Is mathematics a young man's game?

[Sankaku]

Well i am usually considered a failure at most things outside academia...

You will have to find self-worth outside of mathematics, otherwise you will never enjoy it. The same can be said of any field. We are all human, recognition is ok. However, if it is your only sense of value, any road-block will send you into depression.

 

[Neil.yc]

There are many things in which one can gain recognition; if not having ones work recognised makes one suffers, one must do something else. After all, despite we're all humans, we have all but a limited amount of time to enjoy our lives, to appreciate things around us.

While I am not one of those having six packs, I know physical strength can be gained over time.

 

[Dembadon]

...

I don't think he was clearly ready to give it up. I'm pretty confident he doesn't lack the love of mathematics or physics. Wanting to contribute at an international level can mean wanting to be in dialogue with the most exciting stuff happening, and not working on something trivial that misses the point. This isn't an entirely unfounded worry.

...

Here's what he said in his first post:

... I can't think of being anything else, but I am feeling quite low about any semblance of mathematical talent I have. ...

my emphasis

The conjunction "but" is used to introduce something contrasting, so my inference was valid. Perhaps he didn't mean to imply that he was considering alternatives. However, that is what the logical structure of the sentence implies, even if it wasn't explicitly stated.

 

[Functor97]

Here's what he said in his first post:



my emphasis

The conjunction "but" is used to introduce something contrasting, so my inference was valid. Perhaps he didn't mean to imply that he was considering alternatives. However, that is what the logical structure of the sentence implies, even if it wasn't explicitly stated.

Well Dembadon, i am not going to give up on mathematics, no matter how badly i feel about myself. I think there is a culture within the mathematics community which upholds these notions of preciocity, by handing out numerous awards, such as the fields medal which have age restrictions. I have found that the only community which seems more caught up in the notions of the cult of genius is that of the theoretical physics community, which seems to admonish those who dare to question the status norm. I am not sure either of these effects are conscious decisions on behalf of the "perpetrators", more an emergent effect of working within a community which values rigor and absolute truth.

 

[Dembadon]

Well Dembadon, i am not going to give up on mathematics, no matter how badly i feel about myself. ...

Good to hear.

 

[intwo]

I don't think that age should be a deterrent.

Recognition generally follows determination and effort. Sure, you may never win a Nobel Prize or solve a Millennium Prize Problem, but those around you will certainly recognize and appreciate your hard work.

Think of every class as another step in a never-ending staircase. Think of all the people who stopped at the stairs below you. Think of what you can teach them. Think of the step you were on a year ago. Now think about two years ago. I am sure you'll be surprised with how much you have learned. The best part is that you still have a lot more to learn!

 

[Flaneuse]

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 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.

Functor97,
I don't have much useful advice, but if it is any condolence, this is exactly the way I have been feeling for the past year or so (if you replace "mathematics" in your case with "physics" in my case). Strangely though, I am a few years younger than you, so I would certainly not say that your problem necessarily has to do with your passion being a "young man's game;" if physics were a young man's game, I would have fairly little to worry about right now, yet I feel as if I've already burned out and any potential I may have once had is absolutely in a state of decay. Yet I don't ever, ever want to give up on physics, because I don't love anything else.

I will give you the advice that I have been give though (though it may not be useful, as it has not helped me much): perhaps you should have some hope yet, or, if nothing else, at least know that you still have time, and the fact that you are 21 does not have to mean that you have passed up anything for good. If there is something that you really want to do, or if you really want to seek a certain fulfillment, there is time yet to do so.

 

[deRham]

The conjunction "but" is used to introduce something contrasting, so my inference was valid. Perhaps he didn't mean to imply that he was considering alternatives. However, that is what the logical structure of the sentence implies, even if it wasn't explicitly stated.

Well, I don't think I was trying to question your reading of the logic, so much as state what I'm nearly certain is the case, based on my reading of what's going on and perhaps even other things the same individual has posted. To me, when someone is depressed about career, the real question is to figure out what the question is.

Also, it is possible that the but was to have been followed not by an alternative he would think to pursue himself, but rather the possibility that his career would end independent of his desiring it. Or for his career to take a turn whereby he is never able to have that love "reciprocated", for instance if he is unable to reach a point of being in dialogue with all the great stuff happening. That is, of the structure "I can't think of being anything else, but perhaps what I think of isn't meant to be."

 

[Dembadon]

Well, I don't think I was trying to question your reading of the logic, so much as state what I'm nearly certain is the case, based on my reading of what's going on and perhaps even other things the same individual has posted. To me, when someone is depressed about career, the real question is to figure out what the question is.

