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Ask HN: Where did you top out in math classes?

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Re: Ask HN: Where did you top out in math classes?

#41

Post by mlinsey »

g00dn3ss wrote: post #6

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…

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.

Re: Ask HN: Where did you top out in math classes?

#42

Post by Tichy »

nazgulnarsil wrote: post #39
Tichy wrote: post #28

Seems to me all or most human understanding of maths is poor. Most things, even if we can prove them, we can not really understand them. I wonder if there is a different way to understand maths out there.

you're probably a victim of rote learning math classes. learning math for real (getting it) is not a linear process. lots of aha moments where lots of concepts fall into place suddenly and then you move on to more advanced things. that said, I would consider everything below calculus to be merely clever ways of tallying stones. algebra can be tricky at times (abstract algebra sucks) but it is really not that interest…

I did understand a lot of maths, I just mean that I think the way we do maths often is not really understanding. If we have proved something with a hundred step proof, I might be able to verify every single step of the proof and conclude that it is correct. But we might not really have a feel for why it is correct. Can't really think of a good example right now :-/ I mean usually we jump through quite a few hoops to prove something - maybe there are other ways of looking at it that would make more sense.

One example might be the autistic people who just know if a number is prime or not. Not sure if they are really doing anything special, or just calculating really fast, though.

Re: Ask HN: Where did you top out in math classes?

#43

Post by muriithi »

mnemonicsloth wrote: post #21

With one notable exception, math seems very easy to me. I open the book, write down verbatim anything labeled Definition , Theorem , or Lemma , and trace through anything labeled Proof . There's nothing particularly hard about it -- you just have to make sure you actually do every step listed inside your head. It is a little slower than reading for pleasure, but with practice, I'd say only by about half. I think the…

Do you take adderal because you suffer from ADHD or you take it get focused?

Re: Ask HN: Where did you top out in math classes?

#45

Post by Shortnick »

plinkplonk wrote: post #26
rtf wrote: post #12

I don't know, how about every subject? Multiplication. Long division. Algebra. Geometry. Trig. Calc. I was never very motivated to study math. The problem was, my older brother was very into it(and now is a math grad student, ever-so-slowly getting his thesis together). This set a model that I could not hope to emulate, but it only meant my mom pushed me more, talked to the school to get me into the advanced/accelera…

"The former Soviet educational system, OTOH, had probably some of the strongest math education, and much of it has been translated to English - pick up a book from that period and you will probably see a small and dense text that introduces high-level concepts in great, if unforgiving, detail. Very different from the thick drill+practice textbooks I'm used to." Could you provide a url for some of these? Should I look…

Not pure maths, rather applied, but one would have to mention the Landau course as sharing those characteristics.

http://www.amazon.com/Landaus-Course-in-Theoretical-Physics/...

Re: Ask HN: Where did you top out in math classes?

#46

Post by davo11 »

mnemonicsloth wrote: post #17
jfarmer wrote: post #11

I have yet to find it, but Algebraic Topology took me a long, long time to get.

My first thought on reading this was "dude, you stole my answer." After thinking about it for a while, though, I think General Topology is worse. I still don't get it. Or, what's worse, maybe I do get it, and just don't care enough about the subject to register that fact.

I got it I think and still open up the books every now and then, but it was about topology and model theory that I started to question its applicability. I remember asking my lecturer this (I could have phrased it a little better in hindsight, I sort of burst out during a lecture 'whats the point of this' The lecturer got a little upset :-)).

Transfinite numbers are always my favorite example of something way out there, different sorts of infinities and which infinity is bigger than the other, the models are beautiful, but I couldn't spend my life arguing about them. I think for most people maths starts losing its relevance a lot earlier, it justs takes some longer to admit it, because it's prettiness is so seductive :-).

Re: Ask HN: Where did you top out in math classes?

#47

Post by davo11 »

nazgulnarsil wrote: post #39
Tichy wrote: post #28

Seems to me all or most human understanding of maths is poor. Most things, even if we can prove them, we can not really understand them. I wonder if there is a different way to understand maths out there.

you're probably a victim of rote learning math classes. learning math for real (getting it) is not a linear process. lots of aha moments where lots of concepts fall into place suddenly and then you move on to more advanced things. that said, I would consider everything below calculus to be merely clever ways of tallying stones. algebra can be tricky at times (abstract algebra sucks) but it is really not that interest…

funny, I always thought it was the other way around, calculus was just a clever calculating trick, but give me a good algebra, then we can really do something :-)

Re: Ask HN: Where did you top out in math classes?

#48

Post by byrneseyeview »

elai wrote: post #37
doubleplus wrote: post #33

Earlier quoted context omitted.

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…

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…

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.

Re: Ask HN: Where did you top out in math classes?

#49

Post by thorax »

I don't know if I topped-out, but I did lose interest. Calc III felt hard with not very much useful information (my comp sci advisers basically gave me grief for taking it). Linear Algebra sparked my interest again, but only because it started out wicked hard and then (just like with Calc years before), it just "clicked" and suddenly it was a lot easier/interesting. I didn't pursue further because after I graduated I preferred diving into new compsci (and engineering) concepts rather than focusing in math areas.

Re: Ask HN: Where did you top out in math classes?

#50

Post by g00dn3ss »

doubleplus wrote: post #33
g00dn3ss wrote: post #6

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…

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…

Here is a pop-sci version of some recent research:

http://www.sciam.com/article.cfm?id=the-secret-to-raising-sm...

However, this isn't particularly surprising. Research on "grandmasters" in many activities, like chess or pilots, usually shows they've put in 25K hours of practice in their field.

I'm certainly not in favor of saying anyone can do anything. Especially in physical activity. There are definitely physiological advantages.

The same is also true in mental activities to some extent. A kid with down syndrome probably isn't going to become a math professor. However, I think the point is that most normally developed folks probably haven't hit a ceiling in their math aptitude. They just stopped caring or putting in the effort.

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