# Becoming a mathematician - how important is IQ?

• Math
• Levis2
In summary, the conversation is about a 16-year-old Danish boy who loves math and aspires to become a mathematician. He struggled with math in the past but has found his passion in it through more advanced topics like pure math. He worries about his intelligence, as he is not a child prodigy and his IQ is only 130. However, he has taught himself basic calculus and can solve differential equations at a young age, which bodes well for his future in mathematics. He wonders if he can still achieve his goal of getting a PhD in math and becoming a successful mathematician despite not being a prodigy. The other person in the conversation reassures him that his love for math and inquisitiveness are more important than

#### Levis2

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!

Levis2 said:
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 !

Nobody would expect you to do topology and real analysis at 16 years old! But if you're aware of these subjects at such a young age, you have a very bright future ahead of you.

Levis2 said:
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.

Don't let an IQ test hold you back from doing what you love. To be honest, a lot of IQ tests aren't very good anyways. And the ones that are decent measure how good you are at thinking logically. Mathematics is filled with logic and a lot of it comes with time and understanding of the subjects.

Levis2 said:
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

If you're doing stuff like this when you're 16, you'll be fine. I taught myself calculus from a book when I was 18, and a teacher I had didn't believe I'd do well in AP (college-level) calculus because I skipped a class, but I rose to the challenge and did just fine in the class. What's great is that you're only 16 and studying this stuff.

Levis2 said:
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 sounds like you've got a lot of potential. Don't let an IQ test get in the way of what you want to do. A better question is how you do in your math classes?

IQ isn't the end all test(You should note that 130 isn't bad. You're in the top 5-10% of the population.). You can do anything you can learn to do. Differential equations for a 16 yo is crazy. That's awesome.

IMHO, love for the sciences, and inquisitiveness is the most important ingredient to a great mathematician.

I really want you guys to be right :) pretty much all i care about (besides girls lol :P) is mathematics .. And no 130 isn't low, but seen from a a top mathematicians perspective, it is really low.

I want to make a meaningful contribution, and become a good mathematician! I don't want to scrabe by, barely able to make it, and balancing on the edge of flunking out :(

Its because when i read about mathematicians who have made contributions, they have always been child prodigies or near to .. So my future doent look very bright :)

My GPA in math classes is A (or max here in denmark - don't know what it translates to in the US) but the stuff they teach in class is trivial, and not worthy of a mathematician :)

High IQ's are meaningless indicators of future success. That's all there is to be said.

Pengwuino said:
High IQ's are meaningless indicators of future success. That's all there is to be said.

meaningless in the financial world maybe - but i have always been told that iq almost exactly translates into mathematical ability? I hope you're right though :)

If that is true - and i hope it is - how come every great contemporary mathematician has an iq of >145-150? It's a strange coincidence then, nevertheless a good one :)

Levis2 said:
My GPA in math classes is A (or max here in denmark - don't know what it translates to in the US) but the stuff they teach in class is trivial, and not worthy of a mathematician :)

What's trivial to you might be very difficult to many other people. It's good that you want to do really well, but don't worry so much. Go out and play some basketball. You'll be fine.

Levis2 said:
meaningless in the financial world maybe - but i have always been told that iq almost exactly translates into mathematical ability? I hope you're right though :)

If that is true - and i hope it is - how come every great contemporary mathematician has an iq of >145-150? It's a strange coincidence then, nevertheless a good one :)

Well you aren't going to find many "great" people with IQs of 85 and 95. Having such an IQ means you are part of a small but not minuscule part of society. To be a "great" person in any field, yah you probably are going to be part of that end of the bell curve but that end of the bell curve represents tens of millions of people. There are plenty of threads around that talk about how meaningless IQ tests are when you begin to move away from the 2 standard deviations.

Levis2 said:
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!

Hey Levis and welcome to the forums

There are quite a number of people who weren't the so called "child prodigies" that saturates the history of our so called "genius" minds.

One example off the top of my head is the late George Polya. His last position if i remember correctly was at Stanford University. He actually did a law degree (and publicly noted how boring it was) before commencing study in mathematics.

Personally (and this is just my opinion), one of the more important traits, especially in a scientific field is to have a high level of curiosity, and also persistence. With genuine curiosity, you're bound to explore things deeply and find things that are unknown to the majority of people. The persistence part is just as crucial, because in most endeavors it separates the successful from the not so successful.

