Math Becoming a mathematician - how important is IQ?

[Sankaku]

Having a non-genius IQ will not keep you from becoming a mathematician, but confusing correlation with causation might!

Best reply so far...

 

[arildno]

3 years is arguable, but ahead - yes idd :) The funniest thing is, that it was right around christmas i decided to study ahead. It was actually then, where i decided to become a mathematician of the highest quality, and i realized the high school math wasnt enough atm.

Men som du nok har bemærket, så er jeg MEGET interesseret i faget :) Jeg ser næsten ikke tv mere, efter at jeg begyndte på mit "forløb" her for 1 måned siden haha !:) Dog irriterer det mig at vi her i danmark kun har 6 universitet .. Konkurrencen er virkelig hård, så der skal fandme skrives et ret så banebrydende bidrag, hvis jeg skal undervise på en af dem senere, hvilket er min store drøm !:P

Hei, Levis2!
Husk at du ligger minst 3 år foran de fleste av konkurrentene dine, så du burde ha meget store sjanser.

Forslag fra meg:
Snakk med læreren din. Han vet hvor god du er. Spør ham om han kan skrive et brev, eller noe slikt, til nærmeste universitet, at han har en unik elev (du!) som trenger konstruktiv veiledning i høyere matematikk.
Prøv å få i stand et møte med noen professorer på universitetet nærmest der du bor, og fortell dem hva du holder på med på egen hånd nå, og har fått til på egen hånd. De vil bli gledelig overrasket over ditt faglige nivå, det kan jeg nok garantere!

Disse vil være de beste til å gi deg forslag om hva du burde lese, og eventuelt, om det er mulig for deg å kunne få prøvd deg selv formelt i noen fag, selvom du ennå ikke har avlagt avsluttende skole-eksamener.

I'll take the rest in English:
You show unique abilities, and the best thing you can do for yourself is, by the help of others, to get a constructive environment of learning suited to your level.
Precisely because you are quite rare, you must be willing to make much of that environment for yourself, but with thoughtful guidance of professionals who are interested in helping you onwards. Your teacher is one such professional, and as I've said, I'm sure some professor at your nearby university will be delighted to help you.
You must be the one to try and find him, though.

 

[Levis2]

Hei, Levis2!
Husk at du ligger minst 3 år foran de fleste av konkurrentene dine, så du burde ha meget store sjanser.

Forslag fra meg:
Snakk med læreren din. Han vet hvor god du er. Spør ham om han kan skrive et brev, eller noe slikt, til nærmeste universitet, at han har en unik elev (du!) som trenger konstruktiv veiledning i høyere matematikk.
Prøv å få i stand et møte med noen professorer på universitetet nærmest der du bor, og fortell dem hva du holder på med på egen hånd nå, og har fått til på egen hånd. De vil bli gledelig overrasket over ditt faglige nivå, det kan jeg nok garantere!

Disse vil være de beste til å gi deg forslag om hva du burde lese, og eventuelt, om det er mulig for deg å kunne få prøvd deg selv formelt i noen fag, selvom du ennå ikke har avlagt avsluttende skole-eksamener.

I'll take the rest in English:
You show unique abilities, and the best thing you can do for yourself is, by the help of others, to get a constructive environment of learning suited to your level.
Precisely because you are quite rare, you must be willing to make much of that environment for yourself, but with thoughtful guidance of professionals who are interested in helping you onwards. Your teacher is one such professional, and as I've said, I'm sure some professor at your nearby university will be delighted to help you.
You must be the one to try and find him, though.

Now if this is the case, then that's what ill do. It would be awesome to have some directions from a professor about what i should study. The only problem is, that I'm only advanced in the topics i have studied by myself - if i were to take a test for university "classes" you might say, then i would probably be able to do okay in calculus and logic, but would problably not be able to pass in, let's say, vectors, which i haven't studied yet. But if i read all of the stuff, i might be able to though :) Could be cool to take weekend classes in higher math !

 

[arildno]

You are confusing mathematical maturity and level of knowledge.
Those are not the same, and it is with respect to maturity that you already are on a university level, from what I've seen.
The professor (AND your regular teacher at school) can easily help you fill in the relevant bits of knowledge, and you'll master them easily enough.

Hopefully, there ARE weekend classes in higher maths.

In a somewhat longer perspective, your school might be willing to give you, say, a few hours off to attend classes at the university, if they are told from a professional there that you are mature for that level of learning (based on what he has learned about you).

