I've never been an olympiad-winning excellent student; is there a chance for me in academia?

I'm wondering a lot if I will be able to stay in academia for the whole career or whether one day I'm going to hit a glass ceiling that only someone who was a genius all along could break?

You don't need to be a genius to stay in academia for your whole career. Excellent maths skills certainly help in STEM, but someone with excellent maths skills but lacking other critical skills might fail, whereas someone with "good enough" maths skills and excellent organisation and people skills might succeed.

True story: a university I know well hired two new professors. They found two with an excellent publication record, many publications in Science and Nature, and hired them, seemingly impressed that such "successful" academics were willing to work at a not-so-famous university. The university soon regretted their hiring decision. The next years were very difficult, as it turned out the two were, to put it diplomatically, lacking in people skills. After many personal conflicts, stressed colleagues, burned out PhD students and postdocs, and several years later, both left. Two others were hired who, on paper, may look less impressive when looking at the publication record, but who are good scientists, teachers, postdoc/PhD supervisors, and more interested and successful in bringing the department forward. The department is now doing better than I have ever seen it, and the "crisis years" a lesson and a time of unhappy anecdotes that soon only the senior faculty and administrative staff will remember.

And if there's a chance for me, what can I do to start to see myself as equals with those PhD students who used to win olympiads in school?

Academia is not about winning olympiads. To succeed in academia, you need to be a good scientist. You need to be well-organised and have good people skills, and it helps to be a decent teacher. Olympiads are at best partly predictive for the maths skills needed in STEM, but have probably no predictive value for any of the other skills you need to succeed in academia (nor in other careers).

Olympiad winners are more like sprinters, whereas success in academia requires more of a marathon runner. It is by no means guaranteed that a successful olympiad winner will have the stamina to complete a PhD project and the patience to write a 100+ page thesis. Slow but deep thinkers tend to fail in olympiads but succeed in academia. There are also psychological factors that favour success, such as being a team player rather than an individualist, or the ability to avoid conflict. Also, the number of unsolved problems by far exceeds the number of geniuses, so there is always plenty of work for everyone.

I too have had colleagues that I consider genius. It's easy to feel like an imposter in such company when your history of grades has been good but perhaps not at the very top.

But then I got into a Ph.D. program (in experimental physics) and started going to conferences. There, I saw what the actual standard of research is: The vast majority of work was incremental stuff I could understand and imagine myself doing (with a bit more specific experience, of course). Even many "breakthroughs" were either chance discoveries or the culmination of a logical series of incremental advances. Pure works of genius, i.e. tours de force of breathtaking creativity and/or intellect, did exist, but they were few and far between. Plenty of people seemed to be making nice careers out of the (hard and plentiful) work of further developing someone else's breakthrough. The breakthrough is just the beginning.

All of this is to say that genius is nice, of course, but in academia it's neither necessary nor sufficient for success. There are many skills needed for research, and they strongly depend on your field. In most cases, the skill of solving tricky problem sets (timed, with limited resources, and where you know there's an answer) wouldn't even rank in the top 10. Real research is different, and you get to choose your field to suit your skills.

There are two major effects in your favor here.

First, being good a math competitions is only loosely correlated to being good at math research. Some skills overlap but a lot of others do not and there are plently of people who excel at one but not the other. The other two answers focus on that aspect in more detail.

Second, there is the quantity of people. There are a lot fewer people who get prices at high level math competitions that people who do successful math PhDs. Even if you assume that the national olympiad winners are better than you in research math that does not imply you are not qualified to become an excellent math researcher.

Personal anecdote: I went to a high school with a strong math focus, well known for being very successful in high school level math competitions. Several students who were maybe slightly below average in math in that specific school had these eye-opening moments when they started college, their math skills were easily sufficient to become very successful mathematicians. So morale, there are always people out there who are better than you. This does not imply in any way that you are not good enough.

While I can't speak for ultimate academic longevity, plenty of people in my department (myself included) never really got into Olympiads. That doesn't make them dumber, or worse academics- the skillset you need to be good at specific styles of problems isn't necessarily the same you need in STEM academia in general. While people start with different levels of innate talents, usually by graduate school, most need to start putting in the hours and actively learning skills.

