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Is it true not all of us can get a math degree?

  1. Mar 24, 2010 #1
    So i was talking with 2 of my grade 12 math teachers. Both agreed that each individual person has their "ceiling" where they max out in terms of mathematical knowledge and advancement. This really got me discouraged because what's carried me through math was because i was always willing to work at it and work hard at it. So bottom line, is this really true? I'm scared because the only subject in school i like is math and anything math related. If i can't do this, i don't know what to do at all with my life. Or is all you need hardwork? I know a phd and masters is an exception but what i really just want is a regular math degree.
  2. jcsd
  3. Mar 24, 2010 #2
    Hard work will get you through a bachelors just fine; talent just makes it a bit easier.
  4. Mar 24, 2010 #3
    No one can really give you a straight answer. Natural ability has some effect on how you do in higher level maths, but no one really knows how much. I have never seen a person who really felt math was interesting who wasn't able to do it. This may of course be because they have dropped out earlier for some reason, but this is purely anecdotal.

    However I have seen a number of people arrive at university and find that they have no idea what math really is. That math is barely about calculations.

    Perhaps you should talk with someone with a bit more perspective on the matter than you. Maybe a guidance counselor at your school (if they have those), or maybe your parents. There are lots of alternatives that require skills that are close to that of mathematics. For instance I find that mathematicians or people thinking about choosing mathematics often find the following areas interesting:
    - Physics (or other science-related subjects like chemistry, biology, etc.)
    - Engineering
    - Computer science
    - Statistics
    - Software engineering (programming)
    What do you think about doing after college? If you just want a "regular" math degree (by which I assume you mean bachelor) there is not much chance of doing research mathematics so you will have to find something else you like (whether it's some applied form of mathematics, or something a bit more remote). I'm not saying math is not the right thing for you, but perhaps you should think a little more about the alternatives before committing to one subject.

    Probably, but different kinds of people needs different amounts of hard work and if you need 23hours/day, then of course you won't be able to make it. However with some intelligent study habit and an interest in the subject I believe you would probably be able to succeed in

    In many ways academics are elitists and a lot of people who went through some kind of degree like to think that not many people could have done that. People like to feel special. Given that their social groups like to as well it's easy to provide positive feedback in a social group that ultimately results in everyone having an exaggerated sense of how hard their degree is. I believe this to be part of the reason why it's common for people to delude themselves into thoughts like "only a select few can do <x>". If you are reasonably hard-working and able to study smartly, then you will be able to get a bachelors in mathematics.
  5. Mar 24, 2010 #4
    thank you rasmhop. I wasn't sure that i could get a degree. I really have no plans on getting a masters or higher. I mean it would seriously be nice if i could but as of now, i'll take it one step at a time. Also, i really do hate elitists. Why can't they just let their ego go away and be nice? I believe math is like a skill where you can hone given enough practice. But having heard teachers who have actually been through the course, and telling me "you either have it or you dont'" is a downer.

    Honestly i hope i do end up getting a math degree and after that, i plan on doing some minor in business or physics. Then i can find employability. Math is the best tool humans will ever have. I truly do believe this.
  6. Mar 24, 2010 #5
    You might like economics then, and the math involved tends to be very down to earth/practical.
  7. Mar 24, 2010 #6
    As the question is currently phrased, I completely agree with rasmhop.

    However, not all math degrees are created equal. In fact, if you tell me that you have a bachelor's degree in math, then you will have told me very little about your mathematical knowledge. Perhaps you went to a relatively easygoing college and you only reached analysis and algebra your senior year. Perhaps you went to Harvard and took Math 55 as a freshman. Perhaps you have a very strong focus on topology but almost ignored the other areas as much as you could. Maybe you got special permission to substitute math-intensive computer science courses for a few math courses. Who knows!

    So whether anybody could do it with sufficient effort depends on what exactly you mean by a math degree. Just a plain old math degree--I don't see why the majority of people couldn't do that with effort. But if by math degree you mean taking graduate courses as a freshman and making As--no, I don't think very many people at all could ever pull that off. But some people do, and they will graduate with a math degree just like the other math-degree-holders did.

    As for whether there's a ceiling or not, I don't think so, but I do think that there are various hurdles and that these hurdles may occur at different places for different people. For a lot of people the first hurdle might occur in transitioning from algebra to calculus and the second hurdle might occur in transitioning from lower-level math courses to upper-level ones, such as analysis or abstract algebra. There may be yet another hurdle in transitioning to graduate-level courses, and then another hurdle in transitioning to open-ended research work.

