I am a high-school student. I have developed a recent affection towards mathematics (especially proofs), although I was always into logic (I've been a programmer since the age of eight). Now I am worried whether I will succeed in mathematics as a career. I have an IQ in the 99.7%ile in India and always score approximately 150 in IQ tests. (I know IQ is irrelevant.)

To judge whether I am capable enough to be a mathematician, I have set myself a challenge: if I clear the entrance exam of ISI, only then shall I pursue mathematics. (Sample ISI exam questions.) I want to know from current math grad students, professors and teachers whether this challenge will be good enough to test whether I have the ability to pursue mathematics as a career. If not, then how can I judge myself?

I don't have access to olympiads, though the subjective questions of ISI are considered on par with InMO, and clearing the exam is also considered a big achievement in India.

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    $\begingroup$ "It is not worth an intelligent man's time to be in the majority. By definition, there are already enough people to do that." - G. H. Hardy $\endgroup$ Jan 25, 2014 at 16:06
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    $\begingroup$ Here's a simple but relevant test. Given the choice would you rather: A) spend your life checking the validity of the proof of the four-color theorem? Or, B) eat. $\endgroup$ Jan 25, 2014 at 16:46
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    $\begingroup$ Your ability matters less than your desire and wisdom is much more important than intelligence. I know plenty of people with high IQs and little success, and others with great ability wasted in trivial pursuits. $\endgroup$
    – Nathan G
    Jan 25, 2014 at 18:09
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    $\begingroup$ If not maths, then computer science. Either way, they're both related, and based on logic. $\endgroup$
    – Lucian
    Jan 25, 2014 at 18:33
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    $\begingroup$ Without any perspective to your question, we have a similar name only that I am Chatterjee and you are Mukherjee...I am targeting ISI too...only one thing I can tell you is that my journey started last year from around last week of March...and the journey I had,involving myself in mathematics is unforgettable...rest is your choice and decision...best of luck! $\endgroup$
    – Hawk
    Jan 25, 2014 at 18:53

7 Answers 7


It will be a very simple answer. If you like (not to say love) mathematics, don't ask this question. Just go and win ! Good luck and see you soon as a brilliant mathematician !

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    $\begingroup$ Indeed that's true. $\endgroup$
    – Kashmiri
    Sep 4, 2020 at 8:32

Tests aren't a metric of professional ability

You should not use tests like these to measure future potential as a mathematician. You should use them as a tool to gauge your current mathematical ability, your strengths and weaknesses.

Mathematics is about learning new ways to think about problems. It doesn't require genius to learn new ways of thinking, just an open mind and willingness to learn. To be a successful professional mathematician you will have to:

  1. Study basic mathematics
  2. Find an area of interest/specialization
  3. Become an expert in that area
  4. Contribute to that area

These things might sound hard but in reality they could be redefined as:

  1. Study mathematics in undergraduate work
  2. Find an area of mathematics that you love
  3. Learn all the different ways of thinking about problems in this area
  4. Publish a new way to think about a problem in this area

None of these steps requires innate genius (though it helps),
they require hard work, a willingness to reason critically, and a little creativity.

If you think you might be interested in being a professional mathematician,
learn all the math you can and search for an area that really interests you.

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    $\begingroup$ Indeed, you shouldn't even use tests as an accurate tool to test your current mathematical ability. $\endgroup$
    – user93957
    Jan 25, 2014 at 17:42
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    $\begingroup$ IMO, this answers the question quite nicely. $\endgroup$
    – Jeel Shah
    Jan 25, 2014 at 18:01
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    $\begingroup$ " You should not use tests like these to measure future potential as a mathematician. You should use them as a tool to gauge your current mathematical ability, your strengths and weaknesses. " Brilliant Line. Never get discouraged. Just keep on going $\endgroup$
    – MathMan
    May 24, 2014 at 20:43

With all the respect, I do not think this is the right question to ask. You can spend your whole life wondering whether or not you are able to do something, but the only way to actually know it for sure is to go and try.

So I did - it turned yes.

Good luck!

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    $\begingroup$ Abir, when I started to study mathematics, I was concerned (and still I am) with this very question, too. The fact is that my reasoning skills have improved over time so dramatically, that from my current point of view it is irrelevant what I was before. Mathematics is probably the best way to find out what you are capable of and as such, trying to do mathematics is answer to the question of being able to. And no, you do not have to be "genius", whatever it means, to be useful - maybe you'll just get a clever idea no one else got before and the whole world will benefit from it. $\endgroup$
    – David
    Jan 25, 2014 at 13:21
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    $\begingroup$ You are welcome. Don't forget to mention me in your thesis :P! $\endgroup$
    – David
    Jan 25, 2014 at 13:27
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    $\begingroup$ @AbirMukherjee. I was just terrible in mathematics (you could not conceive how bad I was). Once I started understanding a little and I followed up (I started as a professional 53 years ago !). If you are a genious, you are lucky. But mathematics wait more from intelligent and hard working people. As David Cepelik wrote, don't forget to mention us in your thesis. I shall always remember this discussion with a big emotion, be sure. Go on, Abir ! Cheers and thanks to you. $\endgroup$ Jan 25, 2014 at 13:31
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    $\begingroup$ @AbirMukherjee. You are really welcome ! $\endgroup$ Jan 25, 2014 at 13:37
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    $\begingroup$ @AbirMukherjee: You may also wish to read Terry Tao's advice here. $\endgroup$
    – J W
    Jan 25, 2014 at 17:52

People are going to tell you different things. I don't know any good universal definition of success. When have you succeeded? Some might not feel like a success before they have received the fields medal, for others success is just getting some random job. For some, being successful in mathematics isn't even about getting the right job or recognition, but about having a personal feeling of accomplished.

