view this is that you are in a world of 7 billion people. Almost without exception, and almost in every field of work or hobby endeavour, everyone will be more capable than some, and less capable than some. That's been the status quo throughout your life, will continue to be so, and is so for almost everyone on the planet, for all of human history. If "not being the best" is a disincentive then its going to be a pretty universal one. Best know that and consider why you might choose such an incentive to nail yourself to in the first place, and if its really a good choice for you. Is it all that keeps you going, in all areas of life?

What would you say to your best friend who said that they won't be a parent and have children, unless they can feel they are the best parent on the planet and no other parent does it as well, because they can't handle if someone else could possibly parent better than them? Is being "best" really needed and the only thing able to motivate you to do all you can and to enjoy what you do, find happiness doing it, and fulfillment in what comes of it? Putting it in other contexts like that may show just how much it really is a choice, how unhelpful and sometimes harmful it can be as a choice, and that other valid choices and measures can and do exist.

And if it isn't the only motivator for all that you do, then what else does?

2

I suspect that you are one of the best.

Look at it this way:

  • the best want to work with you (your advisor)
  • most of the time the best want to work with the best

Maybe you have compensating factors, that when you look more widely or less rigidly, make you a peer - to the best.

1

Leonard Adleman invented the genetic computer.

Hand the paper to a computer science researcher, and they'll find the CS to be really easy, and say "I don't know The computer science in the paper was basic stuff. The biology stuff was basic stuff.

He was an expert computer scientist who decided to study some biology, and wrote a paper that few understood, simply because he knew two different fields.

Hard work isn't enough. But neither is smarts. And neither is both. Hard work and smarts and luck together.

1

At least you will never be perfectly Average.

Just as it is somewhat impossible to be that ideal average of a researcher (Joe Nothing-special), it is likewise impossible to achieve that ideal of becoming some other preordained best in someone else's field. Just be the best in a field of your own choosing. It is much easier to be a big fish in a small pond (or niche of a bigger pond).

There is a story (probably apocryphal) of doctor who wanted to become an international specialist, so studied the diseases of the belly-button to help that focus (navel gazing with attitude). You only need 33 bits of entropy to be unique (the best in the world) anyway, https://33bits.org/about/

1

It's OK not to be the world's best.

Nobel prizes honor disciplines, but they do not in a vague and general sense say that e.g. physics is a good thing. Rather, they pick out (usually) one representative, and give a compliment to physics as a whole.

At least on present terms, there is not going to be a Nobel prize for bilking seniors out of their nest eggs. Even if the Nobel prize parody gave sarcastic honors to 419 scammers.

A Nobel prize compliments a community of research, but instead of a general and faceless way, they give excellence in a particular field a concrete face. But a Nobel prize in physics is in no sense a dig at every community member save the individual recognized as laureate. If a fields has a Nobel prize, that's a compliment to all true members.

(N.B. For mathematics, substitute "Fields medal" for "Nobel prize.")

1

There's a major flaw in your thinking. Research is a team sport. Whether you're "the best" is mostly a factor of social acceptance (aka, popularity), with only a slight correlation to above average competency. The ones often considered "the best" may or may not be above average competency, but they are all popular because of some single discovery, their personality, prevalence in the lecture/conference circuit, or a book/paper they wrote two decades ago. Whatever good you do in research will be from persistence and consistency. Continually provide good work and do your part. Some days you'll feel like the hero, some days the damsel. Most days, you're somewhere in between. But when your team comes together, standing on the shoulders of the ones before you, together you all can be "the best".

0

You have got a lot of answers. Here is my 2 cents.

First of all, as a PhD, you are comparing yourself to some of the most committed, intelligent, and passionate people there are. it is a given that competition will be very rough. Second, looking at where successful researchers come from (institution, country...) and losing motivation because you are not coming from quite as fancy places is very similar to looking kids with rich fathers and losing your motivation in life in general. Academia is just as unfair as any other aspect of life.

