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Featured Can anyone learn advanced maths? (Researches)

  1. Oct 7, 2018 #1
    Hello guys,

    I often ask myself if anyone can learn maths to an advanced level? And get really good on it.
    I think that every healthy person can get very good at maths. The only condition is that the person is interested in math.
    Of course, to get on the level of a Field-Medal winner you have to be blessed a little bit. But I think you can reach and understand a lot just by working out hard.

    But are there researches which proof the current state of science in relation to how much the genetic predisposition affects the learning of math?
    When you are healthy our neural system should work nearly the same as the neural system of a high-level mathematician or nah?


    What do you guys think? Can anyone learn maths to a high level?
    Or is it important to be 'blessed'? Or do you think it is pretty irrelevant and only relevant for the level of Field-Medal member?

    I am really sorry for the grammatic issues. I am still improving my English!
     
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  3. Oct 7, 2018 #2

    Drakkith

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    There is no clear evidence linking genetic differences with mathematical skill except in the case of mutations that result in mental disabilities. Basically, if someone's abilities are anywhere near average or above, we can't really tell who would be good at math just by looking at their genes.

    That depends on how you're measuring and comparing things. The large-scale structure of each person's brain is nearly identical, but if you were to map out each individual cell and synapse there would be enormous differences. You can think of the brain as being composed of 'modules', each consisting of some number of neurons and their synapses and each performing certain processing tasks. To be clear, I don't mean that these cells are isolated from other cells in nearby 'modules', I only mean that they function together as a unit to perform some task. These modules can even overlap each other, with cells belonging to more than one module (as far as I know). The exact position of each cell and the exact layout of their synapses is not particularly important as long as the modules all connect together the right way.

    The reason I bring this up is to demonstrate that there is more than one way to describe how closely the brains of two people match. They may be very different at the level of cells and synapses, but they may be nearly identical if you look at them at the scale of 'modules'. So if you want to look at what effects genetic differences have on someone's brain, you have to start building abstract models of the brain at various complexity levels, greatly complicating the analysis.

    No, I don't think so. Understanding math at a level that puts you within reach of a Field's Medal takes extraordinary talent that most people do not possess. You really have to understand math at a level comparable to the physical skill requirements needed to play a professional sport. Only a small percentage of people have the ability to reach these high levels of physical or mathematical skill in my opinion.
     
  4. Oct 7, 2018 #3

    FactChecker

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    A couple of data points:
    1) Where I went, there were people who anyone would consider smart, but who could never get passed the preliminary exams for acceptance to the Ph.D. program. Some of them worked at it for many years.
    2) I had no trouble with some advanced math subjects, but could never get good at others. I eventually had to switch from abstract algebra as a specialty to complex analysis (geometric function theory). If it wasn't for the geometric aspect, I probably would have nothing.
     
  5. Oct 8, 2018 #4

    Math_QED

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    I think it is false that everyone can learn advanced abstract maths. The first requirement is to be very patient when doing maths. It can take a long time to truly understand concepts. Since not everyone can/wants to spend a lot of time doing math, not everyone can become good at it.

    The second thing I can come up with is the abstraction level. I know a couple of people that said that at some point, they hit a certain "abstraction level". Things became too abstract and/or too technical.

    I hope I'll never reach such an abstraction level.
     
    Last edited: Oct 8, 2018
  6. Oct 8, 2018 #5
    Nobody is surprised that career in music requires a talent. Why it should not be so in math
     
  7. Oct 8, 2018 #6
    First of all thanks for your answers.

    That is a very good point! Since I don't know that much about the cellular level about the brain that is a really good point to think about. I like your comparison with the large scale and the individual cell.

    On a high level, I mean the level like when you study maths in university. That you need some kind of talent to get a Field-Medal or even compete it is obvious. That is not what I meant with high level. High level is university level for me.

    But did you put the same effort into abstract algebra like in your successful math subjects? Or were you less interested in abstract algebra so subconscious you have put less effort into it?
    But on the other hand, I feel you. I don't like stochastics that much and for me, it seems harder sometimes to learn stochastic than analysis or others. But I also know that I subconscious put less effort into stochastic to learn it because it interessts me less than analysis for example.

    I get your point and I am with you but that is what I said at the beginning. The only condition is that you have to like maths or want to learn it otherwise you will never put enough effort into it that's true.
    But the point you are talking about is not a genetic factor. It is more a psychological thing you know what I mean?
    Your point is right. Not everyone wants to learn math to an abstract level or so but I talk about people who want it and who are interested in math.
     
  8. Oct 8, 2018 #7
    Yes of course but I think that people who play an instrument and start a career on that are comparable to mathematicians who compete for the Field-Medal.
    That's a level where you need to be talented, yes. But I think everyone can also learn an instrument like a piano to a good degree but of course not to a pro level like Mozart.
     
  9. Oct 8, 2018 #8
    Most mathematicians aren't as good at math as a Terrance Tao just like most physicists aren't as good at physics as an Ed Witten, at a certain level all you need is to meet the standard and move on from there; barring some sort of mental illness I think most people can meet the average (though it might not hold their interest to do so as this still requires lots of work) but the average is still kind of wide since there's so many sub-fields within math.
     
  10. Oct 8, 2018 #9

    StatGuy2000

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    I disagree with that characterization, and the comparison between advanced mathematics and professional sports is a false one. To have the physical skill requirements to play a professional sport involves a combination of specific physical attributes (typically genetic attributes -- height, ability to develop certain musculature, excellent hand-eye coordination, among others) along with years of physical training.