    For some people these hurdles may be more severe than for others. For a few people the first few of these hurdles may not even exist and the latter ones may be reduced in magnitude. For others all of these may be very significant and difficult hurdles to overcome. It really varies a lot.

    I think the severity of the hurdles is tied to how early you start taking mathematics education seriously and not necessarily talent (although natural talent can't be ignored). If you decide you want to pursue math serious after you're already in college and you've never really known much about it previously, these hurdles will all probably be very extreme because you will have a huge amount of catching-up to do. If you discovered a love of math back in junior high, you may with good preparation and timing be able to avoid essentially all of them. I suspect that many people would mistake your well-planned avoidance of the hurdles with some super-intelligence.
    Last edited: Mar 24, 2010
  8. Mar 25, 2010 #7
    The transition from computational math to abstract math is a real doozy for the unprepared. If you tough it out and work really hard, it'll pay off.

    I have a lot of interesting stories about how I arrived in my major. :biggrin: I was booted out of my high school my junior year for various reasons and ended up graduating from a remedial school with a GPA around 2.0, if I remember correctly. I bamboozled my way into college, and eventually switched over to an applied math major. While I'm clearly not some Ivy-educated Putnam Fellow knocking out grad courses left and right, considering my circumstances, I'm very happy with my accomplishments.

    I'm a slow learner, I mean really slow. I'm not a genious -- far from it. Rather, I've gotten through my degree by having a strong interest in the subject and a good work ethic.
    Last edited: Mar 25, 2010
  9. Mar 25, 2010 #8
    I go to school with prospective teachers. No offense to Grade 12 teachers, but I learned that high school teachers are not too bright. They make special math classes just for them because it's too hard. So in essence, they didn't even do an authentic math degree so how would they know?

    Second, their is a limit or "ceiling" of learning in any field. That's just common sense. Not words of wisdom.
  10. Mar 25, 2010 #9
    There is no such thing as a natural genius or natural talent. These are terms used only as excuses by people who are lazy as a reason to why they don't do something.

    So if you want to do math you can do math. If you want to be the next Einstein you can be. Your "natural ability" isn't going to hinder you in anyway because there is no such thing.
  11. Mar 25, 2010 #10
    I'd like to know what you're basing these grand claims on. Of course many people are more talented. I know someone who can do huge calculations in their head quickly, which I would take a minute+ to do on paper, if I try harder will I be able to do that? I'm not sure.

    A good example I like to think of is that of Sherlock Holmes, you can see what he's doing, and you'd like to tell yourself you'd of seen it, but really he's in another league, it's just like that sometimes.
  12. Mar 25, 2010 #11
    I don't know if I'd agree with the non-existence of "natural talent." People could work their entire lives and not accomplish what Euler or Gauss did in one year. And then there's the child prodigies...

    With that being said, I tend to agree with you in a way. I think this whole "talent" business is blown way out of proportion. I think people underestimate what a little hard work and dedication can get you.
  13. Mar 25, 2010 #12
    I am basing these claims off past successful people and things that I have seen in my life. I am sure it would be nice for people to think that they are more naturally talented than some other people because it gives them a pedestal to look down on other people. And, like I said before, claiming that people are naturally talented gives others an excuse to get out of something which may be difficult to do.

    I don't really consider being able to do large calculations in your head as talent as it has no worth. But yes if you practiced I am sure you would be able to do them as well. Of course there are people, savants, who can do crazy things in their head and obviously you or I no matter how much we practice could do such a thing. So I guess you could use that as an example of being naturally talented if you wanted.

    I would love to hear some examples of people in physics or math who were "naturally talented" because all the ones who I know of were not. Everyone I can think of who was a "genius" or "naturally talented" was so because a result of passion/hard work. Einstein was so smart because he loved his subject and studied it a lot. He wasn't just born smarter than everyone else. All the people today or in the past who were exceptional in their field are not there because they were born with some talent in that area.

    I mean do you honestly think that a child is born with some propensity to kick a soccer ball or throw a football?
  14. Mar 25, 2010 #13
    I really think it's a matter of Will to power, Nietzsche would say we can achieve anything by hard work, all kind of triumphs require suffer, otherwise you cannot claim them as a success. So in fact, yeah, there may be people who has more facility on solving problems than others, or more readiness to understand abstract concepts; but that does not mean that they are going to succeed in physics. Einstein as people is posting as example was really a hard working physicist, also Dirac (oh man, he didn't even have life!). So as a conclusion I'd say that if you really want to succeed on something, you will really need an extreme eagerness for the subject and be totally ready to give up your social life.
  15. Mar 25, 2010 #14
    If we were to slighly rearrange the order in your post:

    But then,

    So you sort of gave yourself an example. Those kid-prodigies fully warrant the term "talented." Even a cursory review of their accomplishments will convince you this is so.