As I mentioned to you, your first step is to have a meeting with your teacher, and see if he is willing to help you contact the university in a constructive manner.
He is the person around you best able to gauge your abilities at the moment, and give a convincing argument to the university why they should be interested in helping you.

 

[Levis2]

You are confusing mathematical maturity and level of knowledge.
Those are not the same, and it is with respect to maturity that you already are on a university level, from what I've seen.
The professor (AND your regular teacher at school) can easily help you fill in the relevant bits of knowledge, and you'll master them easily enough.

Hopefully, there ARE weekend classes in higher maths.

In a somewhat longer perspective, your school might be willing to give you, say, a few hours off to attend classes at the university, if they are told from a professional there that you are mature for that level of learning (based on what he has learned about you).

As I mentioned to you, your first step is to have a meeting with your teacher, and see if he is willing to help you contact the university in a constructive manner.
He is the person around you best able to gauge your abilities at the moment, and give a convincing argument to the university why they should be interested in helping you.

yeah i just realized that i was confusing those two terms as well :) But how does the university/teacher gauge my mathematical maturity, if they are not to gauge them on my knowledge? Is it a teachers instinct?

And attending university (if I'm able to, university aint elementary school:) classes would be a dream coming true!

 

[arildno]

By seeing,relative to other kids your age, what you are competent at, not the least what you've managed on your own.
THAT's the indicator for level of maturity.

And teachers have certainly an "instinct" for that, an instinct distilled from many years of experience, so that they know what they normally can expect from a 16-year old and what is extremely uncommon.

However, it might be that the most that you can hope for is a few conversations with professionals who can give you good,relevant reading tips.

That should be a realistic goal, and quite attractive in itself, agreed?

I believe that lectures at Danish universities are public and, in principle, open for all to listen to.
But it doesn't follow that your school will allow you attendance in school time, or that it is possible for the university to regard you as a regular student (for example, grading papers, allowing you to sit exam and so on).

But there is no harm in exploring such possibilities, is there?

PS:
Ask your Mom and Dad as well. Moms and Dads want to be involved in such decisions, that's their nature...

 

[Levis2]

By seeing,relative to other kids your age, what you are competent at, not the least what you've managed on your own.
THAT's the indicator for level of maturity.

And teachers have certainly an "instinct" for that, an instinct distilled from many years of experience, so that they know what they normally can expect from a 16-year old and what is extremely uncommon.

However, it might be that the most that you can hope for is a few conversations with professionals who can give you good,relevant reading tips.

That should be a realistic goal, and quite attractive in itself, agreed?

I believe that lectures at Danish universities are public and, in principle, open for all to listen to.
But it doesn't follow that your school will allow you attendance in school time, or that it is possible for the university to regard you as a regular student (for example, grading papers, allowing you to sit exam and so on).

But there is no harm in exploring such possibilities, is there?

PS:
Ask your Mom and Dad as well. Moms and Dads want to be involved in such decisions, that's their nature...

In my case it might just be the majority of the other students in my class that share a mathematical disability lol .. i don't know, but compared to them, I'm 10 years ahead lol :)

And reading tips would definately be of imminemt value! And you are correct, that the university lectures are open to the public, but i don't think my school would tolerate the absence :) My chemistry teacher thought that it was ridicolous for my to stay on 1st year chemistry, so he wanted to move me to 2nd year. This was not possible, because i would then be registered for 1 year absence in my regular chemistry clases lol .. And that will get me expelled :)

I just think it would be hard only to attend the lectures at a university - i really can't say since i haven't been to one, but i could imagine that the exercises they do as well will make the information stick. Might be hard to get a good understanding without them, especially for a 16-year old !:) But if i am allowed by my school, i will definately take advantage of the opportunity.

 

[arildno]

It seems that your science teachers know exactly how outstanding you are.

Now, school rules are to be followed. But in following them, they might on occasion..bend a little bit..

In particular if someone with scientific authority outside the local school environment (say, a university professor) can confirm, through his observations what the level of your abilities are right now.
That would carry some punch with the head-master, in connection with your regular science teachers' assessments.

But, anyhow, I think your first step is to have a good, long talk with your regular maths teacher, and explore realistic options for self-study and getting contact with university people.
I'm sure he already has a bad conscience about you; his job is to help ALL his students, but within the strictures of the normal teaching duties, he is at a loss for helping you on YOUR level at the same time as well.

