1. ## INTPs and Mathematics

I think there's a stereotype regarding INTPs that they all love their mathematics. I'm sure that's true to an extent, but it should be kept in mind that math problems are usually extremely detailed, and details are not the strong suit of an Intuitive type.

My high school algebra teacher was an ESTJ. He was completely fixated on the details of doing math problems such that he forced us students to concentrate primarily on the procedural aspects of problem solving. And since this methodology does appeal to the "conventional" Holland Codes - Wikipedia, the free encyclopedia side of me to this day, I am a firm believer in it - despite the fact that it doesn't work for me!

My algebra teacher pounded into our immature skulls the details of solving algebra problems. I understand the concepts. But when applying the concepts I get bogged down in the details. This often means I end up with the wrong answer. Understanding the concepts, but not being able to faithfully apply the teacher's concepts, I ended up as a B student in algebra. And this despite the fact that I loved algebra.

This teacher did not deal well with students who solve algebra problems intuitively. Here's an example I overheard in one of his classes:

Teacher to Student A: "What's the answer to this problem?"
Student A: "32 + X" (or whatever it was.)
Teacher: "That's right. But how did you arrive at this answer?"
Student A: (I don't recall what he said.)

How could it be a mistake to get the right answer? Simple - the student could not demonstrate the proof of his answer. So as far as the teacher was concerned, he just pulled the answer out of his ass.

INTPs love mathematics when it enables them to exercise their intuitive capabilities, the ability to just "see" the answer. The methodology is as personal and individual as intuition itself, and can't be taught.

2. This isn't just related to intuition. The sensing functions are also difficult to explain because they aren't in words. It takes patience and practise to be able to break down your thoughts for mathematics, but it's easy once you've mastered it.

3. Originally Posted by Annihilation
This isn't related to intuition. The sensing functions are also difficult to explain because they aren't in words. It takes patience and practise to be able to break down your thoughts for mathematics, but it's easy once you've mastered it.
Thankfully, psychology isn't limited to Jung's notions of these things.

4. Originally Posted by Mal12345
Thankfully, psychology isn't limited to Jung's notions of these things.
You equated the two. You established that you are an INTP and therefore you can't explain your thoughts. In actuality, as your dominant function is a judging function, you probably have more ease than everyone else to analyse your perception.

Regardless, I'd argue that Te is better at explaining mathematics than Ti simply by its objective nature.

5. Originally Posted by Annihilation
You equated the two. You established that you are an INTP and therefore you can't explain your thoughts. In actuality, as your dominant function is a judging function, you probably have more ease than everyone else to analyse your perception.

Regardless, I'd argue that Te is better at explaining mathematics than Ti simply by its objective nature.
Yes, but the OP contrasts conceptual versus sensing, not objective versus subjective. Conceptual versus sensing can also be considered as general versus particular, where the general (or universal) is not a direct product of the senses. But Ne or Ni, as perceiving functions in general, prefer to deal in broad pictures of whatever can be perceived. The answer to a math problem is thus mentally "seen" by the Intuitive, the methodology of deriving the answer is unconscious and can't be apprehended and shared with others. Therefore it can't be taught.

Although my algebra teacher didn't look at the issue from this perspective, when he prefers the objective methodology to the unconscious one he is obviously teaching that which can be taught, objective methods of deriving answers. And yes it is very much Te. But what he didn't explain to us - since he was so unthinkingly rigid in his methodology - is that in higher mathematics intuitive methods can't be used for deriving answers to complex problems. So it was necessary for him to beat the intuition out of the students and force them into objective methods. (Yes, he was a rough kind of character, although he didn't physically beat us, of course, it literally felt like it.)

What I'm saying is that it didn't work for me. Although I agree with the concept of it, it is very difficult for me to apply because I am neither Te nor Sensing.

6. The person I know who loves math the most is an ISTJ. I think what he likes most about it is its deterministic nature. Once it makes sense, it always makes sense. For the most part it doesn't change. It remains logical and constant. I think this is one of the reasons I don't like math. What he finds exciting and stable, I find repetitive and boring. Not to mention confusing.

7. ISTJ math lover: front row nerd in math class, nostrils flaring with intense interest, pencil ever at the ready. Straight A math over-achiever. Forgets almost everything he learned 10 years later.

8. Originally Posted by Mal12345
How could it be a mistake to get the right answer? Simple - the student could not demonstrate the proof of his answer.
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.

INTPs love mathematics when it enables them to exercise their intuitive capabilities, the ability to just "see" the answer. The methodology is as personal and individual as intuition itself, and can't be taught.
I think intuition can be taught, and I think it's important that we care about how we get answers.

How does intuition get answers? If we don't know, and it gets them in a way that doesn't scale, then anytime we get a harder problem, intuition will get stumped.

If all it does is hand us answers which might be right or might be wrong, sometimes, then it's less useful than a calculator.

9. Originally Posted by ancalagon
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.

I think intuition can be taught, and I think it's important that we care about how we get answers.

How does intuition get answers? If we don't know, and it gets them in a way that doesn't scale, then anytime we get a harder problem, intuition will get stumped.

If all it does is hand us answers which might be right or might be wrong, sometimes, then it's less useful than a calculator.
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.) But the intuition is not based on thin-air, it obviously requires knowledge (of people, of mathematics, etc.). The conclusion however goes beyond the limits of logic which is a merely deductive pursuit of knowledge. The conclusion arrived at by intuition is inductive.

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.

Ni is the faculty of "internal" inductive proof. Its proofs generalize such issues as the nature of man, of consciousness, of the "varieties of religious experience." Rather than adding imaginary lines to triangles (an Ne leap of logic), Ni adds concepts that it finds within its own consciousness or unconsciousness (known by Jungians as "archetypes," but a better term would be exemplars, i.e., excellent or perfect forms or models). (For all intents and purposes, it doesn't matter whether or not these exemplars are collectively or universally held forms, i.e., whether or not the unconscious form is collective versus individual.) These forms, held up as perfect exemplars in the Ni function, force the thinking in a novel direction. The conclusion isn't reasoned toward in any way, shape, or form, although it may be reasoned toward later.

10. Robert Pirsig, author of the famous novel Zen and the Art of Motorcycle Maintenance, is a perfect example of an INTP gone Ni-batshit-crazy searching for an axiom to explain everything. After he found it, they had to zap his brain with jolts of electricity to bring him back to non-Ni reality.

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