Depression, doubt in my mathematical abilities

[hello95]

Hello all,

I am currently an undergraduate student (just finished my first semester) at Stony Brook University. Basically, I'm fairly certain that I want to go into pure math or theoretical physics, it's just that I feel like I may not be up to par with everyone else who will be competing with me for jobs in those fields. Last semester I took multivariable calculus and got an A (perfect scores on the first two midterms and 97 on the final), and also passed out of the school's introduction to proofs course. I don't say this to brag, as my grades in calculus and the rest of my courses were more due to my study habits than any sort of innate intelligence (for example, I spent approximately 100-120 hours preparing for the introduction to proofs course). This coming semester I'll be taking differential equations and a second-year proof-based linear algebra course. Over break I'm running over my proof skills and going through an intro abstract algebra book (to help with my proof writing and intuition of isomorphisms and groups, which I expect will be important in the the linear algebra course).

Basically, my problem is that I have no way to gauge myself relative to other undergraduates who have the same goals as me, and even if I did, I don't know how to set standards for myself. Even in the honors college at stony brook (basically the top undergraduates) I don't feel like any are nearly as dedicated or intelligent as, say, your typical math student at Harvard, so I don't measure myself against them in fear of becoming complacent. This confusion as to my abilities has led me into a lot of depression this semester, and I've started to become really scared that my life will amount to nothing, since in my opinion academic success is the ultimate measure of my life's value. I feel like I am sub-par since I am not going to Harvard or MIT. I graduated a year early from high school, and due to my laziness during freshman and sophomore years, I didn't have stats similar to other students applying to ivy leagues. As a result, I am attending Stony Brook, and I'm afraid that this will affect me later in my career.

Am I up to par for a career in pure math? How do know if my standards for myself are too low or high? And finally, will the most intelligent mathematicians from better universities ultimately be better than me, no matter how hard I work?

 

[FalconOne]

Am I up to par for a career in pure math?

For a freshman, you sound just fine. I don't know how strong the math department is at Stony Brook, but I mean it when I say that it's your department that matters, not so much the name. I left an "elite" private school for a no-name state school because their physics program blew.

How do know if my standards for myself are too low or high?

I struggle with this myself. But I basically came to the decision that there is no standard too high when it comes to work.

And finally, will the most intelligent mathematicians from better universities ultimately be better than me, no matter how hard I work?

Not necessarily. These intelligent Ivy Leaguers may not have a good work ethic. I met a man who hires for TI. He said he would rather take a state school applicant than an Ivy Leaguer.

Also, I did research along with a person from an Ivy League school this summer. I did just as well, if not better, than that student in research technique, data analysis, presentation, etc. and I went to a no-name state school.

 

[Sankaku]

...as my grades in calculus and the rest of my courses were more due to my study habits than any sort of innate intelligence...

You are doing fine. If you keep this kind of work ethic, you can learn anything you want. Just make sure you continue to enjoy yourself, or you will burn out. Don't worry about comparing youself to others. Do it because it is interesting and fun.

 

[FalconOne]

Don't worry about comparing youself to others. Do it because it is interesting and fun.

Don't compare yourself to others at all. You can't control them, but you can control what you learn. Make sure you exceed the standards of what jobs (or whatever) would require, and if someone "better" gets the job, well that means that there'll be space for you someplace else. Keep truckin'.

 

[hello95]

Thanks for the replies everyone! very encouraging.

 

[nlsherrill]

Hello all,

I am currently an undergraduate student (just finished my first semester) at Stony Brook University. Basically, I'm fairly certain that I want to go into pure math or theoretical physics, it's just that I feel like I may not be up to par with everyone else who will be competing with me for jobs in those fields. Last semester I took multivariable calculus and got an A (perfect scores on the first two midterms and 97 on the final), and also passed out of the school's introduction to proofs course. I don't say this to brag, as my grades in calculus and the rest of my courses were more due to my study habits than any sort of innate intelligence (for example, I spent approximately 100-120 hours preparing for the introduction to proofs course). This coming semester I'll be taking differential equations and a second-year proof-based linear algebra course. Over break I'm running over my proof skills and going through an intro abstract algebra book (to help with my proof writing and intuition of isomorphisms and groups, which I expect will be important in the the linear algebra course).

Basically, my problem is that I have no way to gauge myself relative to other undergraduates who have the same goals as me, and even if I did, I don't know how to set standards for myself. Even in the honors college at stony brook (basically the top undergraduates) I don't feel like any are nearly as dedicated or intelligent as, say, your typical math student at Harvard, so I don't measure myself against them in fear of becoming complacent. This confusion as to my abilities has led me into a lot of depression this semester, and I've started to become really scared that my life will amount to nothing, since in my opinion academic success is the ultimate measure of my life's value. I feel like I am sub-par since I am not going to Harvard or MIT. I graduated a year early from high school, and due to my laziness during freshman and sophomore years, I didn't have stats similar to other students applying to ivy leagues. As a result, I am attending Stony Brook, and I'm afraid that this will affect me later in my career.