- How to deal with this unfair or handicapped start?

You need to work your ass off and focus on your strengths when it comes to building your career. Learn as much you can from different but related disciplines. Develop hands-on skills, if it is something valued or sought after in your field. Be sociable, likable. If you know an employer who values a particular thing, being a hardworker for example, don't say you are a hardworker. Show that you are hardworker. Just be the best that you can be with a positive look on life and never give up. Because, I truly believe that the most successful people in this field are not the most intelligent ones, but the ones that have unyielding perseverance.

- Am I just talking out of my butt?

I am at a similar position. It took me far longer than average to finish my PhD (7 years) due to several reasons. I had two colleagues quit during my time without conducting an ounce of research. We were supposed to be working as a team. Instead, I was forced work completely alone in a multi-disciplinary research field. Like, literally alone, no one to get guidance from for lab methods. I am really shocked that I didn't blow up a lab during the early years of my PhD. I have okay amount of journals but compared to other people in my field, I am in trouble.

So I focused on my hands-on experience in the lab and my multi-disciplinary working capacity when looking for postdoc and industry jobs. I had to develop those skills blood and sweat, but they are highly sought for in my field. And very recently I was able to land a postdoc position which I cannot wait to start. The principle investigator of the new group is from Stanford. Her other two postdocs are from top 30 universities in the world (QS ratings). I am from a 200+ ranked university. But The professor happened to need someone who can work with multiple disciplines and conduct hand on experiments. She didn't want just anybody as long as they are from a fancy university.

TLDR: Focus on your strengths, be very good at a few things that are highly sought in your field, be knowledgeable enough at several disciplines, stay positive (people can smell stress!), try to be the best that you can be, persevere (honestly, this is the number 1 quality of a researcher, you cannot give up in research).

-1

What counts are the results you have obtained. Even if you're the dumbest of them all, if you find an interesting results and get it published, you'll have been the first person that has ever lived on this planet to have found that result. This is then analogous to you being the first successful climber of, say, Mount Everest. Many other people have climbed more mountains than you? Yes, but none of them have managed to climb that particular mountain you have climbed. So, even from the point of view of competition (and I agree here with the other answerers that this perspective isn't all that useful in academia in practice for many reasons), it's not the same as in sports where different competitors are trying to out-compete each other.

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    "Even if you're the dumbest of them all, if you find an interesting results and get it published" Sorry, but I'm confused: given that many, many people never find and publish interesting results, how could such a person be "the dumbest of them all"? – Pete L. Clark Apr 7 '17 at 1:51
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    "A requirement to get a Ph.D is that all the results in the thesis must have been published in peer reviewed journals." No, this is not a requirement in (e.g.) any math department in the United States. E.g. I got my PhD in 2003 and published my first paper in 2005. Less than half of all math PhDs publish papers. And since not every PhD student gets a PhD, presumably "the dumbest of them all does not." Finally: claiming some credit for the results is not the same as finding interesting results.... – Pete L. Clark Apr 7 '17 at 2:25
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    ...My point is that the claim "Everyone finds and publishes interesting results" is obviously false. In fact, many people only find results that were already known to others and/or viewed by them as totally routine and uninteresting. I can't read your first sentence in any other way than "Even the worst students can do something good." Sorry, but it's not true. It is not my intent to be discouraging, but I feel that being counterfactually encouraging is not helpful. – Pete L. Clark Apr 7 '17 at 2:26
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    In fact less than half of all PhDs are in the hard sciences. (Note also that the OP is in a branch of mathematics.) "analyzing my answer as if it is a mathematical proof of a theorem" You mean, logically? I have found that this is the best way to analyze things, so I will not apologize for it. If you don't want to be misunderstood, please feel free to reword your answer. – Pete L. Clark Apr 7 '17 at 20:23
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    There's a difference between being the first to climb Mount Everest and being the first to hike up Mount Washington, though. – henning -- reinstate Monica Apr 8 '17 at 6:21