    Again, while nobody is denying the power of hard work, to say that "natural talent" does not exist is ludicrous.
  16. Mar 25, 2010 #15
    My advice to you is take advantage of your youth and go to college with a plan and your passion, but one of the best things about college is the freedom to study what ever you want. My advice is take as many Math classes as you can and work as hard as you can, but if for some reason that isn't enough( which i don't believe) slide into another major that intrest you. You are way to young to feel like life is over no matter what you fail at. Persistance is one of the best attributes you can aquire. Good Luck!!!!

  17. Mar 25, 2010 #16
    Yes! But that's beside the point.

    I believe that most people have the capacity to understand anything. The problem is that the process of realizing that capacity is unknown. It's all about finding the right approach to it, and some people naturally approach certain things in the right way. If you don't have a natural predisposition towards the correct approach, you either need very good guidance, or else you will struggle indefinitely to find it.

    The most influential factor in an approach of math, though, is a love of the subject.
  18. Mar 25, 2010 #17
    Sure if you want to give such a superficial argument. What I am trying to say is that the only sort of talent you can argue is perhaps for a savant. But a savant can't put anything together. They can factor primes or something but they can't publish a paper on general relativity.

    The point I am trying to make is that there is no such thing as being born to do something. Child prodigies don't really exist. Say a kid is amazing at the piano, its not because he was born that way and if you look at his life you would see this.

    There are sort of 2 ways to define natural talent. The way you are defining it is analogous to this:

    Someone is small and double jointed so they can fit in a small box. Therefore she is naturally talented at fitting into boxes.

    And sure thats true and thats one way of defining it I guess. If you are defining it that way then yes its absurd to say natural talent doesn't exist. But I am not defining it that way.
  19. Mar 25, 2010 #18
    This is an extremely bold claim that have no scientific backing at all and do not come from any other logic other than "It would be nice if everyone was created equal and success just was about passion".

    Einstein for example did not just work hard, he had an extremely revolutionary way to look at nature compared to other physicists at that time. His accomplishments are so large and many that he is in his own league, no other physicist in history can measure up to him.

    You could say that he got some random insights that made him who he was and not natural talent, but that is even more far fetched than the ideas of natural talent.

    Also, don't you believe in evolution? Monkeys are obviously not able to learn high level maths. Humans are. Somewhere along the evolutionary line humans developed a brain capable of the abstract thinking needed for maths. Claiming that this is a binary trait is ridiculous, same with claiming that all humans somehow equalized their brains along the way.

    Lastly people are not born to kick footballs, but they can be born with genes encoded with better spatial intuition, better muscle fibres and better hormone distributions than others. Same as how some are born with codes for a clearer memory, better ability to visualize and being better at making connections between relating subjects.
  20. Mar 25, 2010 #19
    I'll certainly agree that hard work is a more important factor in success than talent. Hard work and moderate talent will beat lazy but more talented every single time.

    But great talent *combined* with hard work will leave everyone else in the dust...

    But going back to the OP's question, I think that almost anyone who puts in enough work can get a B.S. in mathematics.
  21. Mar 25, 2010 #20
    Not really, it depends on how you define all of those parameters. I can definitely say that I have a better track record with courses than many hard working people and I am among the laziest and most unmotivated people you can find.

    And it isn't even that strange. Pose that you have a person who have a very good memory and a good intuition. The memory allows him to retain the information after a single lecture and the intuition lets him sort the information to make it practical. VoilĂ , you now got a student who will barely need to study and still get decent grades and those traits aren't even that remarkable.

    Also what is it with this stigma about intelligence? I mean, who cares if you do something through hard work or natural talent? It is not like you can change your motivation or childhood just like that either. I think it is just a remnant of the old "It is not cool to sit and study" you get back in middle school, you are cool if you don't have to study but a nerd if you do or something like that. Why do people still care about that even after they have left high school?
    The other explanation would be that people adore freaks. Kinda like if someone has a strange accent everyone will ask him about it.

    I really admire and am sort of jealous of hard workers, I can't imagine how anyone could be that motivated.
    Last edited: Mar 25, 2010
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