Becoming a mathematician - I am so depressed

[cobalt124]

Apologies if this seems rushed or disjointed or long, repeats what other posters have said (needs re-emphasising anyway), and for possibly sounding like I want to slap some sense into you (I do), but you need a serious (and very well intended) butt-kicking:

i have a dream - i want to obtain a math PhD, and become a mathematician working with mathematical research and teaching at college. I want to become a college professor so hard, that its basically all i care about.

Seems like a reasonable well thought out dream on the face of it.

IQ is irrelevant. There must be loads of threads in PF that will convince you of that, even one about famous scientists having low IQ's (Feynman?). Ah, I see you know that. You seem to be beating yourself up over nothing.

This is just not my case - i have never been a child prodigy, learning calculus at age 12 and so on. I did teach myself calculus at age 16, but that is only 1 year prior to our high school introduction to the subject. It seems that i am of low
intelligence, and i do not have a mathematical talent.

You are seeing this in the wrong perspective. Stop beating yourself up. It would be more productive to be inspired by the likes of Feynman than try to be like them, you cannot make the comparison because at the end of the day you are you.

It seems that i am of low intelligence, and i do not have a mathematical talent.

Crap. Just to emphasise this.

This is of great annoyance to me!

Listening is usually more productive than being annoyed. And listening is different to agreeing. And anyway it sounds like a compliment. From what I am reading you have all the qualities required to complete a maths Phd. That statement has to be qualified by the fact that I am no maths expert and I do not have a Phd.

I suspect your internet reading is skewed/"spun" towards "geniuses". Where are the articles about the "real" mathematicians and what thay have done/do?

Don't rule out seeking counselling. Far easier to do this proactively than wait for a potential situation to get a lot worse, which may result in a "Shouldbe" maths Phd not becoming one at all.

"What does your iq need to be in order to become a mathematician"

Ask the right questions instead of the wrong ones.

From what I've learned from the internet

Aaaaargh, the fount of all knowledge...NOT!

I'd say it's right to aim high with ambitions, but it's wrong to aim high with expectations.

I have no idea if my math teacher may just have gotten unlucky with his students the past 20 years of his teachings

The fact that you even posted this speaks volumes. I'm glad you did. A teacher has twenty years solid of poor students or you are a potential maths Phd! I no know most of your ideas on this are in your head and nowhere else and you need to test your claims in reality. I believe you will be pleasantly surprised.

Your posts hint at you having low self esteem. Counselling.

This is according to my impression an accomplishment reserved for the quickest of minds

My impression is not "the quickest of minds", but "the hardest of work". Bet my impressions are better than yours.

Micro watches Spongebob 24/7 but he is amazing at math, what does that tell you

It tells me I didn't watch enough SpongeBob.

The stuff that i do is easy

I strongly suspect you are saying: "I can do this stuff, therefore it is easy", and "I can't do this other stuff, therefore I'm rubbish at maths". If so, you have set yourself up to fail.

In order to gain success in math, i have to be extraordinary - otherwise, what is the point of trying?

Wrong, and another "setup to fail".

i think its hardwired into me

Do a PF search on neuroplasticity. Things may not be as hardwired as you imagine. Knowing this helped me.

Lol - when i lay it out like that, i really sound like a person who needs professional help ^^

Only one way to find out.

and people do say intelligence is inherited?

Nature vs Nurture is not a black and white issue. At the end of the day you can do nothing about the Nature, but lots about the Nurture.

 

[kings7]

Not to put too fine a point on it, since you have received some great responses already, but there are many types of intelligence.

In any case... sometimes you can never tell what 'aspect' of intelligence it will take to come up with a great discovery. Most of it stems from creativity, perseverance, hard-work, and passion for the subject. My guess is you have all of that, even if you can't see your own creativity right now (which is a life-long process anyway).

Most of the greatest discoveries weren't thought up by even the most "superior" scientists of our species (Darwin, Einstein, Goedel, Curie, etc...) until mid or late into their lives when they have had copious exposure to their respective subjects. You need not worry about things like this now.

Do what you love because you love it. Your life will then be fulfilled and happy. Life is not about money or fame or success... it is about passion.