Also with regards to your IQ test, here is some trivia for you: A great mathematician (and also a qualified engineer) by the name of Henri Poincare failed an IQ test. If you're interested in more details go to a wiki site.

I think you need to be more confident in yourself. You need to be confident enough in pursuing your goals to an end, but not to the point where you are blindly arrogant. Its kind of like how children just try things because they are born not knowing what is possible and what isn't. Its unfortunate that we grow up and develop an attitude of just accepting what other people say is possible and stop then and there in our tracks.

So summing I guess the words, be curious, be persistent, and be healthily confident are my advice for you.

Do not EVER betray your great passions!
What are thinking, quitting maths because you fear you won't be good enough??

What are you planning to do, if NOT maths??

Vær tro mot deg selv.

Levis2 said:
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.

But... 130 is above average... You should have no problem with an IQ of 130. Where did you take that IQ-test anyway? You didn't take it on the internet, did you?

In fact, a high IQ doesn't mean anything in mathematics. What matters is:
- Work hard
- Be creative
- Be interested
As long as you are those three things, you shouldn't have any problem.

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 :(

Hmm, you have basically rediscovered Heron's formula: http://en.wikipedia.org/wiki/Heron's_formula The formula you gave, was first proven by Qin Jiushao. That's nice work.

But really? Doing differential equations at your age?? That's crazy! So you do differential equations, and you still think you're a bad mathematician?? Don't fool yourself, if you can do all of this at your age, then you will have a bright mathematical future!

I don't believe that intelligence can be accurately measured by an IQ-test. So if you didn't do as good as you wanted on an IQ-test, then don't worry! Intelligence can only be measured by your actions in life. And if you discorver Heron's formula and do differential equations at your age, then I've seen enough: you're obviously intelligent enough for mathematics...

Levis2 said:
I really want you guys to be right :) pretty much all i care about (besides girls lol :P) is mathematics .. And no 130 isn't low, but seen from a a top mathematicians perspective, it is really low.

I want to make a meaningful contribution, and become a good mathematician! I don't want to scrabe by, barely able to make it, and balancing on the edge of flunking out :(

Its because when i read about mathematicians who have made contributions, they have always been child prodigies or near to .. So my future doent look very bright :)

My GPA in math classes is A (or max here in denmark - don't know what it translates to in the US) but the stuff they teach in class is trivial, and not worthy of a mathematician :)

Did you know Richard Feynman "only" had an IQ of 126, but he managed to win the Nobel prize in physics. What you are doing at 16 is awesome, you are plenty smart enough, besides, motivation is 99% of success and you seem to have that in spades!

First rule, what ever you want to become don't ever put yourself down. Don't make a list of reasons why you won't make it. If you ask me I'd say IQ is just a figure. If you read about the great once in history, not only mathematics - a personal favourite is Immanuel Kant, you'll often find that they blossomed late in life. Not at 16. ;-) What made them great was the perseverance that gave them the chance of finally prevail. This lead to rule numero duae. Follow your passion! Without it you'll never be more than a day trader, whatever you do. Furthermore, with passion it's easier to be creative, which is good while tinkering with plus, minus and what have you.

An everyday example, I had problems learning how to read and write, still do to an extent. If I had listen to all the things said about me I'd never taken my exam in Engineering Physics.

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If you want your question answered by a so called 'child prodigy' who also happens to be one of the greatest contemporary mathematicians and also a fields medalist. Read this:

I am a senior university student in pure mathematics, who has the same ambitions as you. My experience is that even though having a sharp mind and a high IQ can sometimes help you solve problems faster and more easily (although some experts don't even believe in IQ), working HARD is FAR more important. But the important thing is that if you want to increase your odds of making it big in mathematics, you have to start NOW. There is usually two different approaches you can take. You can either try and learn a lot of new subjects and theories (generally not advised though better than nothing) or you can try and focus on competitions like Mathematics Olympiad. Although the subjects covered in Olympiad competitions are considered "Elementary mathematics" and greatly differ from what real research is like, I find them to be excellent for problem solving. So I recommend you compete (and do well) in as many competitions as you can.

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You should also note that most neuroscientists and psychologists agree that intelligence level can be helped by nature (read:genetics) but must be nurtured (read:hard work). It's something called brain plasticity. No matter how smart a test says you are, you can always get yourself to a higher level by spending your time working at it. There are very few people who are child prodigies, and a lot of highly successful people, even in mathematics, were not child prodigy super-geniuses. Find any person who's famous in mathematics, physics, or another difficult subject, I guarantee if you dig a little deeper you'll find that there was mountains and mountains of hard work to be done before they could get where they got.

