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Math Become a good mathematician without the "threshold" IQ?

  1. Jan 6, 2017 #1
    So I've read this "article"[ http://afiodorov.github.io/2015/12/04/terry-replies/ ] that really depressed me especially because I'm young. Apparently the threshold IQ is around 150, so does that mean someone has no chance?
    Last edited: Jan 6, 2017
  2. jcsd
  3. Jan 6, 2017 #2


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    First of all, an IQ measurement is nonsense. One gets varying results, depending on the kind of test, personal preferences and qualities. You can even practice those tests and get better at it. Does this mean you get smarter?
    Secondly, you may wonder what disabled people are capable to do! Euler became blind and he still proved mathematical theorems. He only needed someone to write them down.
    Furthermore it isn't true, that anyone's IQ (which way ever measured) is fixed. O.k., you cannot make a stupid person a genius, but training, experience and books, a lot of books, can change a lot!

    Mathematics isn't something about IQs. It's very much the same as with everything else: practice, patience and diligence. You aren't supposed to be a genius. Curiosity is much more important, and the other attributes I mentioned. Of course not every runner can be a Usain Bolt, every physicist an Albert Einstein or every mathematician a Leonard Euler.

    However, there is one important lesson to learn: Do not believe something, just because anyone has said so! The other way around makes you a good scientist: Wrong, until proven! In mathematics, you learn to read those proofs which are to convince you. In physics you do experiments.
    What makes you think what you've read is right? It is not. And this has to become your standard assumption: it is wrong unless proven to you.
  4. Jan 6, 2017 #3

    Thanks for the answer
  5. Jan 6, 2017 #4
    I tend to doubt the 150 threshold, but it depends on what you mean by "good mathematician." I tend to define "good" in terms of one's professional work product - satisfying the job requirements, which may or may not require publishing papers in the most esteemed math journals which get cited dozens of times each.

    I've known lots of college math faculty who I regarded as very good by the above criteria whose IQs I would estimate at 115-145, with most from 115-130. But most of these tended to be faculty at teaching rather than "publish or perish" institutions (R1).

    For a high school student, I would worry less about IQ. Work hard and shoot for an ACT score in the 30s if you want to become a mathematician. Not there yet? Keep working. I can give a lot of practical advice on how to improve your ACT Math score and get into the 30s. Success in math can be achieved even without the highest levels of intellectual gifting.

    Just as exercise can make you stronger, hard work can make you smarter.
  6. Jan 6, 2017 #5


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    Terry Tao's reply to the original poster is instructive: there are more and more math problems nowadays that require a "slow and steady" approach where one accumulates intuition across a broad swath of mathematical disciplines and methodically applies their techniques to the problem at hand, rather than a "brilliant flash of insight" approach that is maybe a more entertaining story to tell, but in practice happens only rarely.

    Edit: Of course, Tao is himself a remarkable genius/child prodigy/etc., so maybe he's just stringing us along.
  7. Jan 6, 2017 #6


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    The discussion in the link provided by the OP (and the subsequent discussion here in this thread) somehow assumes that there is a consensus that IQ is a good measure of overall intelligence (or even intelligence with respect to mathematical ability). That is far from the case. Many others have argued (quite convincingly, in my personal opinion) that IQ is in fact a poor measure of someone called "intelligence".

    Consider the blog posts on this topic from physicist-turned-statistician Cosma Shalizi:




  8. Jan 6, 2017 #7
    The reality is, to do much with mathematics or physics(theoretical) requires extraordinary ability. This isn't to say it's not possible to get a PhD without it but in my opinion, to do anything significant in the field requires genius level ability to the point it's probably not worth going into unless you do math 24/7. At this point I view math more as a hobby then as a career, I just hope to create a career that uses some of what I know without being forced to teach a bunch of incompetent students college algebra.
  9. Jan 6, 2017 #8


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    Crek, I do not agree with that premise, because you (like many others) assume that "extraordinary" ability is somehow an in-born or genetic trait. The fact is that to get to the stage where someone could be said to have such ability takes a tremendous amount of effort and hard work.

    Sure, there are some people who may learn certain areas of knowledge more quickly than others, and for whom mathematics may come more naturally. But that does not mean that you need to be a genius to be able to make significant contributions. I would bet that most faculty members in math and physics departments are not geniuses.

    I also find your arrogance towards other college students (calling them "incompetent", for example) to be offensive. In fact, every single one of your posts lately have been nothing but negative. This begs the question -- why are you even bothering to post here on PF, if you don't have anything positive to contribute?
  10. Jan 6, 2017 #9


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    Well said. I struggled to put it in an equally polite way.
  11. Jan 7, 2017 #10
    Like most things in life, you just have to have the passion for it. Presence of Other factors only help more.

    If an online article about IQ can dissuade you from doing it, then you are not motivated enough for it. What good is high IQ whn you dont know how to prove statemrents, differentiate, do actual math first etc...? If you are happy doing and learning math, I am sure with anough hard work you can contribute something to the field. What helps the most in my opinion is being exposed to a variety of math and logic at an early age.
    Last edited: Jan 7, 2017
  12. Jan 31, 2017 #11
    The original link doesn't wourk for me ☹️
  13. Jan 31, 2017 #12
    Why? If you like mathematics you would enjoy teaching it to any group of people. :) The best maths book often start with a thank you note to the college students for their insights and opinions. I also think teaching is one of the best way to remain "fresh".
    Last edited: Jan 31, 2017
  14. Jan 31, 2017 #13


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    Based on my experience and people I've talked to, this is the comment I have to make.

    There are different types of intelligence and people have strengths in different areas. Every one has a unique thought process. Different problems require different skill sets. For example, it is very likely that Stephen Hawking has contributed so much to gravity even though it is difficult for him to move is because he has a special geometric insight that is very useful for the problems he's worked on (gravity is geometry in some sense). People who think this way may find other things unintuitive. I know lots of absolutely brilliant physicists who will readily admit when they don't understand something in area outside of their field. The goal is to identify problems for which you have special insight given your way of thinking.
  15. Feb 5, 2017 #14
    The great computer scientist Richard Hamming had a great, inspiring talk on this:
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