Here's the advice I would give you:

I'm 24 and have pursued two separate paths in life so far (music and maths). I've finally discovered that my true passion is in music and that is what I'll be going to grad school for. For years I was afraid of this because I thought it wouldn't "prove" enough that I had a high intellect. It's a hard phase to get over, especially if you're self-conscious like myself (and most likely you too), but you MUST get over it. It helped me to realize that it takes just as much dedication, intelligence, creativity, hard-work, and PASSION to do music as it does to do mathematics. This is true for most (but not all) subjects, as long as it is your true passion.

The only way you'll make a difference in this world is by pursuing your passion. You're already a step ahead of a lot of people just by knowing what your passion is.

The only other piece of advice would be to stay modest and humble. It sounds like you have a lot of talent, and as you progress, it becomes more and more difficult to be humble. But it is something that will certainly help you in many areas of life, for reasons that are beyond the scope of this topic.

Hope that helps. Good luck.

 

[epenguin]

Looks like your problem is not you and maths.
Your problem is you and concerning yourself with nothing else but maths.

For instance 145 is an object with indubitable meanings in maths, for instance it's 29X5 - though I won't have a depression if I got that wrong.
Whereas an IQ of 145 does not have that quality at all, it is a number that means no more than the methods used to obtain it, and above all justify and interpret it as meaning anything. Still controversial and considered ideologically driven by some. The facts you can solve those eqs. and help other students say much more about you in my opinion (and others' we have seen).

Numbers in real life are a convenience but a curse.

For instance a mathematical physicist may miss tricks if he just takes the numbers that experimentalists give him and doesn't understand how they were obtained. Read e.g. Feynman's 'The 7% solution'.

I am thinking of my experience in (grant) administration. Once a number had been put on something, it became thereby Scientific. Sacred. Unchallengeable. People really ended up believing a project that had got 78 points in evaluations was about 1% better than one that had got 77 points! Even if one was in Physics and the other in Biology! The recriminations I remember when an element of qualitative, policy or relevance judgement was allowed! - This 78-point Project Has Not Been Supported When This Less Good 77-point One Has! In the end justifying and explaining was given up and we just let numbers rule mechanically. But, starting as a convenient help to sieving, people finished believing these numbers (like you do). And it wasn't just contemptibles like politicians, lawyers, economists who were number worshippers either - I can remember theoretical physicists and statisticians who were the worst!

You see now the curse of numbers? They are used to relieve people of responsibility, of judging. (And so once we could say 'your project was not financed because it got one less point than the cutoff' we found ourselves in an unattackable fortress).

Well this has led to something wider than your question but I think this is of general interest to scientists and the assumptions in your question do lead to this.

But my message just to you is forget the foolish figures and also do something additional besides mathematics.

 

[Levis2]

I must say, you guys have really helped me to get a better view on all this. You have encouraged me to at least attempt a shot at my dream. I will do everything to get the education i need - if i even make it to my masters that is.

And you might also be right about the iq thing - i sat down in order to think rationally for a moment about the whole iq setup. Why is it, that i let one number, obtained from some stupid internet mensa test, control my life. Why is it that number to decide whether i am capable or not? Screw the iq - i just hope its a coincidence, that *almost* all mathematicians have a very high iq.

You have really helped me get over my iq obsession - it might seem like nothing to you guys, but the feeling of your future being decided by one single number is horrible. I will not let that number rule my life. I will put no more significance into iq, and i will forget my stupid test result.

The only doubt that i have left, is whether i will be able to complete a phd - my doubt roots in the fact that, if I've got it correctly, when you pursue a phd, you have to come up with something NEW. If the most brilliant of minds struggle with coming up with something new, then how am i suppose to do just that, when i am no match for them?

And about the Paul halmos being close to the "ordinary" mathematician - paul halos obtained his bachelor of mathematics when he was 19 - when i am 19, i will have just finished high school. If the ordinary mathematician is like paul halmos, then I'm screwed.

I seriously consider getting some professional help with the self-esteem complications - as stated before, it has come to a point where it inhibits other aspects of my life aswell.

 

[Levis2]

Also, i might have put one of my statements in a bad way - the issue is not the fact that i may become a bad mathematician. I can definitely live with that - as long as i CAN become a mathematician. That is my fear - spending 6 years in uni, and then lacking the intellect to complete my education.

And if i barely make my phd, then I'm afraid i won't be smart enough to get a job. I do have plans on starting a family in the future, and how is a vacant mathematician, not being capable of acquiring a job, suppose to provide for x number of kids?

