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  1. #11
    Senior Member Mal12345's Avatar
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    Quote Originally Posted by ancalagon View Post
    The problem here is that we tend to call the result 'the answer', when it really isn't. The answer is the proof that the result is correct.

    If you give the wrong result with a flawed proof that demonstrates that you know what you're doing, but made a small calculation error, you're doing well. If you pull a number out of your butt and say 'look, intuition!', and you are lucky enough not to guess wrong, you aren't actually showing that you know anything at all.
    In my example of the student and the former teacher of mine, I did not mean to imply that the student pulled the answer out of his figurative ass. I'm saying that, from the teacher's point-of-view, he may as well as have, because the student provided no formal proof. It didn't just so happen that his answer was right, it was right, only his method of arriving at it was a personal one, a method born of his personal method of intuition and not of objectively demonstrable proof.
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  2. #12
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    Quote Originally Posted by Mal12345 View Post
    Intuition (not in the strange Jungian sense) is any leap of logic that leads to a conclusion (right or wrong) which one feels to be correct. (This is not to be confused with jumping to a conclusion.)
    If there's a difference between leaps of logic and jumping to a conclusion, I can't see it.

    Induction requires knowledge of axioms plus the addition of elements not involved in the original problem, as in geometry, adding imaginary lines to a given triangle in order to induce the mathematical properties of triangles in general. In other words, the inductive form of proof applies to all triangles, also thought of as the universal form of all triangles in general, whereas deductive proofs only apply to particular situations.
    Inductive doesn't mean general, and deductive doesn't mean specific.

  3. #13
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    Quote Originally Posted by Mal12345 View Post
    his method of arriving at it was a personal one, a method born of his personal method of intuition and not of objectively demonstrable proof.
    If you can't explain why it's true after the fact, then you don't really understand it. Who cares how he got to the conclusion, as long as he can say why he's right.

  4. #14
    Senior Member Mal12345's Avatar
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    Quote Originally Posted by ancalagon View Post
    If you can't explain why it's true after the fact, then you don't really understand it. Who cares how he got to the conclusion, as long as he can say why he's right.
    You should research terms like "leaps of logic" and "intuition," in the context of how these differ from jumping to a conclusion.
    "Everyone has a plan till they get punched in the mouth." Mike Tyson
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  5. #15
    alchemist Legion's Avatar
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    I generally had a hard time explaining my working. I've had people describe my approach as intuitive, often when it's geometric (a visual proof). I struggle most on proof questions, where it appears quite reasonable that a thing is true, but you have to use just the right definitions and theorems to make it work.

  6. #16
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    I'm not obsessed about Math. Math was easy for me in school (maybe having a natural ability to do Math is a better INTP stereotype), but Computer Science was clearly my favorite subject.

    As for having to show your work, that makes sense to me, but I always noticed the obsession with getting everyone to do this, and thought it was strange. I also noticed constant attempts to warp and twist everyone's method of thinking until it was dull, dry, and procedural, and until the ability to make mental leaps was gone. I always thought mental leaps and intuitively solving problems is what Math is all about, not clearly and meticulously documenting your failure to do so (if they get their way, you'll go from effortlessly breezing through solving a problem without making any mistakes to consciously and unnaturally applying explicit steps from a textbook and to constantly make mistakes while not being able to think straight and while having their voice linger in your head constantly calling you stupid).

  7. #17
    Senior Member INTP's Avatar
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    I dont like the type of math where i need to learn some formula and then follow it(like some advanced statistical math), but if i need to calculate for example how much is 4.50€ per day for 28 days in my head thats pretty easy and can do that sort of stuff easily. First 3 x 4 = 12, then add one zero to the end = 120. 30 x 0.5 = 15. 120 + 15 = 135. but since i used 30 as multiplier(instead of 28) to make things easy, now i just need to remove 2 x 4.5 = 9 from it, so 28 x 4.5 = 126. Also i used to calculate stuff for diablo 2 back in the days quite a lot to really min-max everything, like how much enhanced dmg adds compared to maximum damage jewels(or min-max dmg or ed/max dmg) and how much stats effect life or to damage etc. which wasnt bad because it gave more room to thinking than learning.. Or it did at first, because i didnt pay much attention to math at school and pretty much just reasoned how those things needs to be calculated.

    I think reasoning is whats the strong side of INTPs, and math kinda requires some reasoning or at least some math does, but you can just memorize math formulas and calculate things correctly using a calculator, which is the way some types like to do math, which i dont think INTPs usually enjoy..
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  8. #18
    Senior Member Hitoshi-San's Avatar
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    I know ISTPs, xSFPs, an ISTJ, an ENTJ, a ExFJ, an ENTP, and an ENFP and they are all great at math.

    I personally hate it and am terrible at it, but always loved science.

  9. #19
    ⒺⓉⒷ Eric B's Avatar
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    I was into the patterns of numbers (such as with polygons), and other symmetries. This is basically the idea of math, but the practical application of it: the forumulas, (which is heavy SiTe), is where I always lost interest and faltered. I look at all those pages of formulas in science (Einstein, etc), and feel chills. Can't remember it, and bored with pre-set logical application. (And will often find fault with the agreed-upon way of putting things, and where symmetry is not consistently followed).
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  10. #20
    @.~*virinaĉo*~.@ Totenkindly's Avatar
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    I majored in math for two years at college, then got both bored and frustrated.

    I had issues with it getting both too detached from reality as well as having trouble with the more complex modelling to describe scenarios. It didn't seem like I was improving even with spending more energy proportionally on math than my other coursework.

    I've always been kind of split in my interest and capability between science and humanistic pursuits, and the level of math i was studying was outside of that "sweet spot" for me -- way too detached.

    As far as doing "numbers calculations," like what my ISFJ ex does for a living and really enjoys (accounting stuff), I can't imagine many worse hells.

    Quote Originally Posted by Eric B View Post
    I was into the patterns of numbers (such as with polygons), and other symmetries. This is basically the idea of math, but the practical application of it: the forumulas, (which is heavy SiTe), is where I always lost interest and faltered. I look at all those pages of formulas in science (Einstein, etc), and feel chills. Can't remember it, and bored with pre-set logical application. (And will often find fault with the agreed-upon way of putting things, and where symmetry is not consistently followed).
    Sets weren't too bad, those and sequences were rather fun.

    I also appreciated the logic theory, but that's basically stuff I pull into more general "logical proof" stuff in regular language. Those concepts were pretty useful to me.

    I found programming more interesting than pure math -- using logic to make the machine do something that interfaced with humans.
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