Is math's study only for the gifted?

[Rono]

So yeah, while I was at high school, I considered math as one of my career choices, but I was invited to the national math olympiads by my school and, even though I enjoyed them, I found them way too hard and looked on those who win it and most of them finish studying math and doing great on it. Since then, I find math career a field only for people gifted in math, who can solve puzzles without much thinking and that are efficient in them.

Am I wrong? Could a person who's good at science-level math (calculus seems way too easy for me) be good as a mathmatician without having talent to do "hard" math?

 

[Number Nine]

If you can't do "hard" math, then you haven't worked hard enough at it.
There was an interesting poll taken a decade or so ago, where they found that most of the rest of the world believed that mathematics was like any other subject: If you want to understand it, you just work hard at it. Americans, on the other hand, believed that the study of mathematics was only for the gifted, and that some (most) people "just aren't good at it". Whether or not this explains the infamous inability of American high-school students to do basic math, I don't know; I just found it interesting.

 

[AlephZero]

If you compare yourself with "the best kids in the USA" (or even "the best in your state") the chances are you will be worse (and most likely, a lot worse) than them.

But that comparison is as pointless as saying you can't run as fast as an Olympic medal winner. It doesn't mean anything much what you can achieve in real life.

 

[MPKU]

No. Simply, no. I'm smart, not GIFTED by any means, just seemed to have stronger priorities in learning and better study habits. All you need is hard word and drive. I'm sick of people saying "I'm bad at math". This only makes me think, "No, you are bad at following directions". Math is straight-forward.

 

[Whovian]

No. Simply, no. I'm smart, not GIFTED by any means, just seemed to have stronger priorities in learning and better study habits. All you need is hard word and drive. I'm sick of people saying "I'm bad at math". This only makes me think, "No, you are bad at following directions". Math is straight-forward.

As false as saying "Mars and Jupiter have the same volume." It's anything but straightforward. If I asked you to find

\dfrac{\mathrm{d}x^x}{\mathrm{d}x}

or

\int_0^{\frac\pi2}\left( \dfrac{\sin^n\left(\theta\right)}{\sin^n\left( \theta\right)+\cos^n\left(\theta\right)}\right) \cdot\mathrm{d}\theta

would you be able to just use the standard methods to find either? Nope! Well, if you're clever, the solutions I've seen to these use standard methods and a little cleverness. But cleverness isn't straightforward. (I guess Weierstrass Sub could be used on the second.)

 

[homeomorphic]

As false as saying "Mars and Jupiter have the same volume." It's anything but straightforward. If I asked you to find

dxxdx


or

∫π20(sinn(θ)sinn(θ)+cosn(θ))⋅dθ


would you be able to just use the standard methods to find either? Nope! Well, if you're clever, the solutions I've seen to these use standard methods and a little cleverness. But cleverness isn't straightforward. (I guess Weierstrass Sub could be used on the second.)

Newsflash: math isn't just about solving hard problems. The question might be whether people can understand the IDEAS of differential geometry or whatever it is. That doesn't necessarily involve coming up with clever tricks. Of course, doing many calculations and exercises would be part of the process, but they aren't necessarily of the "come up with the clever technical trick" variety. And no, it's not straight-forward. But can people who have severe difficulties with math understand it? In general, I don't know, but in some cases, the answer appears to be yes. See, for example, John Mighton's book, The End of Ignorance. He doesn't specifically mention differential geometry, which I arbitrarily brought up, but he tells the story of some severely math-phobic person that he tutored who ended up getting a PhD in math.

It could be that some of the people who struggle really are at least somewhat challenged at it, whereas others just experience some sort of blockage and do well once it is removed. However, to some extent, John Mighton's work demonstrates that almost all students can do much better than what normally happens in today's educational system, or maybe educational hilarious joke, not so much system. I really shouldn't dignify it by calling it a system.

http://opinionator.blogs.nytimes.com/2011/04/18/a-better-way-to-teach-math/

 

[Whovian]

-snip-

Correct. Though, my point was, it's not just a simple "plug and chug" and I offered counterexamples to that.

 

[MPKU]

I only meant there is no ambiguity or uncertainty or anything that is (or should be) unclear in math. For any problem, there is a way to solve it. For any theory there are axioms taken to be true. It's direct, no ifs and or buts about it.

I think there is a difference between something being straightforward and "plug and chug". The latter is implying some mindless activity of placing missing values in an equation one doesn't understand. Being straightforward is different. In Mathematics everything is laid out in a clear and concise manner. Does it involve work? Certainly. Doesn't mean it's not straight-forward.

 

[homeomorphic]

I only meant there is no ambiguity or uncertainty or anything that is (or should be) unclear in math. For any problem, there is a way to solve it. For any theory there are axioms taken to be true. It's direct, no ifs and or buts about it.

Ever heard of Godel's theorem? Or perhaps the unsolvability of the word problem for groups?

I think there is a difference between something being straightforward and "plug and chug". The latter is implying some mindless activity of placing missing values in an equation one doesn't understand. Being straightforward is different. In Mathematics everything is laid out in a clear and concise manner. Does it involve work? Certainly. Doesn't mean it's not straight-forward.

