Is mathematics a young man's game?

[Kevin_Axion]

No, i only wanted to hear people's own stance or experience in regard to these issues. You are a high school student Kevin, i would prefer advice from those who have at least started college in the field.

Yea you're right. I think what you just said was a genetic fallacy, but sure. My point clearly doesn't stand because I'm a high school student. I came here to help you not to try and make you feel bad. If you want to ridicule my statement with something as absurd as being a high school student then I'm fine with that, but you really haven't shown me anything against what my statement says.

 

[Pengwuino]

No, i only wanted to hear people's own stance or experience in regard to these issues. You are a high school student Kevin, i would prefer advice from those who have at least started college in the field.

It's irrelevant what someones experience is. Your issue is not what age you need to be to be a great, world-renown mathematician. Your issue, clearly, is far worse; you have a psychological issue that is hindering your life. Remember, if you obsess over 1 thing, all you'll ever be good at is obsessing over that 1 thing. So if you obsess over doing mathematics, you'll become good at doing mathematics. However, if you obsess over whether or not you're too old to be great, all you'll ever be good at is obsessing over whether or not you're too old to be great. Take a guess at which one is going to get your name in textbooks?

 

[Functor97]

Yea you're right. I think what you just said was a genetic fallacy, but sure. My point clearly doesn't stand because I'm a high school student. I came here to help you not to try and make you feel bad. If you want to ridicule my statement with something as absurd as being a high school student then I'm fine with that, but you really haven't shown me anything against what my statement says.

My original question was expressed towards those within the mathematical community, i am sorry if i did not make this explicit enough. I do not like the condescending tone of your post "you will never make anything of yourself..." I could direct that right back towards you. I simply do not think you are in a position to convey experiences you have never had, i mean how is a high school student of modest ability supposed to advise others on what makes a mathematician?

 

[Kevin_Axion]

My original question was expressed towards those within the mathematical community, i am sorry if i did not make this explicit enough. I do not like the condescending tone of your post "you will never make anything of yourself..." I could direct that right back towards you. I simply do not think you are in a position to convey experiences you have never had, i mean how is a high school student of modest ability supposed to advise others on what makes a mathematician?

I wasn't being condescending, I was being sarcastic. What I mean is if I say that or if anyone says that it isn't going to make any difference because in the end you are the person that you have to face and get over.

 

[Functor97]

I wasn't being condescending, I was being sarcastic. What I mean is if I say that or if anyone says that it isn't going to make any difference because in the end you are the person that you have to face and get over.

I appreciate you trying to help, i just think you went about it in the wrong manner.

 

[micromass]

I appreciate you trying to help, i just think you went about it in the wrong manner.

On the contrary, kevin's advice is very good. Don't disregard his advice because of his age!

 

[nickadams]

Why is this different? I could say the same thing about professional athletes, musicians, about CEO's, politicians, etc.

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?

 

[PAllen]

I would just throw out a clear counter-example to such hysteria. At 21, Edward Witten was working for George McGovern, having completed a history BA. He then studied some economics before switching to Physics and math. What did he end up with*?

I am not suggesting anyone can be Witten, just that at 21 you have no idea what you might still be able to do.


*Fields Medal, in case you didn't know.

 

[Kevin_Axion]

I would just throw out a clear counter-example to such hysteria. At 21, Edward Witten was working for George McGovern, having completed a history BA. He then studied some economics before switching to Physics and math. What did he end up with*?

I am not suggesting anyone can be Witten, just that at 21 you have no idea what you might still be able to do.*Fields Medal, in case you didn't know.

Awesome example! I was going to mention this but Ed Witten is very particular case, I mean, look at his forehead!

For those inquiring about said forehead: http://www.iopblog.org/wp-content/uploads/2010/06/ed_witten.jpg

 

[nucl34rgg]

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 traveling 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.

