Are INTPs Good At Math???

[nick22]

Hi. I'm a high school sophomore and I was wondering if most INTPs are good at math. Personally I am horrible at it and just manage to barely pass. It's interesting because I have an A in every other class and their all Honors classes. I feel like I'm being fed a formula and told to just plug things in. I'm not told why it works or how it works.

Also because of this do you think it is still a good idea for me to aspire to be an engineer? I hate math, but I love solving problems and figuring out how things work. I love history and would much rather major in that, but I cannot be a teacher and my parents refuse to pay for any degree that is not "productive."

 

[Artsu Tharaz]

I'm brilliant at it. I won't use a formula if I don't know why it works. I'll figure out why it works on an intuitive level, and only then be comfortable using it. Not being told why makes it more fun.

Don't do something if you can't see yourself in the position. I don't know much about what engineers do exactly.

--
If INTPs aren't, who is? What functions does it use?

 

[Words]

Temperament is not ability;it is preference. Supposedly, INTP's like math. Hence, the notion of "INTPs are good at math" is because of the tendency for people to be good at what they like doing.

The definition of "math" must also be taken into consideration.

Personally, right now, I think I am only slightly better than average. I have not focused on it because as much as I prefer the raw subject, I do not like the common approach in studying mathematics. I do not like reading, practicing, memorizing etc. Instead, I like to verbally participate in class or elsewhere.

You can be anything as long as you are curious in it.

 

[kinetickyle]

I'm god-awful at math even though aptitude tests say I should be good at it. I guess I developed a mental block somewhere in my early childhood. I'm brilliant in English, history, and most of the other humanities, though.

If you're no good at math, you should probably think of something besides engineering. There's a lot of math there. Look at the degree requirements for biology, medical technology, economics, etc. They all have math requirements, but usually not as much as engineering. If you're OK at math, you might look at accounting. My dad's an accountant and he's good at that sort of math, but can't do anything more advanced than basic algebra to save his life.

Or you could try to convince your parents that English or journalism is a good bet. A lot of jobs hire people with exceptional writing abilities.

On a side note, it always pisses me off to hear about parents that won't pay for college if the degree isn't "productive." Most people end up working in fields that are unrelated to their degrees, anyway. I say let your kids study what they want and trust them to figure out the rest.

 

[DannyBoy]

Math never interested me either I think the "mental block" applies for me aswell.

 

[The Gopher]

I am in a high percentage for problem solving ability however my theory is that it 'would be' to easy and predictable (if I put my mind to it) so I don't even try.

 

[BigApplePi]

nick22. INTP's presumably think. So they probably have an aptitude for math. The problem with math is you must learn the starting points. It's like a game. If you don't know the rules and are thrown into the game, you can't do well. Learn the rules.

Where are you at in math? Geometry? Algebra? I learned to think with high school plane geometry. Loved it. Depends somewhat on the teacher though for inspiration.

I have the equivalent of a Master's in math. Taught calculus in grad school. Feel free to ask questions. I'm starting to forget.

 

[Cogwulf]

I'm "good enough" at maths.
I think the main problem is throughout life people have tried to teach me to memorise equations and formulae, rather than teaching me how they work.

 

[Fedayeen]

I hate math and I love it.

School type math I hate its boring. its all use this equations in this way to solve these problems. Now do it 50 more times.

I like having a real life problem to figure out and using math in my own way to solve the problem. Unfortunately I dont generally have problems that need solving IRL. So most of it is spent on RPGs or other video games....mostly RPGs though

 

[BigApplePi]

I like having a real life problem to figure out and using math in my own way to solve the problem.

Here is a math problem:

If 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... adds up to 2 in the limit, what does

1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + ... add up to in the limit?

Can you make sense out of it? What do you think?

 

[SpaceYeti]

I'd say we have a propensity for it, but we don't like to study the more complicated stuff.

 

[descendant]

I like solving math problems but I'm just too lazy to learn it
but even though I don't study much I'm better than some of my friends just not the best

 

[BigApplePi]

I'd say we have a propensity for it, but we don't like to study the more complicated stuff.

We don't like the pain of frustration. Easy is more comfortable. But if too easy, boredom results. People will turn to challenges which if solved can make other problems easier. Then we have specialists who LOVE the complicated stuff. They will struggle and struggle over long periods of time to solve a problem. The satisfaction is in solving it ... or in contributing to solving it.