I can live with not being the best mathematician - or at least i can now, after you guys have helped with my understanding. But I'm afraid of complete failure. Even though i'd still love what i do, then how am i suppose to provide for a family, if i can't get a job because everyone is smarter than me? I don't think i will ever be able to contribute to mathematics - so far all I've done is learn topics, which smarter people invented.

 

[micromass]

Levis2, you worry too much about things. I recognize this because I tend to do the same.
I can imagine that you lie awake at night pondering about all these things. And the more you think about it, the far away the solution will be. And you will see, that if the moment comes that you feared so much about, then it will turn out to be alright. And you will feel silly for worrying this much.

It is not only your self-esteem that is an issue here. It's your lack of self-confidence and your worrying about things. I'm not a psychologist, but I'd say that you seem to have some kind of anxiety disorder. Definitely go seek professional help.

I struggled with worrying too much as well. Seeking professional help was the best thing I ever did in my life!

 

[Kevin_Axion]

Spend less time thinking about your I.Q and more time brewing coffee and proving theorems.

 

[Levis2]

Levis2, you worry too much about things. I recognize this because I tend to do the same.
I can imagine that you lie awake at night pondering about all these things. And the more you think about it, the far away the solution will be. And you will see, that if the moment comes that you feared so much about, then it will turn out to be alright. And you will feel silly for worrying this much.

It is not only your self-esteem that is an issue here. It's your lack of self-confidence and your worrying about things. I'm not a psychologist, but I'd say that you seem to have some kind of anxiety disorder. Definitely go seek professional help.

I struggled with worrying too much as well. Seeking professional help was the best thing I ever did in my life!

May i ask what issues you had? And which carrier path you chose? And how advanced you were at my age?

I know the last question is inappropriate - but i think i need some facts, that tell me i can do this. The issue here is that a lot of people, people who hold math phds or proffessorships, tell me that i can easily do this. The issue is that its not a proof - i have nothing to compare myself to, and this "you can do this" may just root in plain modesty - of course one doesn't want to brag about their level of intelligence. If someone asks if everyone can accomplish what you did, of course one will answer an uplifting yes.

But i definitely worry a lot. I have always thought a lot about the different consequences/outcomes of my actions, and sometimes it has been a pain, and at other times this ability has been a blessing. Imagine how many stupid teenage choices i have avoided, by using this curse/trait... But on the other hand, it is also keeping me from pursuing my passions once in a while, and i do not consider it to be a positive trait - at least not all the time.

How did the professional help help you, if i may inquire about such personal details?

 

[diligence]

OP:

I haven't read anything in the thread other than your first post, but did it ever occur to you that this contention of yours, that you need a high iq to be a successful and respected mathematician, is just flat out false?

I know you're young, but damn dude, pull out of it! Have some confidence in yourself! It sounds like IQ will be the least of your problems if you don't even have thick enough skin to get past some arbitrary and irrelevant IQ score. What are you going to do when faced with a true challenge in life? If you keep up this attitude, sounds to me like you'll just wither and quit, and seriously I doubt there's EVER been a successful research scientist in ANY field possessing that outlook.

 

[micromass]

May i ask what issues you had?

I had (and somehow still have) a low self-esteem, I worry too much, I have OCD, I am very uncomfortable when I have to talk to people (although nobody ever notices that about me), I have attempted suicide several times, I'l hyper-sensitive about things, etc.

My issues are far from solved at this moment. But seeking professional help was a real blessing. I encourage you to do the same.

And which carrier path you chose?

I have always loved mathematics more than anything. So I studied that. I'm now a PhD-student.

And how advanced you were at my age?

I would say that I was quite comparable to you. I was no child-genius at all. I'm just an ordinary guy deeply in love with mathematical theories. I certainly have no IQ of 145, not even of 135. But IQ doesn't matter.

The thing is that it doesn't matter how advanced I was. I am who I am, you are who you are. Don't mirror yourself towards other people, this will always make you sad. The thing is: there will always be people smarter than you (unless you are Grothendieck). The trick is to do what you love and not think too much. This sounds easy, but it's true. Counceling will help you with this.

How did the professional help help you, if i may inquire about such personal details?

I have received medication which made me worry less about things. Medication doesn't solve everything, but it helps a lot. Therapy is also quite helpful as it allows you to see things in perspective.

