How to test whether I am suitable to pursue mathematics?

Question

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.

Answer 1

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!

Answer 2

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 !

Answer 3

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.

Answer 4

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!

Answer 5

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.

Answer 6

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.

Answer 7

"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.