Flying comes to mind (it doesn't have to be math). Man couldn't fly and tried to build something which would get him off the ground. After much effort, finally succeeded. Math is like that.

 

[Zionoxis]

I am not bad at math, but I am not good at it either. My issue is that I always strive to learn WHY it works and HOW. My school's math department is rigged in such a way that if you ask such a question, you are ignored and pushed aside. With the "No Child Left Behind", there is nothing for me to do but sleep through class and memorize the basics so I can get a B on the test. I see little to no point in putting in the effort to not know why it works. I am not even completely sure if I could understand it to the level I need to make an A without understanding the How and Why.

 

[AlisaD]

I used to be very good at it until I started really thinking about it and realized it's all crap.
Then I got bored and stopped doing it.

 

[AnAudienceMember]

I'm able to BS my way through passing most of the tests while sleeping through the notes i was supposed to be taking.
and just knowing that... i cant say i know anyone who can tell me.

 

[EyeSeeCold]

--
If INTPs aren't, who is? What functions does it use?

Have you forgotten about INTJs?

 

[SpaceYeti]

Yes, INTJs are all up ons math.

 

[gruesomebrat]

Here is a math problem:

If 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... adds up to 2 in the limit, what does

1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + ... add up to in the limit?

Can you make sense out of it? What do you think?

The problem here is that
1+.5+.25+.125+.0625+... =/= 2.
You're describing an inverse exponential problem, which will come close to 2, but never actually equal 2. The best you'll get is 1.999 repeated.

Since the assumption of the first problem is incorrect, any solution found using that assumption will also be incorrect.

 

[Fukyo]

http://www.intpforum.com/showthread.php?t=7178

 

[gruesomebrat]

I was never much of a math person myself through elementary school. I found it to be incredibly boring, but that was primarily because of the way that it is taught. In Grade 9, I found that it was much easier to learn the course if I just read the book, rather than listening to the teacher, and because I read considerably faster than the average person speaks, I ended up speeding ahead of the entire class. By the end of Grade 9, I had not only taught myself everything that was required for the course, I had also taught myself most of what was needed for the Grade 10 Math course, and even the first month of Grade 11 was merely review for me of what I had learned earlier. I ended up walking out of my Grade 9 with he highest mark in the class (>99.5%), but that was primarily because I had informed the teacher that I was working ahead, and I was able to demonstrate to him that I had satisfactorily taught myself the curriculum. I got lucky, in that I had a good teacher for this.

If you feel your biggest problem with Math class is that the teacher simply tells you the formula and wants you to plug in the problems, then the best bet is to do some extra reading about the formulas. It's considerably easier now than it was when I was going through my problems with Math, as now you can just look up the formula on Google, or elsewhere online. I had to look through the textbook for the equation to do my reading. But, that aside, a little bit of extra studying, looking into the why and how behind the equations you're being fed, will go a long way to helping you succeed in Math class.

 

[SpaceYeti]

The problem here is that
1+.5+.25+.125+.0625+... =/= 2.
You're describing an inverse exponential problem, which will come close to 2, but never actually equal 2. The best you'll get is 1.999 repeated.

Since the assumption of the first problem is incorrect, any solution found using that assumption will also be incorrect.

1.9999 repeating is 2.

Proof; .999... / 3 = .333...
.333... x 3 = 1

1.999... = .999... +1.

 

[gruesomebrat]

1.9999 repeating is 2.

Proof; .999.../3=.333...
.333...x3=1

1.999... is .999... +1.

Really? I would have thought that if .999.../3=.333... , then .333...x3 would equal .999...

After all, division and multiplication are just two sides of the same coin. If you divide y by x, then multiply by x, you will be right back at y, regardless of what y is.

 

[SpaceYeti]

Really? I would have thought that if .999.../3=.333... , then .333...x3 would equal .999...

After all, division and multiplication are just two sides of the same coin. If you divide y by x, then multiply by x, you will be right back at y, regardless of what y is.

You're correct, but so am I.

1 / 3 = 1/3 = .333... = .999.../3

.999... and 1 are the same number.

 

[BigApplePi]

Here is a math problem:

If 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... adds up to 2 in the limit, what does

1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + ... add up to in the limit?

Can you make sense out of it? What do you think?