Since you're just starting out, some miscellaneous points from a non-genius who completed a PhD in STEM in Europe:

• Weight other people's opinions of your academic potential based on their qualifications. You mentioned that you think your high school teachers didn't believe in you, yet you have multiple positive recommendation levels from people who have actually worked with you in a research context. I would give more credence to the latter.
• Avoid trying to compare yourself based on being the "type of person" who succeeds at X. We all know various stereotypes of the "genius scientist": some people will fit this more than others, but arguably every person is a bit more nuanced than that. There's also strongly gender/ethnicity related aspects to this question that I don't want to start a flame war about. But to keep it short, don't waste your time thinking about if you're the kind of person who can do X: just give X your best attempt.
• Try to avoid putting other academics on a pedestal. Yes, plenty of them are incredibly bright. But these are also now your coworkers, and they're still normal human beings. Have some coffee with them, and chat about your projects. You're not in a competition about who is the most smartest most deservingest with the bestest brain: these are potential collaborators, maybe friends (the other students) who share a lot of interests with you.
• Things will get better: I'm not saying your advisor isn't a genius, leaving cryptic messages for other geniuses (genii?) to decode in a bizarre merit-competition. But to play the devil's advocate here, maybe they were someone very smart who worked very long hours for very long years on some specific topics, and now is very good at them, to the point where they sometimes lost sight of what is obvious. Once you've settled into your PhD, the methods you work with will also be "obvious" to you, and you'll seem like a genius to the undergrads.

As a corollary to the last point: if you're feeling impostor syndrome or insecurity, it can be helpful to have others to talk to who have also struggled. Are there any ways to meet other new students? Especially at the start, it can feel difficult to admit (perceived) weakness or failures, even though most everyone will face some sort of challenge in their PhD at some point. Finding some community can be very helpful here.

I was a (quite) successful Olympian and my MSc was not difficult. MSc is the level where you get a grasp of the topics of your studies without going into scary details. I loved all my courses.

Then I went for a PhD. It was something really different - I had not only to learn but also to discover something. That was quite a change because this something (the core of your thesis) is not written anywhere and obviously people do not know about it.

What I am trying to say that learning, teaching and research are really different beasts (though teaching is awesome for learning). They use different muscles in your brain and some have them, while others do not (everyone has some of them but you never know until you try).

A PhD sounds grandiose and sometimes is. But in everyday life there is a lot of wandering around, thinking and sometimes you get an eureka moment (and the day after you realize that it is wrong).

I do not think that you can "guess" that you will be good or not during your PhD studies (as opposed to MSc) but if you are curious and love your topic go for it. This is a wonderful time in your life, a once-in-a-lifetime experience. Do not forget to party.

PS. After getting my PhD I realized that I would not be a good scientist after all and moved away from Academia. I sometimes miss the teaching and the joy of doing research though.

I hope I didn't miss anything, but I want to list two important factors I haven't seen in the other answers.

First, being able to find unsolved problems or that certain kind of creativity to realize that you could apply method A, that has previously been used on topic T, to your topic S and get amazing results. Winning an olympiad means the others were able to solve problems they are given, but that doesn't mean they are able to come up with problems themselves. If you go to industry, you might be perfectly fine solving problems you are given by your boss or your customers. In academia, this might be enough to get a PhD, but after that, you are expected to find your own topics.

Second, networking with others. Discussing with other researchers in your group or at a conference / workshop. "It's no competition" has been mentioned a few times, but I think it's actually more than just that. Not only can more than one person work on a topic, but the best ideas often come from interaction with others, when you share your findings and suddenly realize that the other party has / knows the missing piece to your problem. Not to mention that hiring commitees love people with active cooperations so they can "brag"...

I once had a colleague / fellow PhD student who was much better than me in these two aspects, while I was the one that had received better grades in most classes. She's a professor today while I'm a teacher - and while that seemed to be a breeze for her, I'm pretty sure that I would have been up for a rough time finding a tenure track position in academia (plus, I always liked TA-ing much more than research, so I consider myself in the right place now).

As Thomas Edison so famously said:

Genius is one percent inspiration, ninety-nine percent perspiration.

He went through literally thousands of different concepts and materials in his quest to invent the light bulb before discovering something that actually worked. The (arguably) most transformative invention of the modern era was not some grand idea that sprung into the mind of a savant, it was the product of many years of hard work, a continuous process of refinement and experimentation. Edison isn't unique in this, either. The same is generally true about just about any great invention or discovery that you can imagine.

Your colleagues aren't more capable than you, they just have a different set of strengths and weaknesses. The best teams are made from people with diverse skills and strengths. Chances are, they'll end up feeling the same way about you because there are things you can do much more easily than they can. You're not competing against these people, they're your teammates. Learn what each person's skills are and use that to help advance your team's objectives.

