Math degree for math non-genius

[Nonlinear]

This is my first post here, so allow me to first say hi and introduce myself a little.

I'm currently a finishing Master's student in computer science with a prospect of PhD, but for certain reasons I am contemplating pursuing an undergraduate degree in applied mathematics.

However, I never was a mathematical prodigy. I only entered the local (city or regional level, can't remember) mathematical olympiad once and the results were dismal, as I didn't know how to approach those problems, and I didn't do particularly well in a local math contest either. I wasn't bad in standard classroom math - I got the equivalent of A's during most of my primary school years as the grade from the subject (except for one or two years I think), even though I did not consistently score A's from tests. I certainly had to work for the results, though. I didn't have problem solving creativity that is required for the contests.

This resulted in me fearing the subject up until high school, where I got interested in it, but still, the success was won with hours and hours of excercises, and even then I was able to occasionally make a numeric mistake or struggle with some more difficult textbook problem (usually in geometry :) ). I enjoyed the subject tremendously, however. I didn't bother with math contests at high school - due to the instilled fear and the fact that I had to put in a lot of effort (i.e., it did not come by itself) I thought the results would be largely the same. I liked the subject so much that I did not want to part with it entirely during my uni studies, though, which is the reason why I went to study computer science instead of psychology.

I did some stupid things during my undergrad - skipping lectures, not preparing regularly, taking more courses than what was manageable - so my math grades reflect this. But even if I didn't, I would still have to put in hours to get very good results; I learn math by solving piles of problems of increasing difficulty. My GPA from undergrad is quite average, even though it puts me among the 1/4 of the best students of the degree. The degree was more theoretically oriented (quite proof-based - computation and complexity, automata and formal languages, algorithm design, and of course math) and as a result more tough, but I don't take that as an excuse for my performance. I improved dramatically during my Master's, though - even though I still rank approximately the same, the GPA is much better.

During my studies, I took a course in statistical methods and fell in love with the field, especially after finding out that machine learning and data mining, fields that are not taught at our uni but fields I find very interesting, are quite related to that. Our uni offers a Statistics degree (under the applied math umbrella), which is essentially the standard math degree minus some standard math courses + loads of statistics and probability related stuff. Given some of the bad memories, however, I am afraid of pursuing the degree. One thing is getting the degree, and a completely different thing becoming an (applied) mathematician.

I am no math olympiad stuff. There are people around me that are. Plenty of them. They just look at the theory, or sit in the class, and understand it straight away; they can solve difficult problems quick and with little exposure to the material. They get top marks with little effort.

I have to sit down with the textbook and conquer the theory by re-reading it again and solving problems, plenty of them, and even then absolute success is not guaranteed. I just like the subject and its applications, and would like to be able to become good enough to apply math to solve problems and create new applications in computer science. Or get a creative enough job that actually utilizes the math and the theory to solve interesting problems.

Is natural aptitude to solve math contest problems required to study mathematics as a degree, and become reasonably good in the field? Do I have to be "mathematically gifted" to do well?

 

[MathematicalPhysicist]

I don't know if you will succeed in becoming a professional mathematician, but at least you should try if that's what you desire.

I know I at least going to try and do it, even though I haven't participated in any math contests (I am starting Msc in pure maths).

 

[Nonlinear]

I don't know if you will succeed in becoming a professional mathematician, but at least you should try if that's what you desire.

I don't want to become a uni professor in mathematics. Mathematics to me has always been a tool - to solve a particular problem or to describe occurrence of an event. In the context of computer science, it is a tool yet again.

There are plenty of interesting applications of mathematics in the industry, but the difference between these and theoretical research in math at a uni (from what I've seen) is that in the real world, math becomes a tool to solve a problem, whereas in the uni world, math is a problem in itself.

I applaud your determination to go forward with pure mathematics, however - this is a field which requires an enormous amount of focus.

 

[MathematicalPhysicist]

My assertion as being a mathematician isn't restricted to pure math, there are professional mathematicians outsied academia as well, who exploit there knoweldge for the industry problems.

 

[Nonlinear]

Yet there is very likely a difference between the problem sets of the two. It will surely depend on the position within industry itself, but I would assume, by nature, for the problems in industry to be applied. Whereas the problems in the academia mathematics are pure, i.e. one builds new theory, as opposed to applying existing theory to model or obtain a solution of a problem.

