Is mathematics a young man's game?

[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.

 

[Mathguy15]

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

Ok I do. Happy?

 

[Dembadon]

Ok I do. Happy?

I just realized that you might've never seen the movie I'm referring to. So here it is:

https://www.youtube.com/watch?v=q3hn6fFTxeo

 

[Mathguy15]

I just realized that you might've never seen the movie I'm referring to. So here it is:

https://www.youtube.com/watch?v=q3hn6fFTxeo

Star Wars! Nice!

 

[Mathguy15]

Oh, and there is a really good article on math competitions and genius. While its not very directly related to you, I think you will find it helpful functor97. The article has many quotes from fields medallists and wolf prize winners, including some who doubted there own abilities. Enjoy!



http://lesswrong.com/lw/2v1/great_mathematicians_on_math_competitions_and/

 

[Functor97]

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.

Thank you for posting that Mathwonk, it has helped a lot!

 

[Functor97]

Oh, and there is a really good article on math competitions and genius. While its not very directly related to you, I think you will find it helpful functor97. The article has many quotes from fields medallists and wolf prize winners, including some who doubted there own abilities. Enjoy!



http://lesswrong.com/lw/2v1/great_mathematicians_on_math_competitions_and/

Yeah i saw those yesterday, it is quite interesting.

 

[kings7]

So is pursuing a PhD in math to become a postdoc analogous to playing basketball 6 hours a day for ten years in hopes of going to the NBA? Or practicing guitar 6 hours a day from age 18-28 to become a musician?

You can spend 6 hours per day every day for ten years and become a postdoc in math, yes.

The amount of work is what matters. If you want to compare differing intelligences, I suggest you define intelligence first and then let the rest of the neuroscience community know.

I'm not sure if you meant it this way, but your post seems slightly ignorant. If you knew the actual amount of work and intelligence (rigorous intelligence, nonetheless) it takes to become an actual musician (read: not just a pop star), I posit that you would not have used this as an example.

 

[mathwonk]

Let me put it another way functor, with all the good feedback you have received, it is far more likely that you have more potential than you can easily believe, than that you do not have enough to succeed. Your talent is a gift from your ancestors, the development of it is your gift to them and to yourself.

40 years ago I was unloading meat from a truck at $4/hour. When I finally made the commitment to become as good a mathematician as I could, my intellectual journey began. Once you start on the path, many people will assist you, because they have all gone on the same search.

If you still lack confidence, let me assure you I believe you can succeed. Choose and pursue your goal. But be measured in all things. Math is not everything. Work hard when you are young, but as a parent, play with your kids when they want you to. There will be time for math when they are asleep. There are a lot of pins to keep in the air.

 

[mathsciguy]

I think everybody who's seriously trying to pursue a career in academia or even someone who just want to do good in science in math should read this thread.

I'm quite surprised that most people who posted their experiences and anecdotes parallels mine's. I'm also having a hard time on my science/math education. As I'm always haunted by the thoughts of my own flaws. I guess it's something that's usually experienced by anyone who's serious in math and science.

Looking back, the reason why I'm set to do science/math was because I just thought it's too damn cool, now I don't know why I'm stressing too much about it.

 

[PhDorBust]

Think about it this way. The really good people wouldn't be deemed really good if they didn't have people like you to say they're better than.

 

[jk]

...
40 years ago I was unloading meat from a truck at $4/hour. When I finally made the commitment to become as good a mathematician as I could, my intellectual journey began. Once you start on the path, many people will assist you, because they have all gone on the same search.
...
.

$4/hour was good pay 40 years ago...equivalent to 22/hr today. This roughly translates to $40,000 per year..better than a lot of postdoc salaries

 

[tclos]

People who are really talented at an early age are born with it. I'm not sure of your situation, but you would know by now. Even if you are not born with it, it takes years of patience and hard work (sometimes a decade or more) to achieve greatness (it also depends on what your definition of 'greatness' is). However, I would seriously consider counseling if your self worth is solely determined by your mathematical abilities.

 

[ivan77]

A couple of things come to mind:

“Genius is 1% talent and 99% percent hard work...”
― Albert Einstein

second, I've heard a thousand times before that you shouldn't choose a career path because of the money, do it because you love it.

Wanting to be a professional mathematician because you want to win awards is going for the money.

Also, I find it kind of strange that you suggest that the theoretical physics community admonishes those who break from the status quo when the most revered in that community are precisley those who introduce some kind of a disruptive concept.

 

[mheslep]

This sounds appropriate:

Feynman zinger for the NAS!

 

[nazarbaz]

Kant, one of the greatest philosophical minds ever, wrote his first interesting piece at the age of 57... The most precious thing you can reach in our professions is to develop a perspective of your own, a new way to look at things... It is very hard and, for most of us, dangerous, both on a personal and professional levels... I doubt you can reach it when you only want it... You must have to... It can't be an act of "free will" and it can't be a mere result of some "inner qualities"...
In humanities, the world must shake around you when you are thinking if you do not intend to mainstream and to reproduce the same intellectual clichés that you despise in the litterature... I can understand that ambition... Though, doing it for fame is just ridiculous... People who look for this kind of psychological and social rewards are the true failures... True genius does not need others recognition... It doesn't even depend on you to attribute yourself some merit in it...
Genius reveals what is bigger than us...