Becoming a mathematician - how important is IQ?

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  • Thread starter Levis2
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  • #51
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Hey Levis. Im 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, im 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 :)
 
  • #52
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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.
 
  • #53
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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&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&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.
 
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  • #54
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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?
 
  • #55
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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. :tongue2:
 
  • #56
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i recommend watching the big bang theory for some career ideas for high iq people like yourself
 
  • #57
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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...
 
  • #58
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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...
 
  • #59
Hello - im 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 im lucky, end up making a useful contribution. That's what matters most to me of all things atm.

But there's a problem - im 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, lets 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 doesnt 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 wont 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!
 
  • #60
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THis is like the 4th time I have seen this thread posted.
 
  • #61
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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.
not true at all. You can't train for a professionally administered IQ test, you can only become familiar with the type of questions.
IQ is a deterministic factor for one's ability to grasp and synthesize abstract concepts.
 
  • #62
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This comment might get overlooked, but I hope not: while IQ seems decidedly NOT the right measure, I believe there are other traits which are also rare. Being a mathematician takes not IQ but ... Surprise surprise, mathematical inclination and talent, as well as hard work.

By mathematician, if you mean a researcher, well it depends if you like the career path, which comes with a lot more than just loving and doing mathematics!

Having a knack for mathematics as a career mathematician is not the same as solving hard puzzles, being very quick, or being able to ace math competitions. That does
not mean all there is to it is working hard even if you love math!

You should learn from an early age that eventually you have to stop using measures like these tests to assess yourself. Rather, ask yourself at all successes and failures what SPECIFIC TO YOU is holding you back or pushing you ahead. You can dazzle someone else with promises that you have a promising future with a high score on X or Y test, but if you have not made honest attempts at figuring out if your specific talents and inclinations are a fit for that future, then you won't fool yourself and will remain anxious.
 
  • #63
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So how did Feynman do it with an IQ if 125?

Suggestions:

"... an early aptitude for mathematics, a preference for "hands-on" learning, a passion for tinkering with modern technology (radios in Feynman's day) and a strong indifference to reading (even as a university professor, Feynman hardly read more widely than the "Physics Review" journal)."

http://anne.julienne.org/feynman.html
 
  • #64
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an early aptitude for mathematics

Right there, it's clear he had a skill which is not immediately explained by IQ. It's not that everyone has the same level of skill of course, just that the skill is different from what IQ immediately measures.

I mean, as a different example: not every professional mathematician is a star at the game chess. Both require intellect, practice, skill, etc. But they're simply different things.

So it's not right to ask "Do I have the IQ to become..." rather, do I have the ability. Hard work and smart work go a long way, but a bunch of factors simply give some people a leg up. The key is to learn your specific strengths, so you can bring them to achieving in the fullest way.
 
  • #65
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The key is to learn your specific strengths, so you can bring them to achieving in the fullest way.


how can you do this?
 
  • #66
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At some level, it happens automatically if you put in a ton of effort into something. You get a lot of ideas as you persevere, make dumb mistakes, and observe what you did. Being an active observer helps quicken the pace of getting better, though.
 
  • #67
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... it's clear he [Feynman] had a skill which is not immediately explained by IQ. It's not that everyone has the same level of skill of course, just that the skill is different from what IQ immediately measures.
I agree, so the question is "how do you develop this skill?" Saw Wilckjek in his front room talking to an interviewer recently, and he seemed to be more proud of his large bookshelf full of puzzle books than his Nobel prize medal!

Rather than rushing to get into university I think the OP would be better reading a lot of puzzle books for laymen, or school level mathematics books with lots of puzzling, interesting problems.

University mathematics involves a lot of learning, and quite a bit of "plug and chug", perhaps at the expense of developing mental flexibility.

Maybe doing a lot of puzzles, or fixing old TV sets, develops that kind of flexibility in a young mind? Then when it comes time to "plug and chug" you can go to it with added flexibility.

I remember being impressed by an account by Feynman of winning a school level Mathematics contest through an incredibly flexible approach to a problem - how do you develop that kind of flexibility? Are you just born with it? Is there something beyond IQ - the AQ, the Amazing Quotient, that only people like Feynman and Einstein have? All we can say is that science hasn't found this yet, if it exists. So, as with string theory, we shouldn't take it too seriously. Those with Feynman's IQ should assume, for now, that they can do it! Just do as he did...
 
  • #68
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I don't think Feynman was trying to model himself after somebody else. While it could be interesting to see how Feynman ended up being Feynman, I think it would be better if one (anyone, really) developed his own kind of talent if that makes sense.

