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Recent evidence tends to indicate that 'not smart enough' is probably a myth. Almost everything can be attributed to exposure and effort at some point rather t

Recent evidence tends to indicate that 'not smart enough' is probably a myth. Almost everything can be attributed to exposure and effort at some point rather than some innate smartness. A lot of advanced math takes some serious concentration to understand. For some non-practical aspects, I found that I lacked the motivation rather than ability to understand it . One particular class where I seemed to hit my tolerance was a theoretical linear algebra class. I could understand the practical applications of most of the topics but some of the theory seemed just out of reach. The book was extremely dry and I think the professor may have been taking lessons from Ben Stein. Give me a private tutor, a theoretical linear algebra for dummies book, and a pending disaster for which this is the solution, and I bet the outcome would be a little different.

aneesh 18y ago
Very true. I really enjoy math, but after abstract algebra and real analysis, I slowly lost the motivation to go deeper into pure math. Interestingly the most enjoyable areas of math for me are those arguably most applicable to CS: graph theory and number theory.
flashgordon 18y ago
Totally agree. Case in point. Up until highschool I was very good at math. Mainly because I would actively seek out books and try to solve problems where ever I could find them. As soon as I started Uni, my interest dwindled (was replaced by love for all things CS). People who I had dominated back in highschool were now getting a good 10-20% higher than me. All in practise I think.
manvsmachine 18y ago
Haven't gotten to that point yet, but I can definitely attest to the significance of good materials and enthusiastic teaching. Because I started out as a engineering major, I had taken the entire Calc sequence up through Diff. Eq's, but I ended up having to take Prob/Stats and Discrete when I Switched to CS. I was sick of taking math classes at that time, but my Discrete prof was awesome and motivated me to see how far I could go with it. I went into fall semester never wanting to take another math class again; now I'm taking more so I can get a minor in it. I'll be taking combinatorics in the fall and topology(?) the following spring to close it out.
bkovitz 18y ago
Yup, motivation is the blocker. I have repeatedly gotten tired of math when it seemed like meaningless puzzle-solving. Why do I really care, for example, how many nonabelian groups of order 36 exist? When math seems to me like it's providing a vocabulary for framing and answering deep questions about the world, or making it computationally feasible to find the stamp of causal influence in data or design real things that are impossible to make without out, then the motivation is there. This might just be an artifact of the way math is often taught. For example, real analysis is often taught as meaningless proof-finding (e.g. proving things that seem either pointless or obvious). But there's a fantastic book, _A Radical Approach to Real Analysis_ by David Bressoud, that teaches the exact same subject matter as the fruit of deep, pressing, and non-obvious questions that stirred debate among mathematicians for around 100 years.
- manvsmachine 18y ago
  Many branches of math start out as being "meaningless". Number theory was once widely considered meaningless until it was given importance through cryptography. The current head of Microsoft's Cambridge research location literally said to Bill Gates as she was being hired that her work was completely unrelated to computer science; her work was in combinatorial optimization. I think that may be a part of the problem: not enough math professors teach their subjects with any regards to what they are used for. Sometimes, they don't even know themselves.
doubleplus 18y ago
Would you happen to have any links or book references to this "recent evidence"? While most of success comes from effort and discipline, I've always been under the impression that only the naturally gifted (who also have discipline and drive) can/have achieve/achieved certain things. The dwarf down the street from me will never be a professional football player, and someone with a 100 IQ will never be an astronaut. I've always felt the you-can-always-achieve-whatever-you-want-no-matter-what-if-you-want-it-bad-enough approach to be more than a little cliched and misguided. If recent scientific evidence has disproved this stance of mine, I'm open to changing it.
- elai 18y ago
  To be honest, I believe that all intelligence comes from innate motivations and practice. You suddenly become 10x more "intelligent" when you actually give a shit or get some innate joy or obsession relieved when you do it. If that is something that is constant within you, you become more and more practiced and a virtuious cycle results. Nothing is too hard to explain, it's just mathematicians are really horrible at communicating.
  - byrneseyeview 18y ago
    For whom, though? Brains are complicated, but if yours is severely damaged (through a stroke or head injury) motivation is not necessarily going to fix that. And as far as I know, there aren't any permanent ways to raise IQ. Some environmental factors lead to higher childhood IQ, but these vanish by adulthood. And there are tricks people can use to bump up their scores on IQ tests, but I haven't seen a situation in which practicing for test A raises your score, years later, on test B. This stuff is just more static than that. The danger with what you're saying now is that someone with an IQ of 90 -- someone who could be a fine contributor to society in lots of practical, necessary fields that don't require lots of abstract thinking -- could be inspired to throw away lots of time and risk lots of frustration trying to be a mathematician. We should deal with the fact that wasting education on someone who can't use it is as much a tragedy as failing to educate someone who can use it. By pretending that 'smart' just means 'trying hard', you're doing more harm than good.
mlinsey 18y ago
I don't think this is true - or at minimum, higher math/theory certainly comes easier to some people than others, and there probably comes a level of intelligence where you were progressing slowly enough that it really wouldn't make a good career option for you. I hit my brick wall in theoretical classes when I felt like I would understand everything I had been taught up to that point, but to actually construct a proof to solve certain problems I had to come up with some flash of insight which just wouldn't come to me. I simply wouldn't know where to start. I don't think that this is uncommon. When many people write about famous mathematicians and how they solve extremely difficult problems, it usually happens that they have a certain intuition or insight which didn't really follow logically from the problem as stated up until that point. Perhaps anybody could put enough effort into these problems that these insights would come to them as well, but I think this is doubtful considering just how brilliant these insights are. Put another way, when you reach a certain level of math it starts requiring a large degree of a particular kind of creativity, which simply not everyone has.
- g00dn3ss 18y ago
  Actually, there was a recent article on YC news about the large number of discoveries that were made independently at almost the same time. Our made-for-tv histories usually show a lone scientist toiling away for years, making huge discoveries. But in reality, most discoveries are incremental. The stories we are taught about these discoveries are usually mythologized. It is true that there is some level of creativity needed. But it's probably way more common than our histories would lead you to believe. The recurring theme you will hear from scientists is that "chance favors the prepared mind."
  - nsrivast 18y ago
    To summarize: intelligence, motivation, and creativity are important.