 

[Nonlinear]

Ok, I just read a piece of similar concern over at a blog of someone from MIT here - http://www.mitadmissions.org/topics/pulse/the_match_between_you_and_mit/am_i_smart_enough_for_mit_1.shtml (Mind you, I'm not thinking about doing the math degree there, if they even offer one. :) )

I like the term she used to describe herself in terms of mathematics - peasant. Lots of repetitive, hard work, and no grand things. The following reply kind of gives me hope that I'm panicking prematurely.

(There's also the last post in this thread - https://www.physicsforums.com/showthread.php?t=272101 . Ok, panic levels dropping, there are apparently normal people doing maths and physics as well, not just super-intelligent, god-like math olympiadians. Even though they're doing it as well.)

 

[kramer733]

You know not many people in this world have the "intellect" of euler or galois or einstein.. or etc. Yet most people still pursue what they like to do because they like what they do. Perhaps it interests them or it's a pre requesite for something bigger, but in the end we do it because it's fun. If you like it, the degree will be a fun journey. Best of luck.

 

[sEsposito]

I see an awful lot of these types of post lately. It's a bit disturbing to me, honestly.

Firstly, whoever said being a mathematical genius was a requirement to get a degree in mathematics -- or even to become a working mathematician for all that matter. There's way too much emphasis placed on "genius" and "intellect".

It'd be ignorant of me to say that natural ability plays no role in studying and doing mathematics, but it certainly is not everything. Also, without being... Pretentious... In my opinion, those who are so concerned with "genius" are probably not studying mathematics for the right reasons. You think Euler shoved his genius in everyone's face? Newton? Gauss?doubtful.

Bottom line: if you love mathematics, pursue it. Forget about all this genius stuff. It adds undo pressure and clouds the mind. There's a Feynman documentary somewhere on the internet about this topic, if you can find it (I cannot currently) it's a real treasure.

 

[lisab]

I see an awful lot of these types of post lately. It's a bit disturbing to me, honestly.

Firstly, whoever said being a mathematical genius was a requirement to get a degree in mathematics -- or even to become a working mathematician for all that matter. There's way too much emphasis placed on "genius" and "intellect".

It'd be ignorant of me to say that natural ability plays no role in studying and doing mathematics, but it certainly is not everything. Also, without being... Pretentious... In my opinion, those who are so concerned with "genius" are probably not studying mathematics for the right reasons. You think Euler shoved his genius in everyone's face? Newton? Gauss?doubtful.

Bottom line: if you love mathematics, pursue it. Forget about all this genius stuff. It adds undo pressure and clouds the mind. There's a Feynman documentary somewhere on the internet about this topic, if you can find it (I cannot currently) it's a real treasure.

You're right, there has been several similar threads lately. Wonder what that's all about.

You give good advice, btw, I second it. If a student finds himself/herself wondering if they're 'good enough' to go into a particular field, they should remember this, from Desiderata (if you don't know what that is, ask an old hippy ):

If you compare yourself with others,
you may become vain or bitter,
for always there will be greater and lesser persons than yourself.
Enjoy your achievements as well as your plans.
Keep interested in your own career, however humble;
it is a real possession in the changing fortunes of time.

 

[Nonlinear]

Thanks a lot, everyone who contributed - this really did help.

 

[l'Hôpital]

From my understanding, being a genius can sometimes even harm you!

Allow me to quote a great paragraph from a great book A Mathematician's Survival Guide by Krantz:

In my own mathematics department we had recently a very gifted student who went off to one of the best graduate programs in the country. He had written two terrific papers with one of the best and most famous faculty in the department. He won a major national prize for his undergraduate research. But his graduate career was dreadful-a failure by any measure. And let me assure you that this individual was plenty smart and plenty able. The fault for his travails was in another part of his head. He finally squeaked through graduate school, received his Ph.D., and was by then so disgusted with mathematics that he quit and went to work in a genomics laboratory. Of course this is fine-he now has a promising and productive career-but what happened to his mathematics? I asked his thesis advisor (who in fact was his fourth thesis advisor-he had been fired by the first three ) , and the answer was as follows: this young fellow had the "Putnam Exam mentality". He was accustomed to getting quick results without a lot of hard work. He did not have the discipline and tenacity that is necessary for the long and protracted study that is advanced mathematics. As a result, he found himself (in graduate school) in a hostile environment. And he failed.

Sometimes being not-so-smart forces you to build up patience and endurance, which you'll need for grad school.

 

[Klockan3]

From my understanding, being a genius can sometimes even harm you!

Not really, but people who aren't smart won't go into maths unless they have a good reason to since they have to work so much for it, while people who don't need to work as much can get quite far by just going with the flow and then one day realize that she actually don't enjoy the maths that much.