Of course, you love mathematics. You have to keep working at it, and you have to believe that the harder you work, the smarter you get. Even if it turns out to be a crock, you're still helping yourself a lot. I, and many other scientists who study the human brain, think it's not a hoax, and think that you really can 'get smarter' through hard work. As long as you don't overwork yourself to the point of hating the subject and burning out, do what you can, and always make sure you're doing it because you love to do it.

It took Einstein 10 years to come up with GR, and he was not a child prodigy. Don't go imposter syndrome on yourself, have some confidence in your ability and potential.

OP, 130 is not "above average", but in the top 2% of the population (it's defined that way!). That means it is *very high*! Common understanding in psychology is that IQ 120 is sufficient to pursue any career in any field. This includes physics and mathematics.

The main factor in getting into the top levels is to do hard work, and a lot of it. Interestingly, this is precisely what is keeping many smart children from achieving any level of success: They stop once things get complicated, because they are not used to things being difficult, and it challenges their self-concept if they can't easily handle a problem:
http://www.highlightsparents.com/parenting_perspectives/interview_with_dr_carol_dweckdeveloping_a_growth_mindset.html [Broken]
http://nymag.com/news/features/27840/
(actually, there were some better articles on Carol Dweck's research, but I did not find any non-original articles in a hurry). This is also why in science, just like in any other field, you will typically find smart-to-very smart people (IQ 120-140) in top positions, but actual genius level intelligence is very very rare (I've yet to meet one such professor in person, and I work in a branch of theoretical physics!).

Becoming an expert is simple -- just constantly keep on improving your skills, never being satisfied. For 10 years or more. Note that this actually also applied to child prodigies like Mozart and the like. They just started earlier.

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cgk said:
The main factor in getting into the top levels is to do hard work, and a lot of it. Interestingly, this is precisely what is keeping many smart children from achieving any level of success

Hard workers can take advantage of opportunities but if one is not competitive, there will be limited opportunities. Innate ability does count, as well as opportunity, as well as hard work. If one has the ability and opportunities are there, hard work becomes sufficient.

It sounds like Levis2 has the ability, and with hard work he may make use of whatever opportunities there are, that is up to him.

At some point in time, grades would be meaningless for you anyway.
You could care less what IQ you have.

I once took something like 2-3 IQ tests, and I wasn't given any metric scale grade (even when I asked for it), I don't think genuine IQ tests which are conduceted by professional psychatrists give you any answer as for your grade.

Levis2 said:
And no 130 isn't low, but seen from a a top mathematicians perspective, it is really low.

This isn't true. Mathematicians are just human beings too, though I suppose some might argue

You don't need to be a 'genius' to make a meaningful contribution. I am not a genius, and I work in mathematics research. I work with some people that I do consider to be 'genius' - but the majority of us are just regular, every-day, human beings.

All that, and I would just totally ignore the result of an IQ test anyway. There's no point in letting some (essentially arbitrary) number define anything about you. My thoughts are that they are a remnant of an antiquated way of thinking about intelligence and how people process information.

Thx a lot guys .. This really gives me hope you know! The reason all this insecurity sprouted in my mind, is due to all the reading I've done. I keep reading about "great mathematicians", and it always follows that their iq is >145 .. They are always very good in an early age. Einstein may not have have been a true child prodigy, but from what I've read he was a VERY good math student even in his 13's. When i was thirten, i was doing stuff like this; 2x+15=1x .. This may have been due to my lack of interest at that time - i wasnt really interested in math, so i didn't have the drive to study to become better. I will never know if i would have been able to grasp more advanced content in that age ..

It may all root in my perfective nature - i want to be the best! I want to be the best in everything .. Approx 1 year ago, i got a whim about airguns. I saved up, and bought an airgun worth 2200$, because i wasnt satisfied with my garbagety gamo springer airgun .. 1/2 year ago, i had a whim about hunting, and i spent approx 3300$on weapons and equipment (yeah had to sell lots of stuff.. and i work a lot too) .. I always want to achieve and do my best! I'm a very stubborn person.

Therefore i am worried that i will simply be a mediocre mathematician, not brilliant enough to achieve his dream; teach in a university, and hopefully discover something of significance.

