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Math How important is it to understand math?

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Hey, I'm a senior in a high school in Canada and I'm thinking of pursuing mathematics and philosophy in university. I'm quite interested in mathematics and philosophy but I am also interested in lots of other topics. The main reasons that I want to study math and philosophy at university is that:
1. I want to acquire better skills in analytical and logical thinking so that it would be easier for me to learn about any other scientific discipline in the future and
2. I want to enrich my personal experience by challenging myself to hardships and difficulties that I have never put myself into for the past 12 years of my school life

Why I'm asking the question:
A few days ago I was talking to a friend of mine who majored in mechanical engineering at University of Toronto and also have a masters in Artificial Intelligence at a good school in the States(smart guy, didn't have to work really hard during uni to get through), and since I want to study math I asked him about it and he said he couldn't really understand any math he learned after sophomore year. He said he could still do the problems and do good in tests but he just doesn't understand them. This scared me a lot because I don't want to spend four years just learning how to solve some problems without understanding what I've learned.

More info about me:
- I have good grades(95s) in all subjects at school (other than English, it's my second language :(((() with minimal effort(I hardly do any homework or pay attention during class because I find things boring. The only reason that I'm getting high grades is because I'm good at analyzing what the test taker wants and making out answers from the test).
- I take all the sciences(physics, chemistry, and biology) and find them extremely easy. (I'm not taking any IB or AP courses)
- I'm a very lazy person with really bad work ethics (I don't like memorization. I find the easiest way possible to do things. I usually procrastinate to the last moments to do something and finish it with high efficiency only to find that I have more time...)
- Sometimes I'm a little slow to process information because they just don't seem to register in my mind when I'm not in the mode, but once I grasp things I grasp them really thorough
- I have great short term memorization when I try(like before tests), able to cram lots of things in a short amount of time however also forget really fast. My mind seems to automatically delete things that I find unimportant.
- I have depression which makes it kinda hard to be very passionate about anything. I find it hard to convince myself to face difficulties because nothing is that meaningful to me.
- I do enjoy thinking, introspection, and somewhat abstract thoughts a lot but doing that too much aggravates my depression :(((((

I'm really scared and insecure now because I think all I'm good at is taking tests, I'm just really good at finding out test maker's pattern and preferences. I'm also really afraid that as much as I want to challenge myself to some vigorous thinking I don't want to put myself in the position of trying to climb an unreachable hill. Any opinion? Sorry this thread is really incoherent and hard to read...
 
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symbolipoint

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I'm a senior in a high school in Canada and I'm thinking of pursuing mathematics and philosophy in university.
Change the "Philosophy" part to something else. Keep the Mathematics part though.
 

symbolipoint

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1. I want to acquire better skills in analytical and logical thinking so that it would be easier for me to learn about any other scientific discipline in the future and
2.
Now with that, more than a DIFFERENT choice than Philosophy, you want maybe Physics, English (I am not kidding), Computer Science, some few good choices from Biological Sciences (especially Microbiology), and maybe some selection of courses from Engineering.
 

WWGD

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Well, Fanger, for one, you can participate in discussions here in PF, gauge your ability to understand and participate and adjust accordingly.
 

StatGuy2000

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Hi @Fanger , welcome to PF forums! To start off, there is nothing wrong in having an interest in mathematics and philosophy and pursuing these studies (although keep in mind the importance of acquiring marketable or employable skills). I myself studied math at the University of Toronto and consider it among the best decisions I have made. So if this is what you want to do, I would encourage to pursue it.

To address your specific concerns, I will respond to these one-by-one:

Why I'm asking the question:
A few days ago I was talking to a friend of mine who majored in mechanical engineering at University of Toronto and also have a masters in Artificial Intelligence at a good school in the States(smart guy, didn't have to work really hard during uni to get through), and since I want to study math I asked him about it and he said he couldn't really understand any math he learned after sophomore year. He said he could still do the problems and do good in tests but he just doesn't understand them. This scared me a lot because I don't want to spend four years just learning how to solve some problems without understanding what I've learned.
It's important to keep in mind that students in engineering do not study the same math courses as the math majors/specialists. The focus tends to be on math that is specifically geared toward engineering applications, which often doesn't require any conceptual understanding beyond those applications.