 

[Robert1986]

And about the Paul halmos being close to the "ordinary" mathematician - paul halos obtained his bachelor of mathematics when he was 19 - when i am 19, i will have just finished high school. If the ordinary mathematician is like paul halmos, then I'm screwed.

And why did he obtain his BS when he was 19? Was it because he was a super-genius? Not at all. He had immigrated (or is it emigrated, I never know) from Hungary to the US and when he started school, I think he went from about the equivalent of 7th grade to being a sophomore or junior in high school. This doesn't make him a genius; this was just a clerical error, essentially, and he was able to do well enough in his classes. I am 25 and will be 26 when I get my Bachelor's degree. I am trying to go to grad school in math and if I can make it, the absolute earliest I can reasonably expect to be done is when I'm 30. Do I care? Well, a little, but not that much.

Here's a question: which grad school application asks for your IQ?

 

[Functor97]

Spend less time thinking about your I.Q and more time brewing coffee and proving theorems.

This.

 

[Dembadon]

... but i think i need some facts, that tell me i can do this. The issue here is that a lot of people, people who hold math phds or proffessorships, tell me that i can easily do this. The issue is that its not a proof - i have nothing to compare myself to, and this "you can do this" may just root in plain modesty - of course one doesn't want to brag about their level of intelligence. If someone asks if everyone can accomplish what you did, of course one will answer an uplifting yes.

...

What "facts" do you believe you'll receive from therapy that will guarantee your success in mathematics? I'm not saying you shouldn't go to therapy, however, I don't think that you should give it up should you receive a disappointing diagnosis.

This is also what most everyone here has been trying to tell you. You need to pursue your interests because they are interesting to you, not because of some external evaluation/affirmation. Don't trade the meaning of the IQ test for your therapist's assessment--you're trying to get away from needing external validation, not substitute it for a different form of the same idea.

 

[dalcde]

Who cares if i can proof some arc length formula, or the taylor series.

It's not that you can prove them that matters. It's that you even bother to prove them. Just that is enough to make you a mathematician.

 

[cobalt124]

Don't trade the meaning of the IQ test for your therapist's assessment--you're trying to get away from needing external validation, not substitute it for a different form of the same idea.

Good point. The whole current mindset and attitude needs to be seen, and changed.

 

[Evo]

Ok, first, online IQ tests are junk. Only an IQ test administered in person by a psychologist is acceptable. It can take 5-9 hours to take.

There was a noble prize winning physicist that had an IQ of 127 and was refused by MENSA. MENSA is a politically motivated group of snobs that aren't all that smart, trust me.

If your IQ is truly 135, you are near genius, 130 used to be considered genius, now 140 is genius.

Get over it.

High-IQ Definition


110 = top 1/3rd of population; about average for HS grads, but only 50-50 chance of college graduation
115 = superior IQ (top 1/6th); approximate average for individuals in professional occupations
120 = potentially gifted (top 10%); average for college graduates
130 = borderline genius; eligibility for Mensa (top 2%); average IQ of most PhD recipients

High-IQ Definition


140 = genius level IQ (top 1%); about average for PhD’s in physics or who graduate Phi Beta Kappa
150 = Fewer than 1 in 10,000 this high
160 = eligibility for Four Sigma Society; 1 out of 30,000 score this high
165 = 1 in a million; eligibility for Mega Society
228 = Record IQ claimed by columnist Marilyn Jarvik (née Vos Savant)

http://webcache.googleusercontent.com/search?hl=en&rlz=1T4GGLL_enUS339US339&q=cache:8PWSbtQYJrQJ:http://psychology.ucdavis.edu/Simonton/GeniusCreativityTalent.ppt+140+IQ+is+genius&ct=clnk

 

[HeLiXe]

Yeah I supposedly have a high IQ and I think I'm one of the dumbest ppl on this forum

IQ is not as important as your ability...if you are good in maths and love it go for it! :)

 

[flyingpig]

If you had met my professor teaching us a 3rd year course, you wont' feel so bad.

 

[Bourbaki1123]

Ok, first, online IQ tests are junk. Only an IQ test administered in person by a psychologist is acceptable. It can take 5-9 hours to take.

There was a noble prize winning physicist that had an IQ of 127 and was refused by MENSA. MENSA is a politically motivated group of snobs that aren't all that smart, trust me.

If your IQ is truly 135, you are near genius, 130 used to be considered genius, now 140 is genius.