Ahh. I understand where you were coming from now.

Also, it is possible that the but was to have been followed not by an alternative he would think to pursue himself, but rather the possibility that his career would end independent of his desiring it. Or for his career to take a turn whereby he is never able to have that love "reciprocated", for instance if he is unable to reach a point of being in dialogue with all the great stuff happening. That is, of the structure "I can't think of being anything else, but perhaps what I think of isn't meant to be."

Good point.

 

[deRham]

Glad I could clarify : )As general advice for the main topic, I would say you should really try to enjoy how interesting what you are learning is. We've established you won't quit the subject even if you're not as good at it as you wish. Get busy enjoying it, because it will be years and years before the best of you in the field comes out, and you have to keep enjoying it to even get there. It will be worth it, I think, regardless of how much of a star you become.

There will be enough pressures on you without your adding a toxic one (regarding beating yourself up).

 

[Functor97]

Glad I could clarify : )


As general advice for the main topic, I would say you should really try to enjoy how interesting what you are learning is. We've established you won't quit the subject even if you're not as good at it as you wish. Get busy enjoying it, because it will be years and years before the best of you in the field comes out, and you have to keep enjoying it to even get there. It will be worth it, I think, regardless of how much of a star you become.

There will be enough pressures on you without your adding a toxic one (regarding beating yourself up).

Thanks deRham, very good advice.
Out of curiosity, do other math majors here attempt to prove various theorems as they come to them independently of, say the textbook, before looking at the presented proof?

I do this myself, but find it quite frustrating when i fail to do it myself. The result is me looking at the proof and having to memorize the "crucial step" that i had been unable to reach myself. The problem is that when i try and generalize this principle of proof to a similar problem, it turns out useless, and in the end i feel that i am simply memorizing tricks, not understanding the mathematics. I mean i understand where i go wrong, but i "feel" that because i have relied upon the proofs of others, that i am somehow taking their credit, taking the easiest road.

I know how to construct proofs, but the problem seems to be that one step i do not take.

That being said i don't feel i spend as much time doing mathematics as i should. I often procrastinate, out of fear of failure i guess. I mean i do all my problem sets and do well on my exams, but i do not feel like i am achieving all i could. Sometimes i get in a zone, and work for several hours straight, sometimes on things that are beyond the scope of my current courses, but other times i put it off to watch a movie or play a video game, despite knowing full well that i should be doing mathematics. I find these activities relieve my stress when i have a less successful session of attempting to make my own independent proofs, but they seem to delay my return to the subject matter. To be honest, i feel like i am procrastinating as i write this

 

[deRham]

do other math majors here attempt to prove various theorems as they come to them independently of, say the textbook, before looking at the presented proof?

It's usually a good idea to try this. However, the real question is if the theorem is hard or easy. Some theorems are the result not just of the work in the proof written below, but of LOTS of additional thought that had inspiration from various settings, but which fits in around one page. So attempting to prove these naively from scratch is a bad idea.

I think one good way to keep yourself honest is to occasionally try a really really difficult exercise, which really makes you generate quite a lot on your own. Sometimes you can try a theorem the way you say. But you should expect to devote tons of time and be unsuccessful for a long time.

Different people need different kinds of relaxation to get back on track, and you aren't to be faulted. It's not a bad model to work by bursts of inspiration, as long as you do eventually return during the day (even if it's not for as long as you wanted).

 

[deckoff9]

Out of curiosity, do other math majors here attempt to prove various theorems as they come to them independently of, say the textbook, before looking at the presented proof?

I used to do this a lot more, but now the courses I take moves so fast I find I don't have time to do stuff like this.

 

[jedishrfu]

From one who has gone thru these trials many years ago, you should be aware that each year of college is like 3 years of high school. When you start college, your high school training can propel you along without a lot of study, but then you become a sophomore learning stuff you hadn't seen before and things get tougher, next you become a junior and might seem like you've hit a wall you just can learn things fast enough and you hit the wall. Keep going, keep your eye on your goal and you will make it through. Remember there will always be someone that's smarter and/or faster than you but college is not that kind of race. Its a race to open your mind to new ideas and absorb as much as you can. Once you begin working in the field things get easier and easier until one day you look back and say college was child's play just like you do now with elementary school math.