Think of it this way, the world's already heard The Beatles and four of them is enough, while trying to emulate them or present another take of their work (see: Beatallica!) can indeed prove to be interesting or a good learning experience, I find that musicians are better off trying some new. I wouldn't be surprised if the same applied for science in general.
 
  • #69
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Read this very carefully:

http://www-history.mcs.st-and.ac.uk/Biographies/Feynman.html

"Richard, [Feynman] learnt a great deal of science from Encyclopaedia Britannica and taught himself elementary mathematics before he encountered it at school. He also set up a laboratory in his room at home where he experimented with electricity. In particular he wired circuits with light bulbs, he invented a burglar alarm, and he took radios apart to repair damaged circuits. When he entered Far Rockaway High School his interests were almost entirely mathematics and science."

So instead of going to University early why not get a set of Encyclopedia Britannica, read through maths & physic articles (only!), get an expensive electronics hobby kit to build all these kinds of things, and experiment with fixing your friend's broken down electronic equipment?

I've been bouncing around John Gribbin's "Q is for Quantum" recently - an encyclopedia of quantum physics - and I can see how doing that might develop flexibility of mind.

"At school Feynman approached mathematics in a highly unconventional way. Basically he enjoyed recreational mathematics from which he derived a large amount of pleasure. He studied a lot of mathematics in his own time including trigonometry, differential and integral calculus, and complex numbers long before he met these topics in his formal education."

Note the stress on *recreational* mathematics - same as Wilczek.

"He entered MIT in 1935 and, after four years study, obtained his B.Sc. in 1939. He went there to study mathematics but, although he found the courses easy, he became increasingly worried by the abstraction and lack of applications which characterised the course at this time. He read Eddington's Mathematical Theory of Relativity while in his first year of studies and felt that this was what he wanted from mathematics. His mathematics lecturers presented him with the view that one did mathematics for its own sake so Feynman changed courses, taking electrical engineering. Very quickly he changed again, this time moving into physics."

I just read a biography of Dirac and Eddington's book was very important to him as well!
So put that on the "must buy" list...

"He took Introduction to Theoretical Physics, a class intended for graduate students, in his second year. There was no course on quantum mechanics, a topic that Feynman was very keen to study, so together with a fellow undergraduate, T A Welton, he began to read the available texts in the spring of 1936. Returning to their respective homes in the summer of 1936 the two exchanged a series of remarkable letters as they tried to develop a version of space-time..."

Here the important points to take are:

(i) he really stretched himself by taking a tougher course. Watson (the DNA guy) said he did exactly this as well, taking tough Math classes that biologists were not expected to take...)

(ii) He found a friends to discuss these things with at the highest level - I always felt jealous of Einstein's coffee bar lifestyle where he would go and chat with friends who later became almost as famous as him! If only I had had famous friends! ... But I didn't get chatting to the brightest guys in my class, so it's partly my fault - SO *push yourself forward socially* make friends with the bright guys and talk about important stuff.

(iii) Don't moan that your school doesn't have a class in string theory/LQG/whatever , plough through the tough books, with your like-minded pals, in the breaks! And try and have your own ideas, push them to the limit...

"By 1937 Feynman was reading Dirac's The principles of quantum mechanics and seeing how his highly original ideas fitted into Dirac's approach. In fact Dirac became the scientist who Feynman most respected throughout his life."

Another must read book! (Not too early though ... you need a couple of years of the toughest theoretical physics classes in Uni. before thinking of this...)

"He had the best grades in physics and mathematics that anyone had seen, but on the other hand he was close to the bottom in history, literature and fine arts."

Lesson: Focus on what's most important! UK citizens don't have this problem so much, they don't have to do "history, literature and fine arts." at Uni. They just do physics. So you might want to consider Manchester, like Bohr :), or Lancaster or even Cambridge (wish I had!)

"His doctoral work at Princeton was supervised by John Wheeler, and after finding the first problem that Wheeler gave him rather intractable, he went back to ideas he had thought about while at MIT. The first seminar that he gave at Princeton was to an audience which included Einstein, Pauli and von Neumann. Pauli said at the end..."

Lessons: Find the best mentors, listen to them, use them, hang out with them, but when it comes to the crunch go with your own ideas...

"At twenty-three ... there was no physicist on earth who could match his exuberant command over the native materials of theoretical science. It was not just a facility at mathematics (though it had become clear ... that the mathematical machinery emerging from the Wheeler-Feynman collaboration was beyond Wheeler's own ability). Feynman seemed to possess a frightening ease with the substance behind the equations, like Einstein at the same age, like the Soviet physicist Lev Landau - but few others."

But as his "lucky" schooling shows it wasn't (necessarily) some "divine spark" that gave him this ability - it was the things he did, the books he read, the courses he took, the people he talked to. You can't reproduce a "divine spark" (if it exists) but there is much in his life worth pondering on and emulating.

