Can one become good at math if one lacks a natural and intuitive grasp of mathematics?
I know someone who coasted through most classes of a math BSc without putting much effort into it, while I had to put in work to understand the basics of calculus, for example.
If math doesn't come naturally to you, is it worth studying a field that makes heavy use of it?
>Can one become good at math if one lacks a natural and intuitive grasp of mathematics?
practice
Is it enough when you start getting into more complex subjects?
No-one has a "natural and intuitive" grasp. You can learn everything people who considered math gods in the classical period knew in less than a year and everything people considered geniuses knew in the neo-classical period in 3 years. The fact Euclid was a fucking genius but you can learn everything he knew quickly shows there's no such thing as people wired for math. We all learn through practice.
>No-one has a "natural and intuitive" grasp
Have you never met someone who just knew how math worked and didn't have to practice or learn anything? I did.
Even without taking such extremes as examples, some people are able to grasp mathematical concepts much more easily, so I'm not sure what you mean.
It's more difficult to make a discovery than to understand a discovery made by someone else.
You can improve, but everyone has genetic limits imposed on them.
For some people that limit is at quadratic equations, for others it's doing differential equations in their head.
Anyway, I think anyones with a triple digit IQ should be able to grasp most university level mathematics, even if it is at a slower pace.
Though for some fields that might be too slow.
>Have you never met someone who just knew how math worked and didn't have to practice or learn anything? I did.
Then notify a neuroscientist, because you may have just found evidence of reincarnation. Look, no-one is born knowing math. The fact its taken us 200,000 years to get this far proves it. You don't think geniuses were born before the Greek classical period? But they had no context or conceptual knowledge of math, no previous body of information to draw from, and so math went on undeveloped, going no further than quadratics until the Greeks. No-one is born with neural connections for math. Of course that guy practiced and learned. And here's a secret: in modern Math, NO-ONE knows everything. Math isn't like science where a scientist can read a paper from another scientific and understand what's happening. It takes decades to fully understand one branch of Math, and if you hand a mathematician who studies one field a paper from another field, they'll probably have a hard time understanding at best and not understand at all at worst. Terence Tao was a genius, he's spent his whole career just trying to solve the Twin Prime conjecture and needed to invent entirely new notation and mathematical constructs to do it. The people who will verify his findings now have to spend a long time learning this new math.
If you feel perplexed and frustrated at math, and that you're unable to understand it, welcome to being a mathematician.
There are some people that learn math easier than others, but even that just goes to a limit, when things start to get real abstract the only option of anyone is just to study and try to get a grasp on math.
Most people can learn math in any level if they have the base math for that covered, anyone can be a mathematician if they'd care to, there is a really good Terence Tau's text about that in his blog btw.
>Terence Tao was a genius, he's spent his whole career just trying to solve the Twin Prime conjecture and needed to invent entirely new notation and mathematical constructs to do it
>one lacks a natural and intuitive grasp of mathematics
You only attain this in a proper sense by going to university and then spending several decades working/improving. It's never natural either, it comes through hard work and patience.
oh yeah? give me the dot product of u and v RIGHT NOW in your head!
>Can one become good at math if one lacks a natural and intuitive grasp of mathematics?
Yes. Nothing about high-level math is intuitive.
I mastered mathematics all the way up to real analysis in less than a year just by working a few hours a day at it and having a genuine interest in the subject. This despite never surpassing geometry in high school (I dropped out).
It can be done. Most student are horrendously inefficient with their time, letting their knowledge atrophy during breaks and never pushing themselves beyond the curriculum.
Of course, you need a reasonably high IQ, but you wouldn't care about this stuff anyway unless you had one.
Are you supposed to do logic puzzles in your head, juggling all the variable information, or is it ok to use paper to map things out?
I tried the 5 ships puzzle and even with paper only got one of the two questions right, even though i feel i fot it wrong because i rushed to assumptions too quickly, i feel like taking forever to solve a problem is the exact same as failing it to begin with.
Yes
some people have it easier than others but at the end of the day, if you persevere, you can grasp anything
people are brainlets not because they do not get it, but because they give up the second things get moderately difficult
x s.t. x = the answer to your question
Heh, nothing personnel kid.
*teleports behind ur problem*
Are u and v vectors? Not that user, just asking.
It's a dot product, so yes.
>a dot product
>a
there's only one dot product
>he still thinks that a vector is a sequence of numbers
You need to be 18 and above to post on Veeky Forums, kid
The purpose of logic and science is to use rigor so you don't need any natural talents or inspiration to investigate a topic.
It is one of the reason that some people who thought they liked science end up hating it.
>No-one has a "natural and intuitive" grasp
Objectively false.
People like John von Neumann existed.
Each space has its own dot product
What people hate is that they can't just make shit up as they go along like in sociology or psychology.
It's been said before but I'll say it again. Practice, practice, and practice. Something that helps me understand a subject is looking at and understanding the proofs for whatever you're using. Some are harder than others to understand, but looking at proofs can give you insight into certain techniques and logic involved in problem solving.
Is there a good reading list out there for getting into mathematical finance?
I'm not a math major, my current knowledge is basically limited to calc. I'm not sure where to start.
>Are you supposed to do logic puzzles in your head, juggling all the variable information, or is it ok to use paper to map things out?
> i feel like taking forever to solve a problem is the exact same as failing it to begin with.
I can't believe I'm reading this. This is what Veeky Forums does to people.
bump
Assume being proficient at a mathematical task makes you being able to "master" it in n years.
Assume then that being less proficient at that task increments the value of n, as does the complexity of the task.
Now, assume your lifetime is finite. What do you think happens for a large enough value of n?
Now, imagine that a mathematical task requires you to store m amounts of information in your head.
Assume that said capacity is finite.
What do you think happens when m is bigger than your brain capacity?
You can of course trade time for capacity, but both are inherently limited. Conclusion, there exist mathematical tasks a person with finite capacity and time cannot solve.
Now, assume that not everyone has the same capacity, or time.
Doesn't follow that there are certain tasks that some persons will be able to complete, and others won't?
And finally, here's the funny part: Training your brain takes time, and some people are faster than others. Have fun with that.
You make a great point. When talking about this stuff, people who mindlessly defend the "Just work hard bro!" mentality don't realize that it doesn't reflect reality at all, since there's a clear divide between the best hard working mathematician and the worst hard working mathematician, and you can find all kinds of people in between whose achievements and shortcomings get completely invalidated because they should "just" have worked harder, making them responsible for not being child genius tier when we're all just slaves to circumstance.
I mean, at least I know I'd find it pretty insulting.
>It can be done. Most student are horrendously inefficient with their time, letting their knowledge atrophy during breaks and never pushing themselves beyond the curriculum.
this is important
another thing that I found very useful is to try to learn and understand stuff well enough to be able to teach it to someone off the street
its all well and good to just answer exam questions, but whats the point if you cant explain what you are doing to anyone?
I'm interested in this too.
you can learn anything, just have to figure out how much time it takes for you to learn it. you might quit after you realize how many hours you need to spend fyi
>you might quit after you realize how many hours you need to spend fyi
Then it means you weren't really interested in the subject to begin with.
And really getting good takes years for any worthwhile subject, anyway.
for someone who just knows arithmetic basic operations (addition, subtraction, multiplication and division) what should be the roadguide to the rest of math?
arithmetic > algebra > geometry ?
its a good order? what after that?
Khan academy