Not to mention that unless your friend is specifically working on research related to conceptual aspects of math, it probably wouldn't matter to him to seek further understanding. Your situation may well be different, as you seem to be interested in exploring mathematics at a deeper level.

So no need to worry about this, IMHO.

[Moderator: IQ related passages removed. Off topic.]

First, you state that you are lazy with bad work ethics. That is a habit that you will need to change -- the level of difficulty at university is far greater than what you experienced in high school, so it is very important that you put in the work and become more efficient in your study habits. The good news is that this is something that anyone can do if you put your effort into it.

Second, you state that you suffer from depression. Is this a clinical diagnosis, and have you seen a psychiatrist about this? Or are you simply expressing how you feel at times? How severely depressed can you get?

Maintaining a healthy mental state (along with maintaining good physical health) is very important for you to be able to function well in a university environment and in future employment. If you are experiencing issues, I strongly suggest you see your doctor or psychiatrist if you haven't done so already.

Anyways, that's my 2 cents worth. Best of luck!
 
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DEvens

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IQ is relevant. But it is by no means the only factor. IQ is not destiny, though it strongly affects it.

If you are IQ 140 you can perform slightly "above your weight" so to speak by working harder. Or you can be a lazy slob and wind up performing much below.

Basically, the way to think of IQ is similar to the way you would think of height in basketball. If you are 6'6" tall, you might possibly be good at basketball. If you have some built-in talent, the desire, and you work hard to develop some skill. If you don't do those things you won't become a basketball star. But if you are 5'6" tall, it is incredibly unlikely for you to become a basketball star regardless of how hard you work at it.

There is definitely something to be said for the guy who works hard. It's one of the few things I like about the movie "GATTACA."


As children, these two brothers had a contest to see who could swim to a buoy in the ocean. One brother always won. Until one day, the other brother won. And the dominant brother could not figure out how. Until many years later, the lesser brother explained. He didn't save any energy for the swim back.

Of course, it would be nice to live past your university degree.
 

DEvens

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As to the original poster. The thing to do is, look for the subject that "glimmers." Look for the thing that, when you are working on it, you don't notice the rest of the world. If it's math, or physics, or philosophy, or whatever. Look for the subject that when you are working on, it draws you in and you find you don't need to be driven to keep working.

If you can find that, then you won't need threats of grades, or worries about a job, to keep you working. You will just automatically keep coming back to your work and get stuck in. And it will be a rewarding life. It will be working on something you find compelling.

If you can find that, then you can always add on stuff to make a career. If it's math, for example, you can add some kind of computing skills. Or project management. Or any of a large number of possible additional skills. Even if you don't become a math prof. Which you should at least keep in mind.
 

gleem

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Assuming your high school is reasonably good and noting that you do not find the curriculum particularly challenging then you should not have any problem at university. However there is a caveat in that university experience is at another level which may call upon qualities that you have perhaps not tapped into in your current educational experience. It has been said numerous times on this forum that while innate intellectual ability is important it may not alone carry you to a successful completion at university without a good dose of effort.

I am not sure of your friends comments on his not understanding the material in which he has been deemed competent . Perhaps he has been able to get through by merely imitating the procedures. Imitating is perhaps the first thing one does in learning a new subject but that can only take you so far. Perhaps this is also what you are currently doing. This sort of approach is easy for the well equipped and does not need any involvement in the subject matter i.e, exploring on your own the complexities of that subject, the questions it poses the hidden underlying relationships and meanings that it contains. Understanding on the other hand does.


I'm a very lazy person with really bad work ethics (I don't like memorization. I find the easiest way possible to do things.
It is best to do something the easiest way as long as it is the right way. On the other hand the quickest way may not be the best way .


I find it hard to convince myself to face difficulties because nothing is that meaningful to me.
Perhaps you are living a sheltered life. Your future will depend on things becoming very meaningful to you.
University is also not challenging because of the academics but because this is often the first time a person lives away from home and get a glimpse of what the world is really like. Adjustment is very important.

I'm also really afraid that as much as I want to challenge myself to some vigorous thinking I don't want to put myself in the position of trying to climb an unreachable hill.
We never know what is reachable or not. The only way to find out is to try.

I leave you with this quote.

“Nothing in the world can take the place of persistence. Talent will not; nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education alone will not; the world is full of educated derelicts. Persistence and determination alone are omnipotent.”