You're quite right that self-study has its limitations.
But it will be much you CAN study on your own profitably, and a professional can help you sort out which themes you ought to begin with (i.e, suitable for self-studying)

 

[arildno]

And, Levis2:
Reproducing theorems of Archimedes, setting up proper diff.eqs and developing a correct formula for arc lengths are NOT common among 16-year olds, it is quite unique, IMO.

 

[Levis2]

And, Levis2:
Reproducing theorems of Archimedes, setting up proper diff.eqs and developing a correct formula for arc lengths are NOT common among 16-year olds, it is quite unique, IMO.

It probably isn't .. most of the guys in my class are fighting adding two vectors with each other, so probably not :)

 

[arildno]

So, you DO know a little bit of vectors already!

I'm not so sure you would find that part of the university maths particularly hard to follow.

 

[Levis2]

So, you DO know a little bit of vectors already!

I'm not so sure you would find that part of the university maths particularly hard to follow.

yea you know, add, substract, multiply with a number, how vectors are defined by a*vector-i including the proofs (lol worlds simplest haha:) etc .. Orthogonal vectors and so on :) Not enough for college though.

 

[arildno]

One more thing to remember:
When YOU prove some theorem that already has been proven before, it doesn't follow that the guy making the first proof was smarter/more professional than you.

Thus, when doing proofs or devoloping formulae, remember that you are not just training to become a mathematician, you are being one as well!

 

[annelies 123]

Hi!
I think that I'm really understanding your situation.. I'm also 16 years old, but I'm already tested when I was young and I'm having an IQ that is more than 140, my parents don't want to tell the exact results of the test. So I skipped 2 classes and now I'm at University and I'm studying maths. But even I'm sometimes thinking will I be good enough to reach something with maths.. I still don't know but I'll hope so.. For now I'm still before my classmates they have to study for it every day and for me just paying attentions in the lessons is already good enough.. The reason for me why I couldn't be much betteris because languages and things like that couldn't interest me so I negliged it in primary and secondary school but after some time everyone has to work a little bit so I didn't have the time to study math at myself.. If you can I'll surerly say do that! Competing in national and international matholympiads is also great I think.. Try it, I can't compete anymore cause you can't be participating and already be at high school..

I can also tell you a story from someone else, he's only 16 too but he's just in the normal class at school. At home he learns lots about maths I think if he should make examens of the first year at university that he would have enough points.. He's learning so much.. Last year he went to the IMO but didn't got a medal but that's kind of logic he was only sixteen and other people were already 18 or sometimes 19..
If you have some questions I'd love to answer cause I think I'm in the samen situation..

 

[Brandon_R]

Don't worry about your scores on the IQ Test. As Mark Twain puts it, there are three kinds of lies in this world - lies, dammed lies and statistics. If you have the passion to learn mathematics, then by all means follow it.

 

[annelies 123]

Don't worry about your scores on the IQ Test. As Mark Twain puts it, there are three kinds of lies in this world - lies, dammed lies and statistics. If you have the passion to learn mathematics, then by all means follow it.

I'm following it ;) but you even have kind of reliable test on the internet http://www.mensa.org/workout" is the best site I've found.. it says not your IQ but wether you could be highintelligent. To be sure you have to do some real test and so on..

 

[micromass]

I'm sorry, but there is no internet IQ-test that is reliable. Not even the mensa-test. IQ-testing is a very standardized procedure, and anything not following that standard, can not be reliable.
I have serious doubts about the tests validity and unbiasedness...

 

[annelies 123]

I'm sorry, but there is no internet IQ-test that is reliable. Not even the mensa-test. IQ-testing is a very standardized procedure, and anything not following that standard, can not be reliable.
I have serious doubts about the tests validity and unbiasedness...

okay I haven't done research on he reliabilty but if i say you that I've recomended this test a couply of times to peught they might by hyperintellingen. the test has always been right in the cases i know. after that most of them did a qualified test and it gave the same results ;)

 

[elfboy]

Hello - I am a 16 year old danish boy. I'm in what is equivalent in denmark to the 10th grade in the US, and i simply love math. It's funny though, since before i attended 10th grade, i dreaded math due to it being so boring - but i think that was due to the simple arithmetics we did in my previous school. Once i encountered a more pure math in 10th grade, i was sold!

My number 1 goal in this world - the thing that matters most to me - is becoming a mathematician. I want to take a phd in math, and teach at a university, and if I am lucky, end up making a useful contribution. That's what matters most to me of all things atm.