"Do not worry about your difficulties in Mathematics. I can assure you mine are still greater." -Albert Einstein

"I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me. " -Isaac Newton

No matter what natural talent the greats had, they still ran into a wall and struggled. Nobody is perfect. You probably aren't the next Hilbert, but that doesn't mean you can't make a contribution. Imagine if you had been a great talented mathematical prodigy. You know what you'd be worried about right now? You'd be worried that your life's work would never uncover some deep, all important, extremely abstract concept that you felt you were aimlessly groping towards in the dark. At least when you get stuck on a proof, you can ask someone who knows more. Imagine being at the top of the pyramid. Who do they turn to for help? Most practicing mathematicians are nowhere near the level of the men you mentioned. They still make great contributions. They just had to struggle a bit more and stick with a new concept a bit longer to understand it.

 

[eddotman]

I'm not really a mathematician, but I think I have some experiences that I can share which may help.

I'm a little younger than you (19), and I can say with confidence that my talents and abilities, compared to "history's greatest," is pretty damn mediocre. And that's nothing to be ashamed of or worried about, because the reality is, even those "child prodigies" face just the same struggles that you do.

I'm not just wildly suggesting this, either. When I was younger, I had a chance to go to some national/international science fairs. I can tell you that these events are littered with the kind of people that almost anyone feels inadequate when compared to - there were kids here who were on math olympiad teams while in middle school, or who had already filed patents or started companies with large VC funding.

But you know what? They face the same struggles that we all do. They get stressed from exams, they procrastinate and barely hand assignments in on time, they worry that they'll burn out or never become truly "great."

I don't think you should feel intimidated or discouraged by the accomplishments of others. We're all working towards the common goal of learning more about the universe, bit by bit, so maybe just think of it as having lots of really great colleagues.

 

[Functor97]

Awesome example! I was going to mention this but Ed Witten is very particular case, I mean, look at his forehead!

For those inquiring about said forehead: http://www.iopblog.org/wp-content/uploads/2010/06/ed_witten.jpg

haha large forehead size does not imply increased cerebral function. Or in Witten's case, cerebral dominance.

 

[DrummingAtom]

It's irrelevant what someones experience is. Your issue is not what age you need to be to be a great, world-renown mathematician. Your issue, clearly, is far worse; you have a psychological issue that is hindering your life. Remember, if you obsess over 1 thing, all you'll ever be good at is obsessing over that 1 thing. So if you obsess over doing mathematics, you'll become good at doing mathematics. However, if you obsess over whether or not you're too old to be great, all you'll ever be good at is obsessing over whether or not you're too old to be great. Take a guess at which one is going to get your name in textbooks?

100% agree with this. If you want something, go get it. Who gives a crap about age, ability, etc. Earning a prize seems like the wrong thing to focus on (at least to me) but if that's your motivating factor then use it to your advantage. Have a plan B if you don't succeed, why not just do it for the love?

http://www.youtube.com/watch?v=a_yW3152Ffc&feature=related

 

[Kevin_Axion]

haha large forehead size does not imply increased cerebral function. Or in Witten's case, cerebral dominance.

I know :), or else blue whales would be ruling the Earth.

 

[bpatrick]

If math and physics is a "young man's game" I should just quit now ... considering I'm in my late 20s and going back to grad school.

I had a physical chemistry professor back in undergrad who was in his early 90s and still rode his bicycle to school every day and twice a week, he went to the university gym and did elliptical machines for an hour.

Assuming I could even achieve being in the field until I'm 75 (let alone my early 90s) and assuming I can get through my PhD by age 35 ... that gives me at least 40 solid years to contribute to academia in some way ... assuming I can actually land post-doc positions and keep research going.

I don't feel that I'm any slower than I was when I was a kid doing math ... and I even took 3-4 years off from doing any type of science back when I was a professional musician (after a graduate music degree).

