Is mathematics a young man's game?

In summary, the author is feeling depressed about his future in the mathematical sciences and wonders if he is a Fields Medalist later on. He is not a prodigy like Terry Tao, Noam Elkies, or Charles Fefferman, nor has he succeeded at mathematical Olympiads before the age of 18. Many great mathematicians finish their PhDs by his current age, and he fears he will not be able to access the higher levels of mathematics before he is too old.
  • #1
Functor97
203
0
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.
 
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  • #2
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.
 
  • #3
You're 21 bro..lol
 
  • #4
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 wouldn't think anything of it.
 
  • #5
mathwonk said:
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.

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.
 
  • #6
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
 
  • #7
Chunkysalsa said:
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

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.
 
  • #8
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.
 
  • #9
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.
 
  • #10
Mmm_Pasta said:
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.

Its the fact that i have so much to learn which troubles me.
 
  • #11
Functor97 said:
...

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.

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.
 
  • #12
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.
 
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  • #13
Dembadon said:
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.

I can assure you i do love mathematics. Doesn't everyone want recognition for doing what they love?
 
  • #14
Functor97 said:
I can assure you i do love mathematics. Doesn't everyone want recognition for doing what they love?

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?
 
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  • #15
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.

Dembadon said:
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 second this.
 
  • #16
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.
 
  • #17
Dembadon said:
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?

I would still pursue 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.
 
  • #18
Functor97 said:
I would still pursue 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.

I do not have much to add, other than the fact that not too long ago (about 3-4 years) I was in a similar position as yourself. During high school I was mislead (mainly by my math professors) to think of myself as a person with high talent in mathematics. So, at that time I always pictured myself as a person who would one day make some breakthroughs in mathematics. Later on, I discovered the harsh truth, that this is very unlikely to happen (while not impossible, never say never ;) ). For a while I started doubting myself to a point where I even considered not pursuing a degree in mathematics at all.

Fortunately, in the comming years I have come to love mathematics for its own sake, and while being internationally recognized for my work would most certainly bring home a great feeling, this is not the reason I study mathematics now.

Your work should be a natural result of your passion for mathematics, not the other way around. That is, you should not be driven to study mathematics by the idea that one day you will be internationally recognized as a great mathematician, on the contrary, studying mathematics should be only a result of your passion and love for it, and as I said, becoming internationally recognized, should merely come as a natural consequence of your work.
 
  • #19
Functor97 said:
I can assure you i do love mathematics. Doesn't everyone want recognition for doing what they love?

The truth is that most people don't get recognition for what they do.

Teachers in high schools put up with so much crap just to get to that one student that gives a stuff and everyone else thinks their job is easy and that they have too many holidays.

Same goes with many professions.

My advice is to give up the idea that you will get a lot of recognitio, because most people don't get it even if they really deserve it. Many will get it after they have died but usually not before.

You'll be a lot happier if you find something you enjoy and like using to help other people: the rewards will come usually from things that are un-announced.
 
  • #20
sutupidmath said:
I do not have much to add, other than the fact that not too long ago (about 3-4 years) I was in a similar position as yourself. During high school I was mislead (mainly by my math professors) to think of myself as a person with high talent in mathematics. So, at that time I always pictured myself as a person who would one day make some breakthroughs in mathematics. Later on, I discovered the harsh truth, that this is very unlikely to happen (while not impossible, never say never ;) ). For a while I started doubting myself to a point where I even considered not pursuing a degree in mathematics at all.

Fortunately, in the comming years I have come to love mathematics for its own sake, and while being internationally recognized for my work would most certainly bring home a great feeling, this is not the reason I study mathematics now.

Your work should be a natural result of your passion for mathematics, not the other way around. That is, you should not be driven to study mathematics by the idea that one day you will be internationally recognized as a great mathematician, on the contrary, studying mathematics should be only a result of your passion and love for it, and as I said, becoming internationally recognized, should merely come as a natural consequence of your work.

Thank you for the reply. You and Deveno are of course correct, it is the joy of discovery that i should strive to achieve.
 
  • #21
chiro said:
The truth is that most people don't get recognition for what they do.

Teachers in high schools put up with so much crap just to get to that one student that gives a stuff and everyone else thinks their job is easy and that they have too many holidays.

Same goes with many professions.

My advice is to give up the idea that you will get a lot of recognitio, because most people don't get it even if they really deserve it. Many will get it after they have died but usually not before.

You'll be a lot happier if you find something you enjoy and like using to help other people: the rewards will come usually from things that are un-announced.

Thank you for the advice Chiro, this has put my childish beliefs in perspective.
 
  • #22
This sounds appropriate:

https://www.youtube.com/watch?v=f61KMw5zVhg
 
  • #23
Functor97 said:
I would still pursue 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.

I'm not sure you're in a position to know what you'll be able to understand 10 years from now. Worrying about it certainly won't improve your mathematical abilities. :wink:

Again, I think your issue is emotional. It will be much easier to address that via a counselor than by attaining the ridiculously high expectation you've set for yourself. I really wish you the best and hope you find what you're looking for.
 
  • #24
Functor97 said:
I can assure you i do love mathematics. Doesn't everyone want recognition for doing what they love?

There's a difference between recognition and being known by every person in your field for centuries after your death. Why do you even care? You won't be alive to enjoy such recognition most likely even if you were to achieve it.