That said, it sounds like what you want to do is to pursue a Ph.D in mathematics.

From my experience, the biggest reason people fail in the graduate school is laziness. I have seen plenty of people who seem quite bright, but who are just not willing to invest the amount of work it takes to succeed. I have unfortunately seen plenty of really smart people who have "failed" just because they didn't do the work. For some this is of course not just related to laziness, but also to outside influences. Do you have a family that you are trying to support while in graduate school? Do you have any medical conditions that will prevent you from spending the required time? Granted, each of these things don't mean that you can't succeed. It might just make things harder.

The big question (IMO) then becomes: how do some people managed to work so hard? Where do they find the motivation to keep at it even when it sucks. How do some people get up at 5:30 in the morning so they can get a couple of hours of studying done before they go to class? Being dedicated to something can be hard.

IMO the key things that drives the engine powering your motivation should be a love of math. If you don't have some deeper of appreciation for math, if math is just work for you, if you are just wanted to do math to get girls (?), then I don't think you will succeed. Getting a Ph.D. in anything means hours and hours or hard work that sometimes seem to have been wasted. You might work on a problem for days, just to find out that it can't be solved (maybe there was a type in the problems statement). You have to have the right mindset to power through things despite this. (Not to sound to negative: Yes, there are/ will be a lot of wonderful moments when you have solved a hard problem or when you have finally understood something, and these moments can make it all worth it.)

So who can tell you if you have the right mindset/attitude/motivation? Well, probably not people on MSE. They don't know you. There are of course math tests you can take, but I only think they give you a partial answer as to whether or not you can/will succeed.

So can you do it? It sounds like you are "smart enough", and if you are willing to work hard and prioritize you studies, and if you have a love of the subject, then yes!

  • $\begingroup$ Thank you for your advise. Yes, I indeed want to pursue a PhD in mathematics. After studying things like Calculus,Algebra,Group theory,etc I have developed a strong interest and now I really like studying Mathematics for long hours trying to find solution to problems. I am ready to work hard. And to me success means to get a phd in a topic of my choice and then getting an academic position(I really like teaching). I hope someday I will achieve it. :) $\endgroup$ Jan 25, 2014 at 18:44
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    $\begingroup$ In my answer, I for got to thoroughly stress the hard work involved in becoming an expert in something. Those 10,000 hours do not come cheap! $\endgroup$ Jan 25, 2014 at 18:56
  • $\begingroup$ @awashburn: Thank you for your help. I will keep the 10,000 hour rule in my mind. Well in the last one year I have given appx 4 hours to mathematics eachday, so hopefully I am on the correct path! :) $\endgroup$ Jan 25, 2014 at 19:16

As others have said, the most important thing is that you should like doing mathematics. Secondly, it helps if you're smart, which you seem to be.

The fact that you liked logic and programming is only a good thing, since logic is an essential part of mathematics and programming is closely related to some areas of mathematics.

I would suggest you just start studying mathematics, and later on you could always decide to persue another career after you've studied mathematics. Most math graduates end up having jobs that are not strictly mathematical to not even closely releted to mathematics. If it turns out you really like mathematics and you're really good at it, you can persue a career in mathematics, and maybe specialize in mathematical logic or (a part of) theoretical computer science (which could be seen as a part of mathematics), if you're still interested in that by then.


Maths is not genius nor popularity. Here is a story: Joshua King came to Cambridge from Hawkshead Grammar School. It was soon evident that the school had produced someone of importance. He became Senior Wrangler, and his reputation in Cambridge was immense. It was believed that nothing less than a Second Newton had appeared. They expected his work as a mathematician to make an epoch in the science. At an early age he became President of Queens’; later, he was Lucasian Professor. He published nothing; in fact, he did no mathematical work. But as long as he kept his health, he was an active and prominent figure in Cambridge, and he maintained his enormous reputation. When he died, it was felt that the memory of such an extraordinary man should not be permitted to die out, and that his papers should be published. So his papers were examined, and nothing whatever worth publishing was found.


"Am I suitable to pursue mathematics?"

The answer is a resounding: YES!

If you already know that you enjoy Math, you are in the privileged minority. Appreciation of mathematical inquiry is something you can deeply value.

It's hard to say exactly what the experience might be like for you, but I can share my perspective:

I'm not the world's best mathematician by any means, but I got along, and when it came time to decide on a major, I picked Mathematics (along with Philosophy). It was a challenging curriculum, but I'm very glad I made this decision. It has opened up so many doors for me, because nearly any other quantitative inquiry is founded upon Mathematics.

It strengthens qualitative reasoning as well, with the heavy emphasis on logic and rigorous proofs. Even though I don't often use it in the same manner I was formally taught, the skills and perspectives from my undergraduate math education are relevant nearly everyday, many times over.

So again: Go for it!! If you love it, you don't need permission. :)

If you're looking for further reading on this: a professor once told me about G.H. Hardy's A Mathematician Apology.

I highly recommend it if you want to learn why so many mathematicians love math. It's a short read: here's a PDF.

  • $\begingroup$ Thank you sir for you advise. I would definitely read the PDF! $\endgroup$ Jan 25, 2014 at 20:40

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