Rephrasing the same problem,

The limit of 1 + 1/2 + 1/4 + 1/8 + 1/16 + ...is 2. (It's said the sum converges to 2.)

What is the limit of 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + ... if it has one? What does it converge to?

There is a known answer to this.

 

[SpaceYeti]

The limit is infinity. Adding an infinite number of minuscule numbers still results in infinity. You're not adding a chain of the same fraction of the last number, you're simply adding smaller and smaller numbers in succession.

 

[gruesomebrat]

You're correct, but so am I.

1 / 3 = 1/3 = .333... = .999.../3

.999... and 1 are the same number.

They are considered to be the same, yes. I think that's probably because the difference between them is so infinitesimally small that they may as well be the same, but the fact of the matter is that we generally assume they are equal, to make certain math problems easier, especially those dealing with thirds, sixths, ninths, etc.

The limit is infinity. Adding an infinite number of minuscule numbers still results in infinity. You're not adding a chain of the same fraction of the last number, you're simply adding smaller and smaller numbers in succession.

On this, at least, we agree. I was going to add that because Pi mentioned a 1 at the beginning of his sequence, that the limit is actually infinity plus 1, but then I realized that infinity plus 1 would still be infinity... approximately.

 

[SpaceYeti]

They are considered to be the same, yes. I think that's probably because the difference between them is so infinitesimally small that they may as well be the same, but the fact of the matter is that we generally assume they are equal, to make certain math problems easier, especially those dealing with thirds, sixths, ninths, etc.

They, in fact are the same. The only way to add a number to .999... in order to get 1, you must add an infinite series of 0s with a one at the end of it... but an infinite series of 0s would never end such that you'd ever get to the one, so you're actually just adding a series of 0s, or in other words just 0. .999... is 1.
http://en.wikipedia.org/wiki/0.999...

 

[Fedayeen]

Here is a math problem:

If 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... adds up to 2 in the limit, what does

1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + ... add up to in the limit?

Can you make sense out of it? What do you think?

that is the school type math i hate

 

[gruesomebrat]

So, Fedayeen... you're more into the questions like:

You are out hiking and come across a river. Not seeing a bridge, you figure it would be a better idea to chop down a nearby tree to use as a makeshift bridge than to go looking for one. You don't know the width of the river, but 15 feet downriver from the tree, there is a boulder on the far side. Your line of sight from the tree intersects the river at 35 degrees. Assuming the river is straight at this point, how wide is the river? If the tree is 30 feet tall, will it span the river, allowing you to cross?

 

[Artsu Tharaz]

Here is a math problem:

If 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... adds up to 2 in the limit, what does

1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + ... add up to in the limit?

Can you make sense out of it? What do you think?

= 1 + (1/2) + (1/3 + 1/4) + (1/5 + 1/6 + 1/7 + 1/8) etc.

lol @ people hurr durring over the concept of a limit

 

[BigApplePi]

Originally Posted by BigApplePi
Here is a math problem:

If 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... adds up to 2 in the limit, what does

1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + ... add up to in the limit?

= 1 + (1/2) + (1/3 + 1/4) + (1/5 + 1/6 + 1/7 + 1/8) etc.

This is what makes mathematics fascinating. There is hardly much difference in the two additions. The 1st one is finite; the 2nd one adds beyond any finite number. The way Artsu has grouped the numbers even though adding to a larger number gets harder and harder, slower and slower. Each grouping is greater than 1/2. So you are really adding 1/2 + 1/2 + 1/2 + 1/2 + ... . It's a trick. Who would have thought of that trick?

 

[Polaris]

Hi. I'm a high school sophomore and I was wondering if most INTPs are good at math. Personally I am horrible at it and just manage to barely pass. It's interesting because I have an A in every other class and their all Honors classes. I feel like I'm being fed a formula and told to just plug things in. I'm not told why it works or how it works.

Also because of this do you think it is still a good idea for me to aspire to be an engineer? I hate math, but I love solving problems and figuring out how things work. I love history and would much rather major in that, but I cannot be a teacher and my parents refuse to pay for any degree that is not "productive."