I think it's just stress and looking at loads of other people that is getting to you. You can't really do that. I remember some of the best advice my trumpet professor gave me and that had to do with comparing yourself to the prodigy people out there ... it's a downward spiral. There was a kid who won the principal trumpet chair of the New York Phil a few years back (might have been 2006 or 2007) ... he was a sophomore or junior at Northwestern studying under the famous husband/wife trumpet professors there. Everybody in the orchestral trumpeting community was stunned (and some got kinda depressed) that some hot shot kid who couldn't even order himself a beer in this country won the most sought after position in the classical trumpeting world at the time. There were literally thousands of applicants who submitted CVs and taped auditions who were narrowed down to the top 150 that were invited to a 3 day long live audition phase ... hell half of those people had doctoral music degrees or were even professors at major music conservatories in the country ... but a 19 year old kid won the job ... why? because he had worked his butt off since he was 10 playing in the San Fransisco youth orchestra because he knew back then that trumpeting was what he wanted to do (and his parents obviously supported him, etc...), but most of us (classical trumpeters) started playing the instrument when we were 10-12, played sports, went to normal schools, etc... and didn't know that we were going to pursue music at a conservatory level (or professionally) until we were late teenagers.

All I'm saying is that guys like that get loads of attention ... it wouldn't have been a big deal if any of those other thousands of guys who were in their late 20s or early 30s would have won the gig, but since it was this kid who did it, well it was a big deal, but in reality, he had been playing just as long as anybody else and had been playing seriously (like 6+ hours a day of practice) for almost a decade, so when you look at it like that, it's no different than any of the older guys who just started serious musicianship when they went off to college.

Anyway, you can't compare yourself to other people really, just do what you do and that's that. If you love math and are doing well in it, you'll find a path that accommodates that (hopefully given the economy / academia). Eventually if you keep up solid work ethic and keep pushing yourself in the field, you'll have just as good a shot as anybody to succeed in the field. Recognition isn't everything either ... I'm sure I'd have a shot still at winning a Fields medal if I did nothing but math for the next 12 years of my life, but Debra would probably leave me, I'd become estranged from my relatives and friends, etc... it's all about balance and you'll find yours.

I'm certainly not motivated enough to ever be a famous scientist (remembered for years) but that's because I know what all I'd have to give up to achieve that ... which just isn't worth it for me ... I'll settle for just being "satisfactory" among other PhDs, hah.

 

[Sankaku]

I know the thread has moved on, but I wanted to address this:

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

This should be a source of inspiration and wonder, not distress. The field is so deep and broad that it has room for many minds to explore.

...

Just a note to people suggesting psychological help: The mathematics community has real issues about projecting the image that it is a young man's game. I mostly blame G.H. Hardy and the Fields committee. It is not unreasonable that a person hitting some natural self-doubt will inadvertently adopt this ghost from the past as their own.

 

[f95toli]

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?

No, because with a PhD in math there are many alternative career paths; not only in academia but also in industry, finance etc.

Also, when you read about "great mathematicians", keep in mind that most of them were educated at a time when just about everyone got their degrees several years earlier than today ("regular" people finished school when they were14, university at say 18-19, and it took maybe two years to get a PhD); it not only depends on how smart you are but also the educational system.

 

[PieceOfPi]

Instead of visiting a psychologist, talk about this to members of Association of Women in Mathematics---I'm sure they will *fix* you up!

 

[epenguin]

Random thoughts.

I believe, whether you ever recognise it or not, the year you spent knocking around the world as opposed to being the tenured prodigy you aspire to be, will not have been wasted time.

(Actually, almost, it is only when you are young or retired you are allowed to waste time.)

I fully agree with Feynman on this. There are too many people who are outside Science, unable to contribute to it directly, who try to promote it setting up prizes etc.. Causes more distortion than anything; you cannot imagine the number of hangers-on there are who try to get in on the act. Starting from preening politicians who want to be seen bestowing and speechifying in the awards ceremonies and a zillion people who try to be invited to the parties. Who mostly understand little or nothing about the discoveries that are the pretext. A fairly revolting spectacle.

Scientific Academies like the NAS are at best a necessary evil, except that some of them are not even necessary.