So my problem is, that i keep comparing myself to the "generel" image of a mathematcian, which is an utter genius, an image that is far superior to me. It's really demoralising to read about the great mathematicians, like Terry Tao, who simply is superior to me in every way .. I keep thinking how unfair it is, that they have been gifted with those superior abilities, and i have to fight my way through math with mediocre abilities. It's of great annoyance to me !:)

The IQ-test was conducted on the internet, but i was told that it should be a reliable test. It's suppose to be the same guy who made mensas test that made this one, atleast for all i know. This is not good though, since it's likely that i would score less on a genuine test.

But math is truly a passion of mine, and i intend to pursue it. I just don't know how to convince myself, that i will be able to phd in math and achieve my goals :S

Sorry for the length of this reply lol .. :)

Levis2 said:
Thx a lot guys .. This really gives me hope you know! The reason all this insecurity sprouted in my mind, is due to all the reading I've done. I keep reading about "great mathematicians", and it always follows that their iq is >145 .. They are always very good in an early age. Einstein may not have have been a true child prodigy, but from what I've read he was a VERY good math student even in his 13's. When i was thirten, i was doing stuff like this; 2x+15=1x .. This may have been due to my lack of interest at that time - i wasnt really interested in math, so i didn't have the drive to study to become better. I will never know if i would have been able to grasp more advanced content in that age ..

It may all root in my perfective nature - i want to be the best! I want to be the best in everything .. Approx 1 year ago, i got a whim about airguns. I saved up, and bought an airgun worth 2200$, because i wasnt satisfied with my garbagety gamo springer airgun .. 1/2 year ago, i had a whim about hunting, and i spent approx 3300$on weapons and equipment (yeah had to sell lots of stuff.. and i work a lot too) .. I always want to achieve and do my best! I'm a very stubborn person.

Stubborness is a very good quality in mathematics, you will need it. Say you can't find a solution to a math problem or say that you don't understand a theory that well, then it is stubborness that pulls you true

Therefore i am worried that i will simply be a mediocre mathematician, not brilliant enough to achieve his dream; teach in a university, and hopefully discover something of significance.

So my problem is, that i keep comparing myself to the "generel" image of a mathematcian, which is an utter genius, an image that is far superior to me. It's really demoralising to read about the great mathematicians, like Terry Tao, who simply is superior to me in every way .. I keep thinking how unfair it is, that they have been gifted with those superior abilities, and i have to fight my way through math with mediocre abilities. It's of great annoyance to me !:)

Please, don't say that you have mediocre abilities, if you say it long enough you will start to believe it. The truth is, you don't know your math abilities. You will only know them if you start doing mathematics.
But if you're already doing ODE's, then I can say that you don't have mediocre abilities...

And you don't need a high IQ to pursue math. Look at Henri Poincarre, one of the most brilliant mathematicians of our time!

The IQ-test was conducted on the internet, but i was told that it should be a reliable test. It's suppose to be the same guy who made mensas test that made this one, atleast for all i know. This is not good though, since it's likely that i would score less on a genuine test.

Enough said. A test on the internet is NOT reliable, no matter what they want you to believe. I repeat: a test on the internet is NEVER reliable. The real IQ-test involves much more then just "complete the sequence"-questions. And another thing: an internet IQ-test probably won't factor in you age, a real IQ-test will.
If you want to know your IQ, then DON'T believe this test: this test will lie to you... Go to a psychologist, they are the only ones that know how to get your IQ.

I hope that test is unreliable .. unless it gave me a higher score than i should have gotten :) I will never do an IQ test again.. if i should happen to score low, then i would properly underestimate my abilities even more, so i think it's best to just not do any iq-tests:)

Although i must admit, that i can't solve differential equations, unless it's simple integration. I can only make models of the real world involving a function and its derivative, you know models about mixing to substances etc... Hell, i haven't even had any classes what so ever in functions and graphs .. If i hadn't looked it up myself, i would know what a function is :) I have not yet looked up exponential functions etc, so i can't really solve ODE's. It's weird we haven't been taught anything about functions yet, which might be one of the, if not the, most important things in math.

