Is mathematics a young man's game?

Functor97

Recently I have been feeling fairly depressed about my future in the mathematical sciences. I am a second year undergraduate studying mathematics and physics (double major), what is more, I am almost 21. In hindsight I wasted a year travelling with friends after high school, and whilst I enjoyed myself I think I should have gone straight to college. I am still stuck taking undergraduate courses, whilst many people my age are working exclusively on graduate courses. My grades are good, but none of my professors praise me, as other future mathematicians seem to be praised. Nor can I create ingenious new insights or re discover whole areas of mathematics. I often forget steps in proofs I have read, and am forced to go back to the books to read them again. I envy my engineering friends who can go out and relax, while I worry about my decaying grey matter, but I cannot give up on mathematics and physics which I see as humanities greatest intellectual mechanism for understanding.

I used to think myself quite intelligent, but now I see that I was fooling myself. I was never a prodigy like Terry Tao, Noam Elkies or Charles Fefferman, nor did I succeed at mathematical Olympiads before the age of 18 like most talented mathematicians seem to.

Many great mathematicians finished their PhDs by my current age, and I have read quite often that if you have not made a great idea by 30, you never will. I have heard countless amazing tales of the exploits of mathematicians my age such as John Nash, working in areas I do not even fully understand yet.

I love mathematics, but I am beginning to doubt this is enough. I can't think of being anything else, but I am feeling quite low about any semblance of mathematical talent I have. I doubt I can even make it into a decent graduate school, or if I do, that I will be laughed out of the faculty by teenagers half my age who can master my area in half the time.
I am aware that I sound like I am feeling sorry for myself, but I really am at a loss at what to do with myself.

mathwonk

see a psychiatrist. Any intelligent young person of age 21, with good success in school who is depressed because he feels he may not be a fields medalist latter on, needs to get a grip. We are not professional psychiatrists here, we are math advisors.

J-ho

You're 21 bro..lol

Chunkysalsa

Seriously? 21 makes you too old?

For the record, I'm 21 (literally just turned that today) and am a junior in college. I'm also one of the younger members of my class since I'm a straight from high school student. Many people are much older (some quite gray). Though I experience the older population more in my engineering courses, but my math courses average around 20-24 probably (I'm a dual EE/math).

Not everyone can be a prodigy. You listed a handful of extremely talented people but neglected all the many successful mathematicians that are not super geniuses.

So you are perfectly fine, infact I'd say you are moreso. Add ten years to your age and I still wouldnt think anything of it.

Functor97

Mathwonk it is not so much a fields medal I want, I simply want to contribute at an international level. It is the fact that no matter how much I try, I will probably never access the higher levels of mathematics which these professionals are capable of. It is not some damn bit of metal alloy I want, its knowledge and it seems that my mind has only a very limited time frame to attain said knowledge. Almost all mathematicians (field medalists or not) seem to make their major contributions before 40, and I fear I won't even begin to understand the fields that interest me before that age.

Chunkysalsa

40 is almost twice your age. Theres plenty that could happen between now and then, don't worry too much about it or you definitely won't accomplish anything

Functor97

Yes, I realize that. I try and put it out of my mind, and it works, but then when i start reading the background and lives of the mathematicians whose work I am reading i get confronted with the same ideal story: Prodigy or early promise, PhD (or equivalent) by 22, world renown by 30.

Mmm_Pasta

You're only a second-year undergraduate. There is still *A LOT* to learn about math and/or physics. You don't need to be famous or well known to contribute. Knowledge is cumulative from many years of work. Your ideas can be failures and sometimes they work. Both can help others come up with other insights as well. To me it sounds like you are afraid of failure and just want success to come at you right away.

Vanadium 50

Again, I think mathwonk's advice is right. If you're 21, successful in school, and depressed that you won't be able to "contribute at an international level", you should be discussing this with a psychiatrist, not us.

Functor97

Its the fact that i have so much to learn which troubles me.

Dembadon

Actually, it sounds to me like you don't like mathematics as much as you say you do. It seems like you desire recognition more than learning mathematics. As others have mentioned, this is a psychological issue. If you really love mathematics, you'll study it for the rest of your life without worrying about whether you are internationally recognized.

nickadams

What scares me about pursuing a career in high level math is that it can take 10+ years before one finds out that they are not smart enough for that path. So I work for 4 years of undergrad and if (big if) I'm fortunate enough to get into grad school I will work for 5-8 more years and if (massive if) I pass my quals, classes, dissertation etc. then I could come out with a PhD. And then at that point there is a good chance I will not make the next cut of getting a postdoc position.

If I find out I am not smart enough to get into grad school, where do I go from there? It will mean I have a low GPA and a pure math degree (or worse: no degree)...

If I find out I am not smart enough to pass the qual exams or grad classes, where do I go from there? PhD dropout with a not very marketable degree...

If I find out I am not smart or devoted enough to finish a dissertation, where do I go from there? ABD....

If I find out I am not smart enough to get a postdoc, what then?



I am currently doing engineering and certainly doing well enough to get a job in this field, but the odds of succeeding in the field of pure math are far lower and trying to find out if I have what it takes has a very high chance of leading to a low GPA, poor job prospects, and debt.

Functor97

I can assure you i do love mathematics. Doesn't everyone want recognition for doing what they love?

Dembadon

I'm not following your reasoning. If lack of recognition is making you question your decision to pursue mathematics, which can you say you love more?

Nano-Passion

Mathwonk, a psychiatrist is someone who has legal rights to hand out pills and medicine to the mentally ill <-- Pretty awkward definition but it will do. That is probably a mistake, I wouldn't want Functor to think you are calling him mentally insane ahah. Psychologist is the proper word.

Functor, you associate your self worth with success at mathematics.. this is very unfortunate. There is so much more beauty to the world. You have a mentality of all or nothing. This is a very destructive train of thought.

I second this.

Deveno

i think there are two related issues, here:

a) a desire for recognition. i think you need to realize that this is intimately bound up with your self-image. while it is somewhat humbling to realize that you may not be destined to be a leader in your chosen field, it is something that most people have to deal with, at some point in their lives. i know of perhaps less than 50 living mathematicians whose names i would recognize. certainly there are many, many more competent (perhaps even brilliant) mathematicians i will never know anything about. most of your instructors probably fall into that category, and yet...they persist in imparting the knowledge of their life's study to you. get a grip, you will never live anyone else's life, enjoy your own.

b) a desire to contribute. this is by far the easier issue to address. research topics off the beaten path. mathematics is a BIG world, and we haven't had the time to explore it all. you won't have time, either. but by the time you are in graduate school, you'll certainly have a big enough tool-kit to start exploring on your own. find something that interests you, spend some time getting to know unfamiliar territory. trust me when i say that fame and glory are nothing compared to the simple joy of discovery. and you can have that, no problem.

Functor97

I would still persue my dreams and study mathematics, i would simply feel like i was missing out on something more. Like i said, it is not so much recognition as the ability to understand at the highest levels which i desire.