And for you educators out there: Why don't you encourage a culture similar to that encountered by Einstein and Feynman? Why not:

(i) Invite the bright students to the coffee bar for long bull sessions...

(ii) Create reading groups to get reading Eddington's book over the second summer break and Dirac's over the third.. ask them to come up with their own ideas for a theory of space time or Quantum Gravity.

(iii) Act like Wheeler (see "Geons" for another great biography...)
 
  • #70
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At some level, it happens automatically if you put in a ton of effort into something. You get a lot of ideas as you persevere, make dumb mistakes, and observe what you did. Being an active observer helps quicken the pace of getting better, though.
no i mean how can you learn your specific strengths
 
  • #71
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no i mean how can you learn your specific strengths
Yes, that's what I was answering. You have to observe yourself and what works for you, and be pretty brutally honest with yourself, then be proactive about how you can turn some seeming weaknesses into strengths. It's not always possible, but it is many times.

"how do you develop this skill?"
I think it's definitely not formulaic. Or everyone would be doing it.

Related to the point I make above, I think it isn't quite the *same skill* that every single person is developing, because people achieve the same thing through different thought processes and strategies.

Some general, non-specific things do include challenging your mind a lot with nearly anything it can possibly find; being humble is also very helpful, because the moment you accept you're not a genius, you take one step towards pursuing actual science, math or whatever, as opposed to pursuing glory; mastering the basic skills definitely -- Feynman invented a lot of things, but he also learned a lot of basic skills needed to express his thoughts; and of course, what I said above: observe yourself and notice what works for you.


One other thing: Feynman did not seem to like to glorify complicated ways of explaining things. Of course, his work is immensely complex, but he believed in explaining it with immense clarity. He was supposedly not afraid to boldly ask questions that other academics usually wouldn't.

I think a lot of people underestimate how much that sort of thing can help. Almost none of the scholarly individuals I know have that kind of boldness, though some are better than others. I think over the course of decades, that kind of attitude *greatly* can affect the kinds of discoveries a mind can make.

I do NOT believe everyone can necessarily develop the same level of skill in everything. It isn't to say that the skill is genetic, but it is to say that the way different minds develop is influenced by so many things (in fact, the same person probably could develop very differently). So above all, forgetting about forcing brilliance or skill and pursuing a subject with genuine interest and being proactive about using *your* specific skills wisely seems the best bet.
 
  • #72
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I remember being impressed by an account by Feynman of winning a school level Mathematics contest through an incredibly flexible approach to a problem - how do you develop that kind of flexibility? Are you just born with it? I
It appears to me that one is neither born with it NOR can one necessarily carefully orchestrate one's life so as to become a genius. A combination of genetics, lots of randomness, one's "personality" (this is NOT fully explained by genetics, at least not our current knowledge), etc etc all contribute.

I think people should note that an individual, whether Feynman, Einstein, or whoever, spends ALL his life with himself. Every moment counts to make him who he is. Surely we all know that not everybody recognized just how brilliant these people would become eventually. I don't even think they themselves did. There is so much unwritten, unspoken, unknown info about what went through these minds at various points in time, what exactly was easy for them, when they had their moments of discovery, etc etc. All we hear are a few stories and that they got internationally recognized.

The complexity of what makes such a brilliant scientist or mathematician is surely immensely beyond what anyone I know has come close to explaining, but I don't doubt that it's still nice (and potentially instructive) to think about it some.
 
  • #73
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Why did you scared?! How many tests for getting your IQ did you passed?! - with just one test you will not know your right intelligence quotient, need pass more its. Maybe you need to try to improve your self, because for to know your true IQ isn`t enough just math. Yes! -that is important, maybe most important ingredient for success, but exist and more-its, how can be your visual memory, your intuition, how you manifest your-self in real life - not just in numbers.
That is great - that you are so smart at your age, but is not so late to change-it, to improve your-self. You can read maybe more information about how improve your self besides math - why not!?
I found a site that`s help me, and caused me to emphasize to another point for be stronger. Maybe it will help you and your-self, try it www.getiq.net/info.jsp, here you will find more information about math intelligence, motivation significantly influences IQ test results! and more.
 
  • #74
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If you really like it as you seem to be, then don't hesitate to enter that field, you might do great success in this field, who knows? life is full of risks, if you aren't willing to take any risk then stay at home, although you should think wisely before taking any risk.. in your case, you look more than ready for it!
 
  • #75
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It`s right, just read any information, a good information about how to improve your intelligence, and after try to pass another test, and we wait your answer... I think that you will be happier when will do it! If you want to be batter, work for that! Don`t worry... :smile:
 

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