One thing of GREAT annoyance occurred to me today .. I was told by my teacher, that archimedes had found a way to calculate the area under a parabola using triangles. I figured, that if that old man could do it, so could i .. :) So i started working on it, and i decided in my mind that i should divide the area into an infinite amount of triangles, and calculate the limit as the number of triangles went to infinity. But to get a rational result, i had to find a proportion between the first and the second triangles .. I made a crappy drawing, and was not able to measure a useable proportion between the heights in the trinangles. So i gave up - i thought i might have got the idea and principles wrong, and i looked it up on the net (when i try figure something out, i must do it myself .. otherwise it's not me who's done it:) and i found out, that i had simply made an incorrect measurement, and my thoughts had been correct all along.. So i measured it in geogebra instead, and i found a proportion between the heights in the triangles to be 1/8. Using this new info, i could calculate the area under a parabola with an infinite sum, where the number of triangles goes to infinity. so i made a formula :);

I have attached a word document containing the formula, since i couldn't post my maple screenshot in any other way .. :) I would appreciate if anyone could tell if it's correct. '

But i must admit, that i am ahead of most students in my school mathematically, but compared to Terry Tao and other great mathematicians, my abilities are certainly mediocre :P One cannot decide whether someone is good at math, just because he can easily do the math in high school .. it's too easy to determine that :) Even though i don't understand why the vast majority of students are almost frightened by my "line" (you can choose different "lines" of study, which are specified for your area and interest") which is Math and physics, with philosophy as a side-class. It's unbelieveable how bad the average student is in math in my age .. atleast here in Denmark :)

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In every area of life you will ALWAYS find people better than you. Smarter, faster, stronger, tougher. However, you should be inspired by them, not frightened by them. My attitude has always been: "They are human. I am human. If I want to, I can do what they do."

If you are going to be crushed by not being the best at everything, you are setting yourself up for serious psychological problems for the rest of your life. Let it go.

Be good. Be really really good. But forget about being 'the best.' It doesn't exist - only in artificial testing systems like IQ or class grades. The real world doesn't work like that. As others have said, hard work counts for much more than raw talent.

@Levis2: Well an IQ test, even an online one, should at least have comparative validity. Perhaps you would like others to take that same test to compare results.

Levis2:
Here's a far better way to gauge your competence as a mathematician than any IQ-test will be:

1. When you read university textbooks on maths (if you haven't begun to read such now, DO SO!), hold your hand over the <i>proof section</i>.

2. Be sure you understand the theorem or conjecture that is to be proven, and then make your best shot at it.

3. Compare your effort with the proof in the text. try to gauge whose proof is the best, and, not the least, <i>why</i> that proof (either your own or the book's) is better.

When asked how they developed their skills, many mathematicians cite this very technique as the most important one, according to their own self-evaluation.

IQ tests were originally designed to determine the level of mental retardation.

arildno said:
Levis2:
Here's a far better way to gauge your competence as a mathematician than any IQ-test will be:

1. When you read university textbooks on maths (if you haven't begun to read such now, DO SO!), hold your hand over the <i>proof section</i>.

2. Be sure you understand the theorem or conjecture that is to be proven, and then make your best shot at it.

3. Compare your effort with the proof in the text. try to gauge whose proof is the best, and, not the least, <i>why</i> that proof (either your own or the book's) is better.

When asked how they developed their skills, many mathematicians cite this very technique as the most important one, according to their own self-evaluation.

Yeah I've done this, not with university books though. i do most of my reading on the internet .. University books are 3 years from my present educational level, but i plan on borrowing some from the library, if i am able to grasp the content :)

And i know iq tests were originally designed for measuring mental retardation, but many people say they have been improved, since they are now widely used to detect brilliance in children.

Levis2 said:
Yeah I've done this, not with university books though. i do most of my reading on the internet .. University books are 3 years from my present educational level, but i plan on borrowing some from the library, if i am able to grasp the content :)

And i know iq tests were originally designed for measuring mental retardation, but many people say they have been improved, since they are now widely used to detect brilliance in children.
You are already more than 3 years ahead than most people in mathematical maturity.

You should pick up introductory textbooks on calculus and linear algebra.
you will have no trouble whatsoever working with them.

Lykke til, fra en nordmann som ønsker deg alt vel!

arildno said:
You are already more than 3 years ahead than most people in mathematical maturity.

You should pick up introductory textbooks on calculus and linear algebra.
you will have no trouble whatsoever working with them.

Lykke til, fra en nordmann som ønsker deg alt vel!

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

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

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

Levis2 said:
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.

arildno said:
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 !

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.

arildno said:
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!