aneesh 18y ago

Very true. I really enjoy math, but after abstract algebra and real analysis, I slowly lost the motivation to go deeper into pure math. Interestingly the most enjoyable areas of math for me are those arguably most applicable to CS: graph theory and number theory.

flashgordon 18y ago

Totally agree. Case in point. Up until highschool I was very good at math. Mainly because I would actively seek out books and try to solve problems where ever I could find them. As soon as I started Uni, my interest dwindled (was replaced by love for all things CS). People who I had dominated back in highschool were now getting a good 10-20% higher than me. All in practise I think.

manvsmachine 18y ago

Haven't gotten to that point yet, but I can definitely attest to the significance of good materials and enthusiastic teaching. Because I started out as a engineering major, I had taken the entire Calc sequence up through Diff. Eq's, but I ended up having to take Prob/Stats and Discrete when I Switched to CS. I was sick of taking math classes at that time, but my Discrete prof was awesome and motivated me to see how far I could go with it. I went into fall semester never wanting to take another math class again; now I'm taking more so I can get a minor in it. I'll be taking combinatorics in the fall and topology(?) the following spring to close it out.

bkovitz 18y ago

Yup, motivation is the blocker. I have repeatedly gotten tired of math when it seemed like meaningless puzzle-solving. Why do I really care, for example, how many nonabelian groups of order 36 exist? When math seems to me like it's providing a vocabulary for framing and answering deep questions about the world, or making it computationally feasible to find the stamp of causal influence in data or design real things that are impossible to make without out, then the motivation is there. This might just be an artifact of the way math is often taught. For example, real analysis is often taught as meaningless proof-finding (e.g. proving things that seem either pointless or obvious). But there's a fantastic book, _A Radical Approach to Real Analysis_ by David Bressoud, that teaches the exact same subject matter as the fruit of deep, pressing, and non-obvious questions that stirred debate among mathematicians for around 100 years.