Get over it.



http://webcache.googleusercontent.com/search?hl=en&rlz=1T4GGLL_enUS339US339&q=cache:8PWSbtQYJrQJ:http://psychology.ucdavis.edu/Simonton/GeniusCreativityTalent.ppt+140+IQ+is+genius&ct=clnk

That chart is nonsense. 120 for an average college graduate? Surely that is based on some handful of flawed and out of date surveys that no longer have any validity. Also, Vos Savant's score was 228 on an outmoded ratio scale, and probably extrapolated to boot since no tests have ever had a ceiling that high. All of these astronomical scorers have been hardcore puzzle enthusiasts and kooks (look at Christopher Langan, and consider that Vos Savant had the audacity to challenge Wiles' proof of Fermat's last theorem with the most outlandish objection imaginable).

It may be possible to measure potential genius with a test, but not one based on a testing modality stuck in the 19th century with some superficial tailoring every few decades.

Also, you should be aware that your iq score can have a pretty wide level of variance; one day you might score 118, the next you might score 140 and the next 126. Multiple factors affect performance, so they typically take the highest score. Someone might score 130 and write a bunch of practice exams and go into the WAIS next week and score 150, then suddenly they can claim that they have an IQ of 150! There is some degree of train-ability there, especially if you took the test when you were young or only took it once. That further undermines the validity of the test.

 

[Cuauhtemoc]

I am thinking of my experience in (grant) administration. Once a number had been put on something, it became thereby Scientific. Sacred. Unchallengeable.

Pretty much this, just because it's a number people think it's some exact, sacred thing.
Psychology is not an exact science, it does have it's merits but they also make tons of mistakes and can't explain much.
It's not politically correct to say it's useless, but I can guarantee it's also far from perfect.


And if the OP took an online test, c'mon, these are even worse, they're pure junk.

 

[Mathguy15]

I know this sounds awful. I know this is just a bunch of whining to you guys, but this really upsets. I have almost entered a state of depression, simply due to this issue.

Im a 17 year old high school student, living in denmark. I live and breathe mathematics! It is my passion, my way of life, and i feel it always will be. It is my greatest hobby, and my dearest pastime. And like luther, i have a dream - i want to obtain a math PhD, and become a mathematician working with mathematical research and teaching at college. I want to become a college professor so hard, that its basically all i care about.

There is just some complications involved in my dream:

1. My iq is approx. 135. When i first found out, it was devastating to me. I had done a lot of reading about mathematicians, and to me it seemed like you would have no chance what so ever to be competitive in higher end mathematics, if you are not 150+. I have tried to forget that i am of low intelligence, but i simply can't. Everytime i work with math, i am always reminded reminded that i am not smart enough to accomplish my goal.

2. Instances have been seen, where low iq ppl (like feynman) are excellent at their field of study. This is just not my case - i have never been a child prodigy, learning calculus at age 12 and so on. I did teach myself calculus at age 16, but that is only 1 year prior to our high school introduction to the subject. It seems that i am of low intelligence, and i do not have a mathematical talent.

3. People around me keep saying that if someone can complete a math PhD, then it must be me. This is of great annoyance to me! Out of all the 600 pupils on my school, i am the best at mathematics. I teach in the schools "homework help cafe", even the 3. year students despite the fact I've just started 2nd year. My math teacher says i am the most brilliant math student he has encountered in 20 years of teaching A level high school math (the 3 year course).

I have created proofs on my own for the Taylor series, the arc length formula etc. I can solve differential equations such as y''(x)+xy'(x)+y(x)=0 by series solutions and understanding what i am doing.

In my head the guy described in the above paragraphs sounds like someone capable of completing a math phd - but the truth is, that's not enough! Why is it that in our subject, mathematics, you have to be an utter genius in order to qualify for a phd program? You can't imagine how discouraged i get, when i read about studying mathematics on the internet. Higher education math seems to be something reserved for the high iq geniuses, and the rest might as well just apply for another job. Why do you have to be able to complete your bachelor at age 10 in mathematics, but not in other fields? I am no child prodigy. I am just a young guy, with a passionate dream about contributing to the world of mathematics.