I was attracted to this thread because of the young mans game in the title and that may be true but only if you're over 40 or in my case nearly 60. I may want to take graduate level math courses but the graduate school always favors recent undergrads and not professionals who work with math, physics and computer science on a daily basis since we're considered too old to teach abstract concepts. They won't say we're too old only that we can't be a full-time student and continue to work for a living. There is no in-between at the elite schools unless I solve a millenium problem and then maybe. One can always hope. :-)

Wrt to doing proofs before you look at the elegant solutions you should try your hand at solving them for a short time to develop a sense of how to do it. Professor of Physics, John Wheeler always said you should know the answer to the problem before you begin to solve it. See if you come with an effective proof strategy and then check The Book to see how its most elegantly done.

I am not a number, I am a quantum entangled leaf on the wind.

 

[Deveno]

i'd like to add something, here.

i turned 50 this year.

i am well aware that my mind is not as keen and limber as it was when i was 20. i agonize over sub- and super-scripts, and (ohmigawd) parentheses in a way that is like trying to wake up when you were out late partying all night.

but...

some things i understand more deeply than i did before. linear algebra, for example, is almost crystalline in its clarity to me, whether I'm dealing with a 5x5 determinant, or an annihilator subspace. i am more consciously aware of how deep the roots of the different areas of math interpenetrate each other. i wish i could give you a really good example of this, but i can't without maybe scaring you away with tech-babble.

Spoiler

(if you must know: i came across a question on another forum, about proving the normality of the subgroup of matrices in the general linear group of degree n over the reals, homotopic to the identity. i'd never seen this question before, and it was more about continuity, than a question in group theory. i came up with on my own a slightly messy "epsilon-delta" proof, and then two people i know said the following:

person A said, well, conjugation is clearly continuous.

person B said, well there's just two connected components of GL(n,R), so the one containing the identity is normal.

can you guess which one is the algebraist?)

life is not a race, nor a competition. it is, at its finest, a gift which we should treasure for everything its worth, while we have it.

 

[chronon]

I think there is a culture within the mathematics community which upholds these notions of preciocity, by handing out numerous awards, such as the fields medal which have age restrictions.

I'm sorry, this just isn't logical. If a prize has an age restriction, the implication is generally that those below that age aren't good enough to compete with older people. Now it might be different for the Fields medal, but it seems that, rather that being some sort of 'lifetime achievement' it is given to younger mathematicians to stimulate them to go on to even greater things. Certainly there's no implication that they're done for after the age of 40.

Also, can you actually name any other mathematics awards with an age restriction.

 

[sweetpotato]

OP, when I was a teenager I felt similar to the way you say you feel now.

I want to share some of my personal experience.

-my doubts about my mathematical ability led me to avoid studying technical subjects for fear I would not be able to be the best at them. Finally I got over this my sophomore year in college and majored in electrical engineering.

- I found out I had depression, which was probably a big part of why I felt the way I did. So, I do suggest, like others have, that you talk to a counselor or psychiatrist if you continue to feel this way about yourself.

-as others have said in this thread, out of all the talented or even brilliant mathematicians in the world, maybe only a handful are well-known or get the recognition they deserve, yet all make meaningful contributions to the field of mathematics. I like to think about this as analogous to musicians. There are many extremely gifted cellists that I would be happy to listen to at a concert, but perhaps only Yo Yo Ma comes close to being a "household name". So, does that mean that only Yo Yo Ma is worth listening to, and only his performances bring enjoyment to people? No, of course not!

-my advice to you is to work your hardest at learning all there is to learn about mathematics, and not to lose your love and enjoyment of the subject. If you do what you love and love what you do, that is worth more than any Fields medal. And, you are far more likely to contribute something important to the field of mathematics if you spend your time thinking about how to increase your knowledge/ability rather than worry about about how talented you are.

 

[deRham]

Certainly there's no implication that they're done for after the age of 40.

This is very true. I do think by age 40, a vast majority of successful mathematicians will have shown significant signs of being productive researchers, but I don't think their activity really dies down beyond then - maybe after age 70, or mid 60s, they might consider writing some books which carefully lay out the foundations of subjects they're experts at for the benefit of other generations, but I do think mathematicians are quite active for a while. They simply wouldn't have it any other way.That said, whether or not the Fields Medal being awarded to younger mathematicians proves anything, I do think a lot of the super-successful mathematicians out there showed signs of genius at a young age. However, there are tons of research mathematicians in between, who do very difficult and interesting work.