In the end, it's all about doing the work. Research is work. A lot of work. Being a stereotypical "genius" might make some things easier, but success is ultimately down to putting in the work. Work hard and do quality work, and I think you'll be surprised at how far you can go.

Our math and physics teachers prepared them for the competitions, but whenever I communicated that I'd also like to try they didn't take me seriously. I always thought they don't see the potential in me because sometimes the homework was quite hard for me

Well, have you ever considered why you wanted to try? To me, it appears as if you were trying to prove yourself, and this is dangerous when you don't recognise that "deep" talent usually only comes naturally. I think it was more about your own self-esteem, than about them not taking you seriously. What is serious, is that they should have sat down and discuss with you about it. Trying to reach ceilings is OK, but trying to break them often causes pain. You can avoid this pain when you don't set out to "break ceilings" but just try to be the best you can be, and it may also lead to some broken ceilings along the way ;)

You appear to be overthinking it a bit, which undoubtedly is causing you the stress that motivated you to write this question.

There is a number of reasons to pursue an academic career; they generally fall on various points on the broad spectrum of egoistic vs altruistic:

• For the money?
• For the fame?
• For the fun of it (common motive of geniuses)?
• For the security it brings?
• For the passion/lust of it?
• To advance science and humanity?
• ...

Depending on the percentage breakdown of the reasons you're in it for, you will have different obstacles hindering your "psyche". In my experience, being somewhere in the middle can definitely down-regulate your feeling of difficulty, but at a proportional cost in your feeling of achievement. In short, rationality can be easier exercised over emotion when in a balance between egoism and altruism.

When you lean to the "sides" of the egoism-altruism continuum, (i.e. much more egoistic or much more altruistic) you have more motivation and can bypass issues more easily, regardless of the size of their actual "footprint". Your emotional strength will help you go through perceived problems more easily, and will not feel the need to intellectualise or even rationalise your conflicts. You will be OK with your sense of self.

The trap, though, is that as you lean towards more egoistic motives in contrast to altruistic ones, you will be more prone to distortions in your perspective, closed-mindedness and immature psychological defenses, i.e. your strong emotions will dominate your pursuits more than rationality. Your enjoyment will then concentrate on the achievements themselves, i.e. the fame, the money, etc, so you will have to wait and fight hard until you get there. Valuable friends are also much harder to make in this modus operandi, I am afraid.

When your motives are mostly altruistic, your enjoyment will be distributed all along the path. This, again, in my experience, starts from day one. You "risk" feeling more content, as you will find satisfaction in much more than just the "goals". You also "risk" being more open to requesting or providing help, viewing problems more optimistically and, maybe somewhat unexpectedly, actively be on the look for "ceilings to break". You will most likely not break any ceiling alone, and not become a household name, but you will also feel you don't need to. Altruistic researchers generally mostly enjoy breaking ceilings together with others and find satisfaction in the process much more than only in the results.

When you reach a fair level of maturity in your academic pursuits, you will eventually understand that what now view as "geniuses", is actually going to be one of your best "tools", to achieve multiple ceiling breaks at once. Truly competitive geniuses are very easy to manipulate, so please treat them with responsibility and kindness when you get there.

Update

In reality, you are asking whether there is a point to get into the fitness/training market if you cannot run as fast as Usain Bolt. Well, what do you think?

True satisfaction comes only by accepting who you are, and trying to be the best you can be, with a reasonable effort. You are not going to be very happy trying to be the best others think you can be, or the best you see in others.

TL;DR

You are going to do great. If you are already a PhD student, someone that has also been trusted in the past to get into academia, also trusted you. Transitive trust is multiplied trust!

Enjoy your efforts!

Good news and bad. First, I wouldn't put too much weight in the Olympiad stuff. If this makes sense, success in that sort of thing can be a predictor of real life success in a person who also has grit, determination, and a good work ethic. But lackluster performance in such things is not a predictor of failure simply because there is so much more needed in life than is needed in one of those exams.

The bad news: I was actually a far and above average student all along, and I dearly wanted an academic career. I didn't make it. Several years ago, staring at a choice of the corporate world or unemployment, I went corporate. The competition for academic positions is fierce, probably because they are just such plum positions. You don't get filthy rich but you will get paid very well to do stuff you would do for free. I would suggest that you talk to some professors and researchers who have made it. Ask them what they did to make it and then ask yourself are you able and willing to do the same?

Also, you probably have a student membership in a some relevant professional organization (or you should) and many of these orgs publish annual stats on how many jobs were open last year, how many people younger people stayed in academia and how many went elsewhere, etc. Get that information in hand and then make an honest assessment of your chances. And good luck.