This text turned out to be one big whine i know - but this issue is ruining my life. You guys - who are so unfairly gifted - have no idea what it is like to have a mind that is so determined to contribute to mathematics, but is simply lacking the raw processing power to do so. I would give everything for a drug capable of eradicating my passion. This sounds horrible, but you have no idea how hard it is to want something so much, but knowing you will never be able to achieve it.

Im sorry, but i had to get this out to someone who understands me. Everyone around me seem to think I'm crazy. If i couldn't complete a math phd, who could? The answer is: The prodigies, the naturals and the people who are born to do maths. I cannot say that i am among equals on this board, but at least i am among people, who understand my deep frustration. Imagine if your mathematical talent was taken away from you, leaving only the deep desire to do and practice math - how would you feel?

Hiya! You seem like you are really depressed about your IQ. I felt the same way, last year even(though it was an order of magnitude less serious)! My IQ was around where yours is (though it is a bit lower). I want to be a mathematician also. There are some great quotes from Fields Medalists (highest honor in math) and Wolf Prize winners(very prestigious) that comment on the notion of genius.

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

There were a few quotes that interested me in particular. These are the ones by Tim Gowers, William Thurston, and Alexander Grothendieck. As it turns out, Grothendieck had similar doubts to yours! He is considered one of the greatest mathematicians of the 20th century! So, always remember that IQ is only a number. You can't let some number on some useless test determine where you are going to go in life! The only way you can determine if math is no good for you is to try some math. This you have done, pretty well too!

 

[Fredrik]

I must say, you guys have really helped me to get a better view on all this. You have encouraged me to at least attempt a shot at my dream. I will do everything to get the education i need

I'm glad to hear that. If you're that passionate about mathematics, you should definitely pursue it, even if there's just a 1/3 chance that you'll be able to make a career out of it. (If you work hard, I think your chances will be much better than that).

And you might also be right about the iq thing - i sat down in order to think rationally for a moment about the whole iq setup. Why is it, that i let one number, obtained from some stupid internet mensa test, control my life. Why is it that number to decide whether i am capable or not? Screw the iq

That's the right way to think. There are lots of other things that affect how successful you will be.

i just hope its a coincidence, that *almost* all mathematicians have a very high iq.

I'm not convinced that they do. I would guess that almost all of them are above average, but the "very high" numbers that you have seen are probably at least in part a result of some kind of selection bias: You are more likely to hear about the ones who scored really well.

You have really helped me get over my iq obsession - it might seem like nothing to you guys, but the feeling of your future being decided by one single number is horrible. I will not let that number rule my life. I will put no more significance into iq, and i will forget my stupid test result.

Good.

The only doubt that i have left, is whether i will be able to complete a phd - my doubt roots in the fact that, if I've got it correctly, when you pursue a phd, you have to come up with something NEW. If the most brilliant of minds struggle with coming up with something new, then how am i suppose to do just that, when i am no match for them?

It's not like you're going to have to come up with an entirely new branch of mathematics, or solve problems that were written down a hundred years ago and have remained unsolved since then. If you work hard on trying to understand the mathematics you're studying, you will probably come up with questions that the books and articles you're reading aren't answering, or even asking. What you're going to have to do is to answer a few of those on your own.

I seriously consider getting some professional help with the self-esteem complications - as stated before, it has come to a point where it inhibits other aspects of my life aswell.

I know very little about what therapists can do, but this sounds like a good idea. You need to have someone to talk to that can help you put things in perspective. I'm not worried that your IQ will be a significant problem for you when you study, but a depression might be an enormous problem. If you get so depressed that you're unable to study for long periods of time, then you're basically ****ed. By the way, it might be a good idea to not reveal to your professors just how passionate you are about mathematics. It's OK to show that you're interested, but if you let them know that it's all you care about, they will demand so much more from you than from others. If you get mediocre results during times when you're depressed, they will think that you are a lot less capable than you really are.

And if i barely make my phd, then I'm afraid i won't be smart enough to get a job. I do have plans on starting a family in the future, and how is a vacant mathematician, not being capable of acquiring a job, suppose to provide for x number of kids?

I very much doubt that math PhDs who fail to get professor jobs remain unemployed very long. You might end up making more money this way. You might want to look for threads about this topic. It has probably been discussed before. If you don't find any good information, consider starting a separate thread about it.

I don't think i will ever be able to contribute to mathematics - so far all I've done is learn topics, which smarter people invented.

What makes you think it's not like that for everyone who hasn't spent at least six years at a university? The days when a patent clerk could come up with a new theory of physics are long gone.