Calvin Coolidge: 30th President of the United States.
 

WWGD

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@Fanger: Any chance you can sit in on some college classes? One way is to just attend and then discreetly, politely tell the prof. after class whether they are OK with you continuing to attend without being registered. Or just keep attending until someone tells you you can't do so. This may give you an idea of what college classes are like.
 

vela

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- I'm a very lazy person with really bad work ethics (I don't like memorization. I find the easiest way possible to do things. I usually procrastinate to the last moments to do something and finish it with high efficiency only to find that I have more time...)
- Sometimes I'm a little slow to process information because they just don't seem to register in my mind when I'm not in the mode, but once I grasp things I grasp them really thorough.
I felt the same way when I was in college. I didn't follow the advice on how to study and often procrastinated, yet I still did well. The important thing, though, was that I was good at learning stuff. Perhaps I didn't study the way we were supposed to, but what I did worked for me. (Though, to be honest, I probably would have benefited from having better habits.) From what you've written, it sounds like that may be the case with you as well.

You might want to consider if you're assessing yourself fairly. For example, you refer to finding the easiest way possible as if it's a bad thing. It often isn't. In figuring out the easiest way, you're typically considering and assessing alternative ways of solving a problem. My classmates would often grind through tedious algebra to solve a problem. I, on the other hand, would spend even more time trying to figure out how to avoid the algebra. But it paid off in the end because I often developed a better grasp of the material. (At the very least, I got much better at algebra because I would often find patterns I could take advantage of to minimize the work.)

I'm really scared and insecure now because I think all I'm good at is taking tests, I'm just really good at finding out test maker's pattern and preferences.
It sounds to me like you might be suffering from imposter syndrome.
 
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Now with that, more than a DIFFERENT choice than Philosophy, you want maybe Physics, English (I am not kidding), Computer Science, some few good choices from Biological Sciences (especially Microbiology), and maybe some selection of courses from Engineering.
I understand that philosophy is kinda a "jobless" major but finance is not really a problem for me as my education is going to be funded by my parents. I do plan to study more after undergrad I'll probably pursue an area that will actually land me a career. Thx for the advice I'll make sure to take some computer classes. I have some doubts about choosing English tho, can you expand on that? How does that help?
 

StatGuy2000

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Are you able to substantiate that claim? Have you seen any reputable research publication that shows no correlation between IQ and success at university?
Psychologist James Flynn has argued in a number of publications that IQ is only weakly correlated with intelligence. If intelligence is only one factor involving success at university, we can thus infer that IQ is only weakly correlated with university success.

I should add that I personally feel that much research related to IQ and mental testing for intelligence in general have been dead ends of dubious scientific value. Physicist-turned-statistician Cosma Shalizi have written great summaries on our mutual skepticism of IQ in his blog.


 

symbolipoint

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I have some doubts about choosing English tho, can you expand on that? How does that help?
English may appeal to your interest in Philosophy. Literature is often a broad area which "English" courses examine, and this literature frequently explores problems about human and group interactions, but in an artistic, written-lengthy-composition kind of way; also including about this instruction and study, literary techniques. One will find that some or many literary artistic works are or fit forms. Such courses also contribute to your skills in PRESENTATION.

My suggestion about English is not that you should consider choosing it as a major field, but that some courses of English beyond whatever official requirements for some sci or engineering major field can be both beneficial for YOU and may well appeal to your interest in Philosophy.

If you were bored from your high school English courses, please realize that English in college or university can easily be much more stimulating.
 

MathematicalPhysicist

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Basically, the way to think of IQ is similar to the way you would think of height in basketball. If you are 6'6" tall, you might possibly be good at basketball. If you have some built-in talent, the desire, and you work hard to develop some skill. If you don't do those things you won't become a basketball star. But if you are 5'6" tall, it is incredibly unlikely for you to become a basketball star regardless of how hard you work at it.
Well, for every rule there's an exception.

Besides my rule :oldtongue:
 
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Moderator: The OP misled us by putting IQ in the title. It is not really his question.

IQ is a hot button issue that we try to avoid at PF. Therefore, I edited the title and the OP post to remove reference to IQ. I also removed all posts in this thread that address only the IQ aspect of the question.
 

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