 

[neyzenyelda]

I think you need an antidepressant prescription.
when I was an undergraduate student of physics in the most prestigeous university of Turkey, I felt I was a teribble physicist because of chronic depression I had.
I graduated and became a graduate student of physics but my depression continued and I gave up graduate study.
years later, after having an antidepressant prescription from a psychiatrist, my feelings had changed. however I waited 18 years more to go back to the university.
now I am 48 years old and a graduate student of physics . I don't feel old. I am sure I will make outstanding contributions to physics and become a famous physicist!
the last sentence is full of manic feelings. antidepressants make you manic and when you are manic you will feel perfect self confidance and grandiosity.
you have depression. depression is an organic brain disorder easily treatable with untidepressants.

 

[Functor97]

I'm sorry, this just isn't logical. If a prize has an age restriction, the implication is generally that those below that age aren't good enough to compete with older people. Now it might be different for the Fields medal, but it seems that, rather that being some sort of 'lifetime achievement' it is given to younger mathematicians to stimulate them to go on to even greater things. Certainly there's no implication that they're done for after the age of 40.

Also, can you actually name any other mathematics awards with an age restriction.

I do not quite follow your reasoning. The age limit is 40 years, which combined with the fact that the Fields is usually considered the "nobel prize of mathematics" would seem to imply that mathematics is a young man's game. I understand that the prize was created to stimulate more research, but this is not what many perceive the prize to be. Maybe the creation of the Abel prize will change this, but i still think that my original point stands.

 

[Mathguy15]

http://www.ams.org/notices/201103/rtx110300444p.pdf

I'm only fifteen, so don't take what I have to say too seriously! I have no experience! Anywho, in the interview above, John Tate, a master of number theory, apparently didn't know he was going to be a mathematician until he was a graduate student. He had similar doubts about his intelligence, yet he became a giant in the world of mathematics. I don't know you and I'm only fifteen, but don't fret! You may be smarter than you think.

God bless
Mathguy

 

[Tosh5457]

I'm an undergraduate in 2nd year of physics and also a good student. I've been in a similar situation as you, but fortunately I've been getting better.

Why are you so worried that you may not be internationally recognized? Wanting to be recognized is normal, I think it's fair to say everyone likes being recognized. But in my opinion you're obsessed with it, which isn't normal at all. Why do you have that necessity to be internationally recognized? Please try to answer to this, because it's the root of all your problems in my opinion. That exaggerated necessity of getting recognized makes you have very high (and unrealistic) expectations of yourself, and that makes you have a fear of failing.

The reason why I say your expectations are unrealistic is because you're in the 2nd year and you're already saying to yourself what you should be doing after you have a PhD. Like others have said already, you should do mathematics because you like it, and the results will come naturally. That's all you can do - if the results don't come, at least you can say you did what you liked and you did what you wanted, and that's all you can expect of yourself.

And about the fear of failing... Failure is inevitable, any successful person in any field will tell you they've failed before. Because of your very high expectations you don't give any room for failure, which is the worst mindset you can have.

 

[SophusLies]

Who cares about winning some stupid medal? Do what you love and enjoy it. If you need decorations to make you feel fulfilled, then join the military. Science and math are not fields you go into to gain fame or fortune; they're fields for people that love to be intellectually challenged with very high chances of extremely little pay off in the end.

 

[Harrisonized]

I do not quite follow your reasoning. The age limit is 40 years, which combined with the fact that the Fields is usually considered the "nobel prize of mathematics" would seem to imply that mathematics is a young man's game. I understand that the prize was created to stimulate more research, but this is not what many perceive the prize to be. Maybe the creation of the Abel prize will change this, but i still think that my original point stands.

That's because math is a "young man's game". People like you should just quit now, but don't worry. People like you can still make an important contribution to mathematics: by quitting, you make room at universities for younger, more motivated and deserving people like Kevin.

 

[phyEngineer]

Hey functor97, do not give up or doubt feeling I went down that path once and now I do not look back at it (only I look back if it is about a place in my life) you strengths will carry all the way, and so what if you are 21 it is taking you long than the normal.

 

[nickadams]

http://www.ams.org/notices/201103/rtx110300444p.pdf

I'm only fifteen, so don't take what I have to say too seriously! I have no experience! Anywho, in the interview above, John Tate, a master of number theory, apparently didn't know he was going to be a mathematician until he was a graduate student. He had similar doubts about his intelligence, yet he became a giant in the world of mathematics. I don't know you and I'm only fifteen, but don't fret! You may be smarter than you think.