Feynman did not mention that even the sound part, having achieved something, though better than not achieving it, and especially than someone else doing it or being recognised for it before you - a constant anxiety of scientists - even the feelings of satisfaction do not last long, at least with any intensity. Read Watson on his feelings after having published the double helix structure. Anti-climax. Or Dirac when Feynman enthused to him about how it must feel to have made his fantastic discoveries. 'It was a long time ago' was all he could respond. You soon have to move on to the next problem or issue. But the temporary high has hooked you, says Medawar.

 

[nickadams]

No, because with a PhD in math there are many alternative career paths; not only in academia but also in industry, finance etc.

What about those who find they are not smart enough to finish a bachelors in math or not smart enough to get into grad school (low GPA) or not smart enough to finish the PhD? I am afraid to risk so much to see if I have what it takes to get a math PhD. I wish they gave you a test when you are 18 that can determine if you have the potential to get a math PhD, because as it is now someone may take 3-8 years and thousands of dollars before they find out they don't have what it takes :(

 

[mathwonk]

I am 69 years old. Is mathematics over for me? I am still active here in that regard at least in giving advice. And i have a role in teaching. But I also have a research presence (see the attached article.) I also read and think about math.

I do think there is a link between energy and health and mathematical productivity, which may be the main reason it is associated with youth. But young persons can be lazy and unhealthy as well. if you get some good counseling and work on your attitude toward creative work and its intrinsic rewards, you can enhance your own mathematical potential in my opinion.

When I was oriented to motivation through scripture I used to assuage my feelings about recognition or lack of it, by recalling the verses that advise doing ones work for the glory of the deity, and giving up credit for it oneself. Whatever works for you, try to take advantage of it.

 

[deRham]

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.

The thing is you have to be very wary of using words like fully understand. When does someone fully understand something? There's something beautiful about learning, which is that you can explain a lot of complicated things in a simple manner (which can still convey a bunch of the intuition) to a young, inexperienced person. Then you up the complexity level over time. In elementary school, I learned biology - the same ideas I learned in high school, but at a much lower level. Then, they told me there is more to the story. In some ways, even the most advanced things are like this. It's important to not view it as a tower, but as discovering more and more about the same things.

I'm not following your reasoning. If you are ready to give up mathematics for lack of recognition, which can you say you love more?

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.

However, the remedy is to maintain one's enthusiasm. Further, you can be in dialogue with the physics/math community whether or not you are an official physicist/mathematician as per career, and you can most certainly do high level work at a graduate school whether or not you end up with a successful career. I'd hardly discount that some of the most passionate individuals don't make it in academia, and not for lack of intelligence or discipline, but for lack of the drive to do exactly what is necessary to make a career in academia.

 

[deRham]

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

This is the key thing you have to stop, and I think my recipe is exactly how - you will never actually learn everything needed to "understand" what you want to. In some years, you will learn enough to contribute something, albeit not the best of the best necessarily.

In the scope of things, the classes you take and where you are now will matter very less. Now is the slow part of your education, where you are trying to figure out how the more knowledgeable think. Eventually, that vocabulary barrier will be gone, and the main barrier will be perseverance - sticking it out long enough for a lot of things to fall into place.

The key is to keep your eyes open and to maintain the idea that what you're doing right now is worth it and important. Once you lose that idea, your progress slows dramatically, and may even halt.

 

[deRham]

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

Yes, although if you work for 15 years in the field and really keep your eyes open, chances are you'll have a few great ideas. The hard part is turning them into something fruitful, and often only one or two great ideas will get turned into several different papers that people read. It's a slow process to turn ideas into writing that takes into account what needs to be taken into account in practice.

It is quite possible that only by around 35-40 will your great ideas start really bearing fruit. There are 10 years for you to go to become 30 and that's a tremendously long time. If I'm not wrong, several years ago, you were nowhere close to where you are today. The goal is that in 3 years, you feel the same way about this past self.