But there's a problem - I am not a child prodigy. I can't do topology or real analysis, and my iq is only 130 ! Ever since i took that iq test, i have been so scared of not being able to make contributions to math, or even complete my degree in college. I'm afraid that it will get too complicated when I'm not that intelligent.

Funny stuff is though, that i have taught myself basic calculus, and can set up differential equations on the saltconcentration in, let's say a lake, based on differences in in-and-out flows of water etc. My teacher says he's never seen anyone like me in 9 years of teaching in high schools, but i presume he hasn't met any real good mathematicians lol .. I have also invented a formula by myself for calculating the area of a triangle if one only knows its sides. It looks this this;

A=1/2*c*squareroot(a^2-(c-(b^2+c^2-a^2)/2c)^2)

Where c has to be the biggest side in the triangle. The order of a and b doesn't matter :) All of this is easy stuff though ... nothing worthy a true mathematician :(

Now my question is, can i take a phd in math and become a mathematician, even though I'm not that intelligent? And if I'm barely able to do my phd, will i then be a garbagety and lousy matehmatician ?

it's a thought that takes up a lot of space in my head atm .. I'm so worried that i won't be able to take a degree or contribute to the art of mathematics :(

Help!

you have along way to go

to succeed in math you must work very hard

 

[Waxbear]

Hey Levis. I am a dane too, and i am currently on my first year of a bachelors degree in physics. I just took my exam in Linear Algebra today (i noticed your remark on how simple vector operations are :) ) and i feel that i can safely tell you, that if you are already this proficient with mathematics (just the fact that you know enough calculus to be constructing differential equations) and if you continue to challenge yourself like this until you reach your first year of university, you are going to have a pretty easy time here.

by the way, I am studying at KU. What gymnasium are you at?

 

[Levis2]

Hey Levis. I am a dane too, and i am currently on my first year of a bachelors degree in physics. I just took my exam in Linear Algebra today (i noticed your remark on how simple vector operations are :) ) and i feel that i can safely tell you, that if you are already this proficient with mathematics (just the fact that you know enough calculus to be constructing differential equations) and if you continue to challenge yourself like this until you reach your first year of university, you are going to have a pretty easy time here.

by the way, I am studying at KU. What gymnasium are you at?

Im at HTX Slotshaven EUC in holbæk :)

Just to give you guys an update; I contacted my teacher, and he was feeling the same way you guys were. He has asked the advisors at the university of Copenhagen, whether i would be able to start even though i haven't got a high school exam. Usually you can, if you can show the same qualifications as one with a high school exam - this is not a problem in math, but I'm not that good in danish class... So i can't be admitted this way. The advisors are currently working on getting me admitted through somekind of loop hole in the university regulations. If that's not possible they will attempt to get me a dispensation.

If all this works out - and I'm afraid it's not possible though - i will most likely be able to start university after the summer break :) If so, i will by then have read all the mathematics for high school, so I'm able to follow and complete any kind of admission tests, they might give me :)

 

[Einherjer]

Okay, first of all. Your IQ is so profoundly irrelevant that it is hard to even get started. The IQ only measures one thing, and that is your ability to solve IQ quizes. A skill like any other. If you train consistently on IQ quizes anybody can get an 300 IQ score.

You can't do statistics with only one data point.

 

[qspeechc]

Hi Levis2.
I have some book suggestions if you are interested. Have you done Euclidean geometry with proofs? This is really where mathematics starts. If not may I suggest Harold Jacobs' Geometry:
https://www.amazon.com/dp/071671745X/?tag=pfamazon01-20
(better than his Geometry: Seeing , Doing, Understanding.). If you think that is too simple then try Moise's Elementary Geometry from an Advanced Standpoint:
https://www.amazon.com/dp/0201508672/?tag=pfamazon01-20

Some other books to read before you start calculus:
Principles of Mathematics by Allendoerfer and Oakley (2nd edition or later). Covers high school math up to the point where you can start studying calculus, but written for bright young students like yourself.
What is Mathematics? by Courant (you don't need the updated version by Stewart). Written by one of the greatest teachers ever. Will start you thinking like a mathematician.

Good luck and work hard.

 

[inknit]

Kid, calm down. If math is your passion, by all means pursue it, but don't make your life goal becoming the next Einstein.


Btw, if you're really intelligent, why not study theoretical physics?

 

[Shackleford]

Kid, calm down. If math is your passion, by all means pursue it, but don't make your life goal becoming the next Einstein.


Btw, if you're really intelligent, why not study theoretical physics?

Yeah, maybe he can fix the Riemann integral.