God bless
Mathguy

"I have told the story many times: I had read the book Men of Mathematics by Eric Temple Bell. That book was about the lives of the greatest mathematicians in history, people like Abel. I knew I wasn’t in their league and I thought that unless I was, I wouldn’t really be able to do much in mathematics. I didn’t realize that a less talented person could still contribute effectively. Since my father was a physicist, that field seemed more human and accessible to me, and I thought that was a safer way to go, where I might contribute more. But after one term it became obvious that my interest was really in mathematics. A deeper interest, which should have been clear anyway, but I just was too afraid and thought I never would be able to do much research if I went into mathematics."

That's awesome! I can't believe someone with a bachelors in math from harvard who was at princeton for their PhD could ever have self-doubt about their intelligence. Good find Mathguy15, i wish my priorities were anything like your's when i was 15 y/o :/

 

[mathwonk]

Let me share a story about myself that may be relevant. I was a star in math in high school and was told I was great but had the same fears you express as to whether I could ever do anything really outstanding. I went to a good college as a merit scholar, was actually admitted over the phone and still thought I was the best thing since sliced bread. In college I did poorly but had all manner of excuses for myself. I bounced through more years without distinction, and kept getting free rides to grad school, and was told I was promising but never performed. Eventually they gave up on me and I had to leave school.

I spent years trying to recover some status, working hard, trying to learn some discipline and some hard math skills. Finally, maybe with the motivation of needing to feed my family, I made a discovery about myself. I had a fear of trying as hard as I could, in case I should find out I was not as great as pretended to be after all.

I realized I only had one last chance at becoming a mathematician. I had to take a chance, the chance that even if I gave it everything I had, I might still never be good. But that is the chance we all have to take in life. If we want to compete in the world, we have to give it our best shot, with no guarantee it will give us the results we hope for.

In my case, indeed I was nowhere near the great mathematician I had fantasized about. But I was miles better than I would have been without trying my best. If you want a guarantee you will succeed before you are wiling to try even the career you want most, you are handicapping yourself almost totally. One strategy is one I mentioned - give up credit for your successes and grant them all to those who helped and supported you, God, your parents, your teachers, your forebears, your students.

There must be other strategies as well. The point is to find a way to have the courage to give yourself a chance to succeed. Good luck. To quote the great Silvanus P. Thompson's "ancient simian proverb", "what one fool has done, another can". Just a joke, please take it as meant.

 

[Mathguy15]

That's awesome! I can't believe someone with a bachelors in math from harvard who was at princeton for their PhD could ever have self-doubt about their intelligence. Good find Mathguy15, i wish my priorities were anything like your's when i was 15 y/o :/

Thanks! I try.

 

[Dembadon]

Thanks! I try.

No! Try not! Do, or do not. There is no try.

 

[Mathguy15]

Let me share a story about myself that may be relevant. I was a star in math in high school and was told I was great but had the same fears you express as to whether I could ever do anything really outstanding. I went to a good college as a merit scholar, was actually admitted over the phone and still thought I was the best thing since sliced bread. In college I did poorly but had all manner of excuses for myself. I bounced through more years without distinction, and kept getting free rides to grad school, and was told I was promising but never performed. Eventually they gave up on me and I had to leave school.

I spent years trying to recover some status, working hard, trying to learn some discipline and some hard math skills. Finally, maybe with the motivation of needing to feed my family, I made a discovery about myself. I had a fear of trying as hard as I could, in case I should find out I was not as great as pretended to be after all.

I realized I only had one last chance at becoming a mathematician. I had to take a chance, the chance that even if I gave it everything I had, I might still never be good. But that is the chance we all have to take in life. If we want to compete in the world, we have to give it our best shot, with no guarantee it will give us the results we hope for.

In my case, indeed I was nowhere near the great mathematician I had fantasized about. But I was miles better than I would have been without trying my best. If you want a guarantee you will succeed before you are wiling to try even the career you want most, you are handicapping yourself almost totally. One strategy is one I mentioned - give up credit for your successes and grant them all to those who helped and supported you, God, your parents, your teachers, your forebears, your students.

There must be other strategies as well. The point is to find a way to have the courage to give yourself a chance to succeed. Good luck. To quote the great Silvanus P. Thompson's "ancient simian proverb", "what one fool has done, another can". Just a joke, please take it as meant.

That's deep mathwonk. I had a similar realization a few days ago(of course, it wasn't as serious). I thought to myself, "Why don't I start putting real concentrated effort into things?" I found that the answer was that my perception of my own intelligence may be too high, and that if I try my hardest, I would fail to meet my expectations.