Am I up to par for a career in pure math? How do know if my standards for myself are too low or high? And finally, will the most intelligent mathematicians from better universities ultimately be better than me, no matter how hard I work?

It's hard for me to imagine that someone who seems reasonably intelligent just by their writing, and someone who aced a calculus 3 course would be asking some of the questions you are. I think you are too wrapped up in societies impression of you compared to other students. It sounds like you are doing great. Not everyone goes to Harvard, obviously. Just keep working hard and stop doubting yourself. Some people have certain skills gifted to them by genetics, but hard work and determination is more important in terms of one's success in life.

 

[MarneMath]

You're worrying too much right now. Your undergradaute matters less than where you do your graduate school. My good friend and I both attended no rank bottom of the barrel schools. We both got our masters at a pretty decent state school. We both got accepted into top 20 (him 10) PhD programs. If you take the time to do research, work with professors and build a good relation with them, then you'll make yourself a good candidate.

I've always felt that people that go to "Ivy League" schools found a level of focus sooner than most people do. It doesn't mean they are just so much smarter than you, but a person interested in math science they were 10 is obviously just going to know more. However, this gap closes fairly quickly as focus within a field becomes more narrow. So anyway, you'll be fine. If I ended up ok (and I got kicked out of college), you'll end up ok!

 

[homeomorphic]

This confusion as to my abilities has led me into a lot of depression this semester, and I've started to become really scared that my life will amount to nothing, since in my opinion academic success is the ultimate measure of my life's value.

It's a very bad idea to measure your life's value by your academic success. Ability to handle failure is crucial. Thus, people who only measure their life's value in terms of academic success are probably dooming themselves to failure because eventually, it gets so hard that anyone who spends their time doing research is probably failing most of the time at what they do. The people are the top are just the ones who either have the least failures or their number of attempts is so large that it overwhelms the failures. Research isn't like some homework assignment where you get 99% of it right when you do all the work and double-check everything. Most of what you do in research is just failing all the time at everything, and through persistence, occasionally something that you try works or it doesn't even work, but you manage to salvage something publishable out of the burning wreckage of your miserable failures and blunders (I suppose some of this happens doing homework, too, if it is sufficiently difficult, but not on the same scale).

Not to mention there is more to life than academics. After years of working like a slave and time flying by at breakneck speed because you never have even one hundredth of the time you would like to have to do the work that you are given and keep up with your field, you may realize you haven't gotten married, you haven't seen the world, you haven't enjoyed yourself, and, indeed, perhaps, you have become a mindless mathematical automaton. And it may be too late to save yourself. I am 31 years old. I am not old yet, but graduate school pretty much robbed me of 7 prime years of my life and turned them into darkness and despair--all for nothing, in the end. I'm quitting this nonsense as soon as I have the PhD, and I am going to have my life back.

I feel like I am sub-par since I am not going to Harvard or MIT. I graduated a year early from high school, and due to my laziness during freshman and sophomore years, I didn't have stats similar to other students applying to ivy leagues. As a result, I am attending Stony Brook, and I'm afraid that this will affect me later in my career.

Plenty of the best people don't go to the top schools for all sorts of reasons--financial, temporary laziness, etc. A big name helps impress people but is by no means essential.

Am I up to par for a career in pure math? How do know if my standards for myself are too low or high?

I would worry more about your confidence than your ability. That could be a real problem later on. I came out of my undergraduate program, feeling like I was one of the smartest guys around, but now, as I am nearing completion of my PhD, I seem to have developed an overwhelming inferiority complex.

And finally, will the most intelligent mathematicians from better universities ultimately be better than me, no matter how hard I work?

Well, if you want to be the very best at something, often, since there are so many billion people on the planet, SOMEBODY out there has tried every possible combination of genetics, learning philosophies, and so on, and so, if you want to be the absolute best, you have to get dealt the best hand in every way possible. But, I think it might not always be that way. Math is a much more diverse subject than, say, running 400 meters. So, the little mathematicians know about all kinds of things that some hot-shot mathematician might have no idea about because it's not his area. So, in some small way, you'll probably be better than everyone else. In your own way.

 

[Alienjoey]

Stony Brook has a great physics department, especially with the C. N. Yang Institute for Theoretical Physics and Brookhaven National Lab nearby. The most important thing is getting experience with research, which you should have plenty of opportunities for at Stony Brook.