 

[Johannes]

Proving general relativity wrong, come on. Of course the Institute for Advanced Study and Indiana University are encouraging him to play with Physics, but of course, if your 4 year old daughter teaches herself how to read and write (which happens quite often compared to calculus, I admit) you won't point out every of her spelling mistake. I am still not sure if this is the right environment, I'd rather see him in the hands of skilled pedagogues until he's like 14. I guess, if you get too smart before you get mature, you might just turn out to be insane. Look at Wolfram for instance, he was about on the same track, but look what happed. He left university because they did not want him to be the only "genius" to work the pre-Mathematica, making him a millionaire but Mathematica fare below it's potential it could have had as a freeware research project. Now he is standing there claiming he practically himself came up with complexity theory and thinks he has already found the Theory of Everything with Mathematica. Everybody is laughing at him but he stands there saying "look at me, I'm a genius".

 

[Kevin_Axion]

In his book Mathematics: A Very Short Introduction, Fields Medalist Timothy Gowers writes

While the negative portrayal of mathematicians may be damaging, by putting off people who would otherwise enjoy the subject and be good at it, the damage done by the word genius is more insidious and possibly greater. Here is a rough and ready definition of genius: somebody who can do easily, and at a young age, something that almost nobody else can do except after years of practice, if at all. The achievements of geniuses have some sort of magic quality about them - it is as if their brains work not just more efficiently than ours, but in a completely different way. Every year or two a mathematics undergraduate arrives at Cambridge who regularly manages to solve a in a few minutes problems that take most people, including those who are supposed to be teaching them, several hours or more. When faced with such a person, all one can do is stand back and admire.

And yet, these extraordinary people are not always the most successful research mathematicians. If you want to solve a problem that other professional mathematicians have tried and failed to solve before you, then, of the many qualities you will need, genius as I have defined it is neither necessary nor sufficient. To illustrate with an extreme example, Andrew Wiles, who (at the age of just over forty) proved Fermat's Last Theorem (which states that if x, y, z, and n are all positive integers and n is greater than 2, then xn + yn cannot equal zn) and thereby solved the world's most famous unsolved mathematics problem, is undoubtedly very clever, but he is not a genius in my sense.

How, you might ask, could he possibly have done what he did without some sort of mysterious extra brainpower? The answer is that, remarkable though his achievement was, it is not so remarkable as to defy explanation. I do not know precisely what enabled him to succeed, but he would have needed great courage, determination, and patience, a wide knowledge of some very difficult work done by others, the good fortune to be in the right mathematical area at the right time, and an exceptional strategic ability.

This last quality is, ultimately, more important than freakish mental speed: the most profound contributions to mathematics are often made by tortoises rather than hares. As mathematicians develop, they learn various tricks of the trade, partly from the work of other mathematicians and partly as a result of many hours spent thinking about mathematics. What determines whether they can use their expertise to solve notorious problems is, in large measure, a matter of careful planning: attempting problems that are likely to be fruitful, knowing when to give up a line of thought (a difficult judgement to make), being able to sketch broad outlines of arguments before, just occasionally, managing to fill in the details. This demands a level of maturity which is by no means incompatible with genius but which does not always accompany it.

Case closed.

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

 

[Angry Citizen]

Why do you care about IQ? You haven't failed yet, so I'll echo the fellow earlier who said to start drinking coffee and proving theorems.

Let me give you a pep talk. You are far, far better at mathematics than I am. I am twenty years old, a sophomore in engineering taking a differential equations course, and to this day I'm fuzzy on the mechanics of Taylor series. Not only can I not prove it, I can hardly do it. The sad thing is? I'm one of the better ones in my class (which is not made up entirely of engineers).

But if I'd gone to a different school with more lax requirements for a second degree, you can bet your depressed *** that I'd be doing a degree in math on top of my degree in aerospace engineering. Why? Because I enjoy math. I think generalized solutions and proofs are very exciting. The thing I'm most proud of in my college career so far is proving a theorem from vector calculus, not anything to do with engineering. You've got the drive and the skill to be at the very least a mathematician. Anything beyond that (read: good mathematician, great mathematician, famous mathematician, etc) is icing on the cake. Do what you love, and go take a piss on that IQ test.