manvsmachine 18y ago
Many branches of math start out as being "meaningless". Number theory was once widely considered meaningless until it was given importance through cryptography. The current head of Microsoft's Cambridge research location literally said to Bill Gates as she was being hired that her work was completely unrelated to computer science; her work was in combinatorial optimization. I think that may be a part of the problem: not enough math professors teach their subjects with any regards to what they are used for. Sometimes, they don't even know themselves.

doubleplus 18y ago

Would you happen to have any links or book references to this "recent evidence"? While most of success comes from effort and discipline, I've always been under the impression that only the naturally gifted (who also have discipline and drive) can/have achieve/achieved certain things. The dwarf down the street from me will never be a professional football player, and someone with a 100 IQ will never be an astronaut. I've always felt the you-can-always-achieve-whatever-you-want-no-matter-what-if-you-want-it-bad-enough approach to be more than a little cliched and misguided. If recent scientific evidence has disproved this stance of mine, I'm open to changing it.

elai 18y ago
To be honest, I believe that all intelligence comes from innate motivations and practice. You suddenly become 10x more "intelligent" when you actually give a shit or get some innate joy or obsession relieved when you do it. If that is something that is constant within you, you become more and more practiced and a virtuious cycle results. Nothing is too hard to explain, it's just mathematicians are really horrible at communicating.
- byrneseyeview 18y ago
  For whom, though? Brains are complicated, but if yours is severely damaged (through a stroke or head injury) motivation is not necessarily going to fix that. And as far as I know, there aren't any permanent ways to raise IQ. Some environmental factors lead to higher childhood IQ, but these vanish by adulthood. And there are tricks people can use to bump up their scores on IQ tests, but I haven't seen a situation in which practicing for test A raises your score, years later, on test B. This stuff is just more static than that. The danger with what you're saying now is that someone with an IQ of 90 -- someone who could be a fine contributor to society in lots of practical, necessary fields that don't require lots of abstract thinking -- could be inspired to throw away lots of time and risk lots of frustration trying to be a mathematician. We should deal with the fact that wasting education on someone who can't use it is as much a tragedy as failing to educate someone who can use it. By pretending that 'smart' just means 'trying hard', you're doing more harm than good.

mlinsey 18y ago

I don't think this is true - or at minimum, higher math/theory certainly comes easier to some people than others, and there probably comes a level of intelligence where you were progressing slowly enough that it really wouldn't make a good career option for you. I hit my brick wall in theoretical classes when I felt like I would understand everything I had been taught up to that point, but to actually construct a proof to solve certain problems I had to come up with some flash of insight which just wouldn't come to me. I simply wouldn't know where to start. I don't think that this is uncommon. When many people write about famous mathematicians and how they solve extremely difficult problems, it usually happens that they have a certain intuition or insight which didn't really follow logically from the problem as stated up until that point. Perhaps anybody could put enough effort into these problems that these insights would come to them as well, but I think this is doubtful considering just how brilliant these insights are. Put another way, when you reach a certain level of math it starts requiring a large degree of a particular kind of creativity, which simply not everyone has.

g00dn3ss 18y ago
Actually, there was a recent article on YC news about the large number of discoveries that were made independently at almost the same time. Our made-for-tv histories usually show a lone scientist toiling away for years, making huge discoveries. But in reality, most discoveries are incremental. The stories we are taught about these discoveries are usually mythologized. It is true that there is some level of creativity needed. But it's probably way more common than our histories would lead you to believe. The recurring theme you will hear from scientists is that "chance favors the prepared mind."
- nsrivast 18y ago
  To summarize: intelligence, motivation, and creativity are important.