 

[elfboy]

i recommend watching the big bang theory for some career ideas for high iq people like yourself

 

[mal4mac]

In high school, Feynman's IQ was determined to be 125, according to his biographer Gleick. I listened to a debate about this on the radio recently where some psychologists said if anyone has an IQ greater than about 120/130 they can do any job - mathematician, physicist, even psychologist :) More than that doesn't matter, what really matters is *hard work*, finding the right opportunities, interacting well with teachers and peers - so keep posting here, and keep in touch with that nice teacher. Ask him the same questions you ask here, try and find out the best universities to go to, what classes to take and so on... Read Feynman's biography, or those of any other great scientists, note how they always had great mentors, friends, and studied/worked in the right places. I never did. I should have tried harder to find the right people & places! At worst you might fail to become a research mathematician, but you will easily find a job as a maths teacher, quant or IT support person - none of which are bad options (ask your teacher!) And, from experience, I can say that programming/IT support can be a good fall back...

 

[Clairut]

Kid, calm down. If math is your passion, by all means pursue it, but don't make your life goal becoming the next Einstein.


Btw, if you're really intelligent, why not study theoretical physics?

That's the most intelligent comment I've heard...Sometimes we just forget about enjoying ourselves..instead we try to be the best..Levis..if you're trying to find a reliable test try Strict Logic Sequence Examination by Jonathan Wai...I was tested when i was 15..scored around 167(sd=15)...But i will never reach my goal...Living in my own world of fantasy..Without any real passion for anything..

But reading about you..i keep asking myself..What am i doing with my life?
I wish i was you...

 

[aneesh.mulye]

Hello - I am a 16 year old danish boy. I'm in what is equivalent in denmark to the 10th grade in the US, and i simply love math. It's funny though, since before i attended 10th grade, i dreaded math due to it being so boring - but i think that was due to the simple arithmetics we did in my previous school. Once i encountered a more pure math in 10th grade, i was sold!

My number 1 goal in this world - the thing that matters most to me - is becoming a mathematician. I want to take a phd in math, and teach at a university, and if I am lucky, end up making a useful contribution. That's what matters most to me of all things atm.

But there's a problem - I am not a child prodigy. I can't do topology or real analysis, and my iq is only 130 ! Ever since i took that iq test, i have been so scared of not being able to make contributions to math, or even complete my degree in college. I'm afraid that it will get too complicated when I'm not that intelligent.

Funny stuff is though, that i have taught myself basic calculus, and can set up differential equations on the saltconcentration in, let's say a lake, based on differences in in-and-out flows of water etc. My teacher says he's never seen anyone like me in 9 years of teaching in high schools, but i presume he hasn't met any real good mathematicians lol .. I have also invented a formula by myself for calculating the area of a triangle if one only knows its sides. It looks this this;

A=1/2*c*squareroot(a^2-(c-(b^2+c^2-a^2)/2c)^2)

Where c has to be the biggest side in the triangle. The order of a and b doesn't matter :) All of this is easy stuff though ... nothing worthy a true mathematician :(

Now my question is, can i take a phd in math and become a mathematician, even though I'm not that intelligent? And if I'm barely able to do my phd, will i then be a garbagety and lousy matehmatician ?

it's a thought that takes up a lot of space in my head atm .. I'm so worried that i won't be able to take a degree or contribute to the art of mathematics :(

Help!

A few observations:

1) IQ is important for mathematical success, no doubt.
2) However, IQ is not stable until the ages of roughly 18 to 21. So the IQ at your age is pretty meaningless, though at 130, highly, highly encouraging - look instead at your results, which seem pretty impressive to me. And there are things you can do to improve it in the short term. (Like exercise, the trick is to keep doing them consistently, so the `short term effect' never effectively ends.)
3) An IQ of 130 is two stddevs above the mean; combined with hard work, this should more than suffice to allow you to get a doctoral degree and teach at the university level. (Original contributions are inherently unpredictable, so I would not suggest worrying about them right now.)
4) Domain knowledge plays a large part in success, even more so in academia. With experience, you will find your mathematical ability increasing. Given how high it is now, that is a VERY good thing.
4) Finally, knowing that you're this far ahead of your age range, and if you're willing to work with dedication, I can say with some confidence that a) your mathematical IQ WILL improve with time, and will perhaps easily reach into 145+ range, and b) you will not have a problem with your further education AS LONG AS you work consistently.



In sum: go for it!

 

[nickadams]

THis is like the 4th time I have seen this thread posted.