Scientists get recognition on a regular basis, through journal citations, conferences, talks, etc. They can even write texts that will be used for generations to come and achieve recognition that way.

Stop trying to live for other people, because that's essentially what you're doing.
 
  • #25
Dembadon said:
I'm not sure you're in a position to know what you'll be able to understand 10 years from now. Worrying about it certainly won't improve your mathematical abilities. :wink:

Again, I think your issue is emotional. It will be much easier to address that via a counselor than by attaining the ridiculously high expectation you've set for yourself. I really wish you the best and hope you find what you're looking for.

Yes i acknowledge that you are probably correct. I do not see how a counselor could aid me in this, so i shall simply try and take the advice given here and focus on the math.
 
  • #26
You'll never make anything of yourself in either mathematics or physics.

What do you want to hear? Do you want everyone on this forum to tell you that you'll do well while you continue to doubt yourself? You're your own problem and saying you'll never make it is only infringing on something you can't change. 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, a self-perpetuating process. I think you can see the illogical consequence in what you're doing, now just make it actionable.

EDIT: I'm not trying to be harsh but seriously, your entire depression is just contradicting exactly what is making you depressed and that will only continue.
 
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  • #27
Functor97 said:
Yes i acknowledge that you are probably correct. I do not see how a counselor could aid me in this, so i shall simply try and take the advice given here and focus on the math.

Counseling can help identify and correct destructive mindsets. If you think about it, you've received some counseling in this thread. It has been of some aid, no? :smile:
 
  • #28
Kevin_Axion said:
You'll never make anything of yourself in either mathematics or physics.

What do you want to hear? Do you want everyone on this forum to tell you that you'll do well while you continue to doubt yourself? You're your own problem and saying you'll never make it is only infringing on something you can't change. 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, a self-perpetuating process. I think you can see the illogical consequence in what you're doing, now just make it actionable.

EDIT: I'm not trying to be harsh but seriously, your entire depression is just contradicting exactly what is making you depressed and that will only continue.

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.
 
  • #29
Functor97 said:
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.

So you think that high school students don't have the experiences you have?? Your problem is an emotional one, I think Kevin can understand quite well what you're dealing with.
 
  • #30
nickadams said:
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.

Why is this different? I could say the same thing about professional athletes, musicians, about CEO's, politicians, etc.
 
  • #31
Functor97 said:
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.
 
  • #32
Functor97 said:
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?
 
  • #33
Kevin_Axion said:
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?
 
  • #34
Functor97 said:
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.
 
  • #35
Kevin_Axion said:
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.
 
<h2>1. Is mathematics really a young man's game?</h2><p>There is a common belief that mathematics is a field dominated by young men. However, this is not entirely true. While there may be a higher proportion of young men in mathematics, there are also many successful and influential mathematicians who are older or female.</p><h2>2. Why is there a perception that mathematics is a young man's game?</h2><p>This perception may stem from the fact that many famous mathematicians, such as Isaac Newton and Albert Einstein, made their groundbreaking discoveries at a young age. Additionally, there may be societal biases and stereotypes that contribute to the belief that mathematics is a field for young men.</p><h2>3. Are there any advantages to being a young mathematician?</h2><p>There are certainly advantages to starting a career in mathematics at a young age. Younger mathematicians may have more energy and enthusiasm for their work, and may also have more time to dedicate to research and learning. However, these advantages do not necessarily make mathematics a "young man's game."</p><h2>4. Can older mathematicians still make significant contributions to the field?</h2><p>Absolutely. Many mathematicians continue to make important contributions to the field well into their later years. In fact, some mathematicians argue that with age comes wisdom and a deeper understanding of complex mathematical concepts.</p><h2>5. What can be done to encourage more diversity in mathematics?</h2><p>To promote diversity in mathematics, it is important to challenge and break down societal stereotypes and biases. This can be done by providing equal opportunities and support for individuals of all ages, genders, and backgrounds to pursue mathematics. Additionally, promoting and highlighting the achievements of diverse mathematicians can inspire others to join the field.</p>

1. Is mathematics really a young man's game?

There is a common belief that mathematics is a field dominated by young men. However, this is not entirely true. While there may be a higher proportion of young men in mathematics, there are also many successful and influential mathematicians who are older or female.

2. Why is there a perception that mathematics is a young man's game?

This perception may stem from the fact that many famous mathematicians, such as Isaac Newton and Albert Einstein, made their groundbreaking discoveries at a young age. Additionally, there may be societal biases and stereotypes that contribute to the belief that mathematics is a field for young men.

3. Are there any advantages to being a young mathematician?

There are certainly advantages to starting a career in mathematics at a young age. Younger mathematicians may have more energy and enthusiasm for their work, and may also have more time to dedicate to research and learning. However, these advantages do not necessarily make mathematics a "young man's game."

4. Can older mathematicians still make significant contributions to the field?

Absolutely. Many mathematicians continue to make important contributions to the field well into their later years. In fact, some mathematicians argue that with age comes wisdom and a deeper understanding of complex mathematical concepts.

5. What can be done to encourage more diversity in mathematics?

To promote diversity in mathematics, it is important to challenge and break down societal stereotypes and biases. This can be done by providing equal opportunities and support for individuals of all ages, genders, and backgrounds to pursue mathematics. Additionally, promoting and highlighting the achievements of diverse mathematicians can inspire others to join the field.

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