 

[deRham]

If you want to do something great, start working on it now and stop concentrating on useless ideas that depress you and only hinder your progress which is what you're worrying about in the first place

The one issue here is that the whole problem seems to be that it's hard to start on something great when stuck fiddling clumsily with the very basic ideas. I attempted above to make some modest contribution to dealing with that issue, but it's still a tough psychological issue.

I think it is better to acknowledge what is depressing you and fix it, rather than dismissing the cause for depression.

That said, I agree with your advice about not allowing the depression to feed on itself (i.e. letting it depress you far enough to feed the lack of progress, and so forth).

 

[Functor97]

I really appreciate all of the responses.

bpatrick, i can relate to you in regards to the story of the music prodigy. Growing up as a teenager i got involved in the American mathematics competitions, such as the AMC, AIME and USAMO, and while i did reasonably well enough to progress to the final round (the USAMO) i never did well enough on this proof based Olympiad to get an invite to the summer program (MOSP). I remember hearing that a 14 year old had got one of the highest scores in the country, making me quite depressed, when i myself could not do as well. I did do some practice, but amongst the Olympiad community (those who i spoke to on forums etc) natural talent seems to have been stressed, equating it with creativity, and those who practiced were hacks.
So imagine my dismay when i realized that so many prominent mathematicians (Tao, Gowers, Borcherds, Perelman, Drinfel'd etc) had also been so successful at the international mathematics olympiad (mostly gold medals) i began to doubt my own ability, as i could not even do well on my own national Olympiad.. I mean out of the four fields medalists last year, three of them were previous IMO medalists.

 

[deRham]

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.

Sometimes you need to hear it from the people in the field, and people outside the field may not quite understand/connect in the same way. I think a psychiatrist is in order when the individual loses control of himself and becomes truly self-destructive...when the issue clearly exits the realms of physics and mathematics and enters psychological damage control.

I like to think we're all crazy, and have made unwise decisions or had unhealthy insecurity...or at least the vast majority, but the key is getting out of there.

 

[deRham]

i never did well enough on this proof based Olympiad to get an invite to the summer program (MOSP).

One comment: getting to the final round is very good already, and I think the talent that it takes to become good in your field is at this point a different one. There are quite a few professors who don't touch competitions, and quite a few successful at competitions who don't become researchers.

The key is that competitions, while still quite thought-provoking at the high levels, are nowhere near as slow as the actual research process. Especially since you seem to be interested in rigor - rigorous research is very, very slow. I think it takes a different sort of firepower to churn out a very interesting paper. It's also a lot more personal than a competition paper - you will be picking what you want to spend all that time on, whereby you have an advantage if you really hit something that you feel is your role in academics.

 

[Neil.yc]

I read this thread twice. Being also 21, I had been through psychological issues of some sort similar to the OP. Here is a story:My friend's brother won national Olympiad, but he lost interest in math afterward. Do you know that there were many prodigies, for whatever the fields they were in, got burned out and disappeared? Perelman's story is quite tragic: His mother set out his path before his birth and having achieved what he did, he was partially betrayed by what he loved(that is, mathematics and its community) I mean, really, what do you care what other people think?

 

[Functor97]

I read this thread twice. Being also 21, I had been through psychological issues of some sort similar to the OP. Here is a story:My friend's brother won national Olympiad, but he lost interest in math afterward. Do you know that there were many prodigies, for whatever the fields they were in, got burned out and disappeared? Perelman's story is quite tragic: His mother set out his path before his birth and having achieved what he did, he was partially betrayed by what he loved(that is, mathematics and its community) I mean, really, what do you care what other people think?

Well i am usually considered a failure at most things outside academia (Few friends, not interesting to the opposite sex, no physical abilities so to speak) by others in my life, so i would like the chance to achieve at least something substantial in a field i love. I don't deny that there is a psychological aspect, at least i am being honest about it. I may enjoy mathematics, but i am still a human, and we have evolved to desire recognition and some form of acceptance.