 

[Bourbaki1123]

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

Ditto. http://lesswrong.com/lw/2ub/discuss_how_to_learn_math/" might also be enlightening for the aspiring mathematician.

 

[hansenscane]

I am in a somewhat similar situation (being a high school student who studies and does so called "advanced mathematics" due to my own intrinsic love of the subject). I am not a prodigy, seeing as I only gained a love for mathematics at around the age of 14/15 (when I started doing it on my own). This naturally causes me to doubt whether I have innate mathematical skill at all. The way I deal with these thoughts of doubt is fairly simple: I just do mathematics. If you let yourself think these self deprecating thoughts, they will only eat away at you, distracting you away from what you really want to be doing: math.

As for whether you "have what it takes to get a PhD", I would suggest not worrying about that. You're in high school. You have plenty of time to work out all the career stuff later. For now just think about mathematics purely intrinsically, not in terms of what it might give you materialistically (career, prestige etc.). Thinking about such extrinsic things excessively can only lead to delusions of grandeur or fatalistic depression.

I hope this was of some help. :)

 

[Cruikshank]

There are 1,000 or so different kinds of intelligence. Which ones have you measured? Do you have perfect pitch? Can you catch a ball like a pro baseball player? Are you red-green color blind? Can you spot a pattern in a list of numbers? Can you spot a pattern in a list of words? Can you visualize in three dimensions? Can you predict emotional reactions of people to common events? What is your vocabulary? How many languages do you speak? Can you draw a mirror image of a given image? I could go on all day. IQ tests are worthless. Seriously. *Worthless.* According to those things, I got 31 IQ points stupider while attending my public school. Bzzt.

Whenever someone uses the word "better", always--ALWAYS--ask yourself, "at what?"
This is also useful for dealing with people with superiority complexes.

One suggestion, from someone who has been there...don't put your self-worth on your brain alone, let alone one narrow aspect of your brain! It hurts to consider you might not be "smart enough" to do some particular thing. It probably also hurts, at your age, to consider that you might not be "the very best ever" at math, and the ego often makes us think, "Well, if I can't be the best then it isn't worth doing at all!" But by that logic, just about everyone on the planet is nigh useless--and again, you should ask, "at what?" They aren't useless at their jobs. They aren't useless to their partners, or their kids.

As you grow older, you will learn that there are better ways to judge yourself...and eventually, you may learn that judging yourself is itself a waste of time you could be spending doing something more fun. Hang in there, kid.

 

[kings7]

There are 1,000 or so different kinds of intelligence. Which ones have you measured? Do you have perfect pitch? Can you catch a ball like a pro baseball player? Are you red-green color blind? Can you spot a pattern in a list of numbers? Can you spot a pattern in a list of words? Can you visualize in three dimensions? Can you predict emotional reactions of people to common events? What is your vocabulary? How many languages do you speak? Can you draw a mirror image of a given image? I could go on all day. IQ tests are worthless. Seriously. *Worthless.* According to those things, I got 31 IQ points stupider while attending my public school. Bzzt.

Whenever someone uses the word "better", always--ALWAYS--ask yourself, "at what?"
This is also useful for dealing with people with superiority complexes.

One suggestion, from someone who has been there...don't put your self-worth on your brain alone, let alone one narrow aspect of your brain! It hurts to consider you might not be "smart enough" to do some particular thing. It probably also hurts, at your age, to consider that you might not be "the very best ever" at math, and the ego often makes us think, "Well, if I can't be the best then it isn't worth doing at all!" But by that logic, just about everyone on the planet is nigh useless--and again, you should ask, "at what?" They aren't useless at their jobs. They aren't useless to their partners, or their kids.

As you grow older, you will learn that there are better ways to judge yourself...and eventually, you may learn that judging yourself is itself a waste of time you could be spending doing something more fun. Hang in there, kid.

Exactly.

 

[cobalt124]

...it might seem like nothing to you guys...

I don't think you would get this much response over nothing.

...And if I barely make my phd, then I'm afraid i won't be smart enough to get a job. I do have plans on starting a family in the future, and how is a vacant mathematician, not being capable of acquiring a job, suppose to provide for x number of kids?...

One step at a time. You are looking too far ahead. In a few years time you may see things totally diffently. Who knows? Long term ambitions are fine, but you have to focus on the "bits at the front" first.

But whatever happens, one thing you will gain is memories of doing something you love doing with all your heart.