To answer your question:

I think it is a myth that "most INTP's are good at math". As someone mentioned before, I think NT-types like to get stuck into problems, hence math could be a possible area that we would thrive in. But there are many other areas where one can apply problem solving. The thing is though, and what you have described, is that we like to understand basic structures so that we can apply it to a greater understanding. We look at a landscape or a painting, or a streetscape, and not only take in what is there, but why and how. How was the landscape formed, how was the painting built up, how did that streetscape evolve to its present state of mingled architecture and road structure? And then, finally, why?


Now present a math formula. How would an INTP react to that? We want to apply the same process of understanding as described above. The worst thing for me at school was being served a formula, and be told not to worry about how that formula was created. Of course, I would get more hung up in the mystery of the formula and spend hours trying to understand it. Always a distraction.

If you really like problem solving, and honestly think you can be satisfied with an engineering degree, then I think it would be wise to get someone to help you with exactly those areas of the maths that you struggle with. You need a different perspective. Are there any senior students who offer math tuition? It may perhaps be a question of only a couple of hours before the proverbial penny drops.

/tangent alert:

I think it is a little sad that parents push their children into what they regard as "safe". It is very old-school, and quite selfish. Their justification is that they have your best interest at heart. And that may be true but only to the extent that this is merely another desperate attempt of controlling you. And thereby protecting themselves from society's possible accusations of "bad parenting". Their consciousness is cleared. Sounds harsh, I know. I think it is essential to pursue what you think is right for you. If you apply yourself to what you truly believe in, you will always do well. And I'm not speking of materialistic success. You can always manage, if you are content with what you are doing. One has to be creative about earning a living these days. A challenge an INTP could easily master, provided hir could get past the procrastination hurdles. I think society breeds the necessary cogs in the machine, but what happened to all the independent thinkers? It is not encouraged because there is no monetary value in fields of history, philosophy, art or linguistics. They are a dying breed. When we finally wake up to what kind of hollow society this has resulted in, we may understand why the world has become the wasteland it is. There is no soul, only structures.

/rant

If you love history, would you perhaps be able to do that as a minor? I don't know how flexible your degree program is, and I don't understans the US educational structure, but perhaps it would help to speak to a subject advisor, or coordinator. You sound like a very talented student, I am sure your high school officials would be very likely to give you the support you need. Talking to people is often a better way to find a solution, rather than sinking into the sometimes entrapment-like limits of one's own perspective.

 

[a detached retina]

I say get past Differential Equations into Linear Algebra and
advanced calculus in University before you make a judgement. Algebra in highschool can be really shitty depending on who's teaching it. Do you enjoy discovering truths and thinking about the theory behind something and less actually iterating the solutions or do you enjoy the problem solving, beating riddles, applying your thinking aspect and less of the theory behind it? Self discovery is probably the most important thing you could do before the age of 25 in my opinion. Who cares if you're INTP INTJ ISTP whatever, if you truly dislike math (and not just the way it's taught in highschool) than avoid it and play to your strengths. That's my advice

 

[Fedayeen]

So, Fedayeen... you're more into the questions like:

You are out hiking and come across a river. Not seeing a bridge, you figure it would be a better idea to chop down a nearby tree to use as a makeshift bridge than to go looking for one. You don't know the width of the river, but 15 feet downriver from the tree, there is a boulder on the far side. Your line of sight from the tree intersects the river at 35 degrees. Assuming the river is straight at this point, how wide is the river? If the tree is 30 feet tall, will it span the river, allowing you to cross?

yea, except I'd just cut down the tree and see if it would work. even if the tree isnt long enough to reach it still might be able to get enough for me to hop the rest.

plus instead of estimating angles and how many feet down river the boulder is, it seems more practical to just guess the height of the tree and the width of the river.

 

[gruesomebrat]

I was hoping that by "using math in my own way to solve the problem", you meant thinking outside the box and making your own answer. I still prefer a simpler answer. Rather than chopping the tree down, which would involve you, a hiker, having somesort of woodcutting tools and experience, why didn't you just swim across the river?

 

[Fedayeen]

generally that is, but giving a hypothetical question there are too many variables I am not aware of. Like I would assume that the river would be too strong/deep to swim across, and given that I was asked to figure if the tree would reach I'd assume I for some reason have an ax or saw or something to cut the tree down with

 

[gruesomebrat]

I love this forum. I actually hadn't thought of that, thank you for pointing it out. I suppose if you're being asked to cut down the tree, you would almost have to have some sort of tool or experience in felling trees, wouldn't you?