    Short of having a mental disability, there is no bar mentally to studying mathematics. To accomplish and understand the mathematics needed to achieve a Fields Medal will indeed involve years of dedication and research, but I actually do believe that the foundations to achieve an understanding of mathematics is accessible to most people. The small percentage you talk about has little to do with ability, but a lot to do with dedication and training.
     
  11. Oct 8, 2018 #10

    PeroK

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    Do you have any research to substantiate these claims?

    It is possible, without evidence, to make precisely the opposite claim: that with enough training a physical skill will develop to any desired level; but, if you just can't grasp the mathematics, then no amount of study will change your brain sufficiently.
     
  12. Oct 8, 2018 #11

    PeroK

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    PS although I submit this without evidence, it seems illogical to me that there are a) people with mental disabilities and b) everyone else. It seems more logical to me that there is a spectrum, from those with no capability to learn advanced mathematics to those for whom advanced mathematics can be learned relatively easily.
     
  13. Oct 8, 2018 #12
    That physically is not true though, it doesn't matter how much someone trains, most people aren't going to look like this due to genetics and drugs:

    Mr.-Olympia-2018-Predictions.jpg
     
  14. Oct 8, 2018 #13

    StatGuy2000

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    If you are asking me whether I have specific evidence to pinpoint this, the answer is no. In fact, there is a surprising paucity of research in regards to the heritability of mathematical ability, in large part because of the questions involving defining what is "innate" versus "acquired" mathematical ability.

    Please note that I have never questioned that certain individuals have an easier time grasping numerical or abstract mathematical concepts than others, and other individuals may take longer in acquiring these concepts. That does not imply that mathematics is therefore completely inaccessible to those who initially struggle or that somehow certain people are genetically incapable of math. If anything, this only points that different individuals will require different teaching techniques to learn certain subjects.
     
  15. Oct 8, 2018 #14

    StatGuy2000

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    The question would be -- what if you take certain people and have them undergo extremely grueling and arduous physical training regimen (as well as use certain performance-enhancing drugs like anabolic steroids or human growth hormones). Could they, in the end, have physiques that would approximate the bodybuilders you just displayed in the attached photo?
     
  16. Oct 8, 2018 #15
    They might start to approximate that, but the ones I posted are the top placings at this year's Mr. Olympia (basically the world championships of professional bodybuilding), there's things that set them apart from the rest of the field that can't necessarily be replicated by training (luck of judging preferences is also a factor, which goes to muscle insertion points and such which are set genetically).
     
  17. Oct 8, 2018 #16

    Drakkith

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    And learning math requires a combination of several mental skills including memory, the ability to abstract, logic, and more. Not everyone is good enough at all of these skills to be successful in math.

    I just don't agree.
     
  18. Oct 8, 2018 #17
    So there are basically 2 opinions here.

    I get the arguments from both sides but does anyone has a research or some scientific proof?
    But we all agree that there are people who have an easier time learning math than other people.
    And even tho I think that every healthy person without a learning disability can learn math I think that you can not achieve the level of a Field-Medal mathematician.

    I am also not 100% sure if you can compare pro sports with learning math. I get the idea but I don't think you can compare this too exactly.
    Every pro player uses some kind of steroids no matter if it is bodybuilding, football, soccer etc.
    And I think the pro mathematician do not take something to boost their brain.

    I would like to know if there is a research or something else at the moment which shows if our neurons work that much different in comparison to a high-level mathematician.
    Or if there is just a little difference, which only matters in extremely high-level maths and that is the reason why we won't be that good like Terence Tao for example.
     
  19. Oct 8, 2018 #18

    StatGuy2000

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    But my contention is that each of the mental skills you listed (memory, ability to abstract, logic, etc.) are acquired abilities, and which require practice and effort to master. Sure, some people have an easier time with these skills than others, but I have thus far seen no convincing evidence that, barring actual physical disability, that these mental skills are beyond the reach of all students.

    Also, ask yourself this -- if a student is struggling with math, your first reaction seems to me that the student is not "genetically" capable of math. Isn't it just as likely that the student have had poor teachers?

    And I disagree with your disagreement.

    Consider this -- it has been widely reported that students in Asian countries like Japan, Singapore, South Korea outperform American and Canadian students in standardized math scores and in math overall. Some people might conclude that people from these Asian countries have a genetic propensity for mathematical ability. I reject this outright -- a combination of cultural values that emphasize that any subject is accessible to all students, better teachers, better support for teachers, better educational materials are the most likely explanations for the superior performance.
     
  20. Oct 8, 2018 #19

    Drakkith

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    I can't say that I do.

    I don't agree that they are purely acquired abilities. I myself have significant memory problems and while I haven't been labeled as having a mental disability, it absolutely affects my ability to learn math (like trying to remember those dang integration tables! :mad:). How can I learn advanced mathematics if I have difficulty remembering all the new rules, tricks, and techniques required at those levels?

    I don't deal with people at the advanced level, so I don't immediately jump to the conclusion that they just aren't cut out for it.

    These studies are not looking at the highest level of mathematical ability, but the lower levels.
     
  21. Oct 8, 2018 #20

    PeroK

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    That's actually more of a "political" analysis, teetering on a false syllogism, than a scientific one.

    Hypothesis: not everyone can learn advanced maths.

    Refutation: in Asian countries people are generally better at maths owing to a more focused education system.

    That is false logic.

    In fact, to prove your point you would need to demonstrate that almost no one in these Asian countries struggles with maths. Or, alternatively, that almost everyone eventually attains the ability to study maths successfully at undergraduate level, say,
     
    Last edited: Oct 8, 2018
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