You're using the word "straight-forward" in a sense that no one else would use.

Also, you sound very undergraduate. Anyone who has gone to graduate school for a few years will realize that modern mathematics is a mess, almost to the point of hopelessness. Often, the motivation for concepts is not clear, even if the definitions are laid out clearly. Ditto for the proofs. May be written completely precisely, but you can go through line by line, get convinced that it's true, but you are left with no idea why. Going through a sequence of formal steps doesn't always answer that why question. And there's so much to know. It's anything but straight-forward. Plus, there a lot of places where you have to fill in the gaps. That's the way math is usually written. Not everything is written out. Sometimes, there are even conventions that are made implicitly, like omitting an isomorphism or something like that and they don't even bother to tell you they are doing it, you just have to figure it out from context.

 

[MPKU]

Also, you sound very undergraduate.

I would only hope so.

 

[MarneMath]

Well, while I don't inherently agree with MPKU premise, I think I understand where he's coming from. I've always felt physics or math were rather straight forward. Once a statement was proven and vetted, it was proven and you moved onto the next statement. Compared that to a field like economics where even if you prove a statement mathematically, if someone comes along and goes, "well on the other hand if we assume this...?" You end up with two very different theorems explaining the same exact effect.

I don't think anyone who has worked with real math will ever really mean to say that it's a simple direct and clear path, but in many ways, it's easier than other stuff out there :).

Nevertheless, back to the original poster. I think one of the worse mistakes you can ever make in your educational career is compete against the top tier people. It's very easy to bog yourself down and lose sight of your ability. The truth is, most people will struggle, and most will suffer, but it's been my experience that most people, in the end, can at the very least understand the ideas to some extent. Not everyone is suited to prove the next big theorem; however, you'll find that good number of professors made careers out of proving a lot of little theorems or even just extending previous results. That's how math works. Some people prove big stuff, a lot of people prove little stuff, but in the end everyone is doing their own part to understand their piece of the pie.

 

[VantagePoint72]

I've always felt physics or math were rather straight forward. Once a statement was proven and vetted, it was proven and you moved onto the next statement. Compared that to a field like economics where even if you prove a statement mathematically, if someone comes along and goes, "well on the other hand if we assume this...?" You end up with two very different theorems explaining the same exact effect.

That is exactly what happens in physics. We come up with a model to explain something, work out the mathematical details, and wait for someone to come along and challenge the underlying assumption. "Two very different theorems [formulas would be a better word in either case] explaining the same exact effect," is the situation in physics every time a new model comes along. Theoretical high energy physics currently has a great deal more than just two different mathematical models purporting to describe the same phenomena.

The difference between physics and economics is fundamentally an empirical one, not a mathematical one. While the mathematics of physics ultimately follows from much simpler ideas than those in economics, the real difference is that the laws of nature just happen to lend themselves to more valid, controlled experimental tests than human nature does.

 

[MarneMath]

Point taken, but at the intutitive level, I still believe there exist some key difference. Perhaps, I'm not explaining it properly, neverthless, I hope my intent is clear enough.

 

[OCR]

I wouldn't say that the study of math is only for the gifted, but... some certainly had the gift, or 'something'...

I have sometimes wondered whether a brain like von Neumann's does not indicate a species superior to that of man.

He was the cleverest man I ever knew, without exception. He was a genius.

Johnny was the only student I was ever afraid of. If in the course of a lecture I stated an unsolved problem, the chances were he'd come to me at the end of the lecture with the complete solution scribbled on a slip of paper.

One of his remarkable abilities was his power of absolute recall. As far as I could tell, von Neumann was able on once reading a book or article to quote it back verbatim; moreover, he could do it years later without hesitation. He could also translate it at no diminution in speed from its original language into English. On one occasion I tested his ability by asking him to tell me how The Tale of Two Cities started. Whereupon, without any pause, he immediately began to recite the first chapter and continued until asked to stop after about ten or fifteen minutes.

http://en.wikipedia.org/wiki/Von_Neumann​

OCR

 

[OCR]

Also, you sound very undergraduate.

I would only hope so.

Lol...




OCR

 

[danzibr]

Math's study is only for the tenacious.

 

[Sankaku]

I like to use the comparison between math competitions and sprinting. Mathematical research is more like mountain climbing. If you have the athleticism and drive to get good at sprinting, chances are you can climb mountains, too. However, lots of mountain-climbers have no interest in sprinting.

Math's study is only for the tenacious.

This!

 

[wrldt]

I believe mathwonk reduced the study of math to mostly hard work, determination, interest, and then finally intelligence.

 

[homeomorphic]

One possible caveat about asking mathematicians about how hard it is to do math is that, although, they themselves probably struggle with whatever level of math they are trying to do, even if they are von Neumann, they also find a lot of stuff to be trivial that might be quite a challenge to most people. So, it seems to us, sometimes that we aren't doing anything special, that anyone could do what we are doing.

For that reason, even though it seems like I am not doing anything special, I prefer to remain skeptical either way about anyone's ability to do this or that. I don't believe they can't do it, until it is demonstrated, and likewise, I don't believe they can do it until it is demonstrated. Of course, this is the proper scientific attitude to take towards anything.