And now... I'm going to leave this horribly derailed thread alone, while it tries to regain some semblance of order... I may be back, but I've done enough damage for one night, I think.

 

[Fedayeen]

I love this forum. I actually hadn't thought of that, thank you for pointing it out. I suppose if you're being asked to cut down the tree, you would almost have to have some sort of tool or experience in felling trees, wouldn't you?

And now... I'm going to leave this horribly derailed thread alone, while it tries to regain some semblance of order... I may be back, but I've done enough damage for one night, I think.

almost every topic goes off topic by page 2

 

[snafupants]

Good at math? Well, I am good at mental arithmetic and word problems, which I have loved since wearing oshkosh overalls; but actual high school math, like advanced geometry and calculus are areas where I could use some help. My high school math teacher essentially was in the process of obtaining his green card and struggled to string together three words of standard written english, so that probably did not help any. Also, I hate following step-by-step directions.

 

[Jean Paul]

I suck at math, but great at history and science.

 

[Womplord]

Maths is quite an unpopular avenue in any case. However, I think INTPs would be more attracted to maths than most other types, simply because they are NT so should be better at solving logical problems. I am fascinated by maths, which is another possibility for INTPs I think. We tend to be interested in complex things.

 

[Architect]

usually but not always

 

[snafupants]

usually but not always

Noncommittal much? I love this response...

 

[Latro]

The problem here is that
1+.5+.25+.125+.0625+... =/= 2.
You're describing an inverse exponential problem, which will come close to 2, but never actually equal 2. The best you'll get is 1.999 repeated.

Since the assumption of the first problem is incorrect, any solution found using that assumption will also be incorrect.

Unless you're using nonstandard analysis (in which case taking standard parts arrives at 2 anyway), this isn't how it works. lim n->infinity sum(i=0 to n) 2^-i = 2.

Anyway, "math" pre-university and "math" post-university have pretty much nothing to do with each other. Calculus I and II are pretty much an extension of the old teaching methods, but then linear algebra, calculus III to some extent, and everything proof-based is entirely different.

One way to make pre-university math like post-university math is to reduce the list of formulae to a minimal one; that is, setting yourself up so that reasoning takes the place of most memorization. This is especially nice in trigonometry, where there are basically only 3 identities that need a geometric proof:
sin(a+-b) = sin(a)cos(b) +- sin(b)cos(a)
cos(a+-b) = cos(a)cos(b) -+ sin(a)sin(b)
sin^2(x)+cos^2(x)=1

From these you can fairly easily (at most 3 or so lines of algebra) derive every other identity in trigonometry.

(The co-function identities sin(pi/2-x) = cos(x) and cos(pi/2-x) = sin(x) also need a geometric proof but these are very rarely needed.)

 

[EyeSeeCold]

Most interesting that I always outshined my peers until PreCalc in highschool, 'til then I could do math in my sleep.

I'd say I'm decent, maybe better than the average person, I'm not sure anymore.

 

[myexplodingcat]

My advice: Go after history. Then use the older civilizations to make one of your own and become a novelist. You'll probably get about twelve different scholarships for your otherwise good grades.

Or: Go after history. Then become a textbook writer. Those things are always being updated.

Or: Go after science. Then you'll understand math better, and you'll get good at it.

After this point, if you don't LIKE math, don't become an engineer. Bad idea. My dad is one, and he uses math every day. If you like to solve problems, you should join the FBI or the police, or become a doctor and research medical science or treat patients. That's probably the best idea.

I don't know about being good at math, personally... Actually, I do know. I'm good at math, but I hate doing it. I always end up taking the long way to solve problems, then I get the right answer, then I can't explain to anyone else how I got the answer because I'm the only one who understands how I did it. Problems should take thirty seconds, but I end up taking fifteen minutes because I'm going nuts using a method that I know will work (and usually which does) but which I figured out by my own warped brain and not by the teacher.

I think it just comes down to this: Being good at something doesn't mean you like to do it. It also sounds like you have a really crummy teacher.

INTPs like to know why the problems are solved, because they want to know how the system works. That's why I like to use my own methods, because I know how they work...

I can relate... I'm a high schooler too...

 

[Cogwulf]

Maths in engineering is very very different to maths in school.
In engineering you are never expected to memorise formulae, except of course for certain basic ones.
And more importantly you are not taught to simply use formulae without knowing how it works.