How do these punks do it?

For the discussion of math. Duh.

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Re: How do these punks do it?

Postby polymer » Fri Aug 15, 2008 8:36 pm UTC

in response to the intended subject, it's been said before, but actually thinking of things in mathematical terms, asking your own questions, and follow through with your ideas helps you think mathematically better. Worked for me at least :/.

In response to the debate over whether talent exists. In defense of the requirement to work to accomplish goals, people have lost half their brains to strokes and other issues, but are however still able to gain most of their functionality back even if specific parts which were responsible for those functions don't exist in that person anymore.
however,
If a person gets and a car crash and loses the right side of their brain as a baby, they'll have a significant disadvantage when it comes to mathematics in particular. The reason for this, is due to the fact that a baby's flexible mind would use the mathematics portion of the brain for spacial relationship purposes. Any attempt to learn Math would then have to compete with the preexisting spacial functions(recognizing spacial relationships is obviously more important for everyday living.)
Final point regarding this, there is a neurotransmitter responsible for heavy duty learning of new skills in contrast to passive learning, I believe it's called NGF, but I'm not positive. It's released during concentration, which implies (not that we didn't already know this) a strong connection between learning and concentration. So the ability to concentrate however can be associated possible with the ability to learn.

just some quick points for understanding the nature of the question...If I were asked if talent existed I would say yes, depending on how much you've historically used a particular function, or whether you're genetics give you a more efficient/potent mind when it comes to concentrate. Knowing what's important to concentrate on is probably pretty important as well...

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Re: How do these punks do it?

Postby Buttons » Fri Aug 15, 2008 9:26 pm UTC

Yakk wrote:DavCrav, 'maths' is British English, and not at all standard in the rest of the English-speaking world.

I assume he was implying that, because 3.14... didn't go to school in Britain, his math education is inferior.

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Re: How do these punks do it?

Postby Yakk » Fri Aug 15, 2008 9:54 pm UTC

DavCrav wrote:Although given the way you spell 'maths', my guess is that your entire undergrad degree is what most people here do in their first year anyway...


Buttons wrote:
Yakk wrote:DavCrav, 'maths' is British English, and not at all standard in the rest of the English-speaking world.

I assume he was implying that, because 3.14... didn't go to school in Britain, his math education is inferior.

Oh. They cover spectral theory, functional analysis, finite element analysis, Duhamel's method, differential geometry, algebraic topology, elliptic curves, Black-Scholes equation, Fractal dimension, Statistical Mechanics, Bayesian games, Control Theory, Lyapunov functions, quantum mechanics, option swaps, Moore graphs, the Chomsky hierarchy, Algebraic Curves, enumerative theory of planar embeddings, Jacobson structure theory, Classical ruin theory, Quantum complexity classes, etc in first year in the UK?

If so, I apologize for the misunderstanding. (That was a relatively random selection of material covered outside of the first year at a medium-sized Canadian university in the faculty of Mathematics. All of the above are from undergraduate material, naturally. I, personally, do not know many of the above subjects well enough to give a discourse on them.)

I'm not saying that ~Pi's university doesn't have a crappy math program. I'm just saying that maybe your nationalism trolling is rather stupid.
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Re: How do these punks do it?

Postby Pathway » Fri Aug 15, 2008 10:16 pm UTC

Alpha Omicron wrote:@3.14...: I refute your argument thus.


Hmm... not quite as dramatic as kicking a stone, but I like it.

I would compare learning mathematics to drinking water. Everyone can do it. But there are people who, in all their lives, would never be able to handle drinking from a firehose. They can't hold it down, and even if they did their stomachs aren't large enough to take it in at that rate. And if you're drinking from a straw instead of a hose (i.e., are able to work at your own pace), then you might get more done.

I admit that the mindset of "I'm talented, and just better than everyone else" is a very problematic one, and can cause arrogance and laziness. But to say that talent is a myth is to insult the work ethic all the people you've known who like this stuff, work at it as much as you do and get worse results.

Buttons wrote:
Yakk wrote:DavCrav, 'maths' is British English, and not at all standard in the rest of the English-speaking world.

I assume he was implying that, because 3.14... didn't go to school in Britain, his math education is inferior.


That's almost as ridiculous a position to take. It's too silly even to take the trouble to refute it. [well, I guess Yakk has made a spirited effort at it; for that I commend him but I continue to believe that it's not worth his time]
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Re: How do these punks do it?

Postby 3.14159265... » Sat Aug 16, 2008 12:07 am UTC

Yakk wrote:The position that "talent" exists is falsifiable -- if there is a nearly perfect correlation between effort spent on learning something, and results from the learning, then there is almost certainly no "talent" factor.
I don't believe there is any way of measuring "effort" accurately enough to show a "talent" difference within humans. That is at the heart of my argument.

DavCrav wrote:Ooh, you did all of undergrad maths in a year. Good for you. Makes two of us. (Although given the way you spell 'maths', my guess is that your entire undergrad degree is what most people here do in their first year anyway...)
Don't be condescending, I wasn't.

I am merely saying, anything you can do anyone else on this forum can as well. Your position that they can't is non-falsifiable so you no longer have a case my friend.

DavCrav wrote:Actually, I can't be bothered to argue, because as somebody who is employed to do mathematics by a university, I've seen quite a few talented mathematicians, worked with quite a few as well. I don't need arguments because I have my own evidence, which is the mathematicians themselves.
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Re: How do these punks do it?

Postby skeptical scientist » Sat Aug 16, 2008 1:06 am UTC

Haven't you ever known anyone who gets amazing grades in all their classes without seeming to do much work? What's your explanation for this, if not talent?

I am merely saying, anything you can do anyone else on this forum can as well. Your position that they can't is non-falsifiable so you no longer have a case my friend.

How is this non falsifiable? Assuming Yakk is taller than at least one person on these forums, he can confirm it by reaching x feet into the air with his feet on the ground. If you are only talking about feats of mental acuity, all that it takes is for Yakk to do something and for someone else to try to replicate that feat, and fail.
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Re: How do these punks do it?

Postby DavCrav » Sat Aug 16, 2008 1:51 am UTC

Right, I'm a little drunk now, but I will say that I was not saying that all courses on offer at a university the other side of the Atlantic were crap, I was merely saying (and this is backed up by various American-trained mathematicians I know) that to get 'a math degree' in the States (for example) requires not a lot of actual mathematics. And it's not nationalism trolling: you should see what the French and German maths programmes involve. I'm just saying that US degrees aren't worth the paper they are written on (at least in the terms of the major. In terms of overall education, it's like comparing apples and oranges, but an average American math major would struggle with third-year maths here. (And potential apologies to Canadians, since I have no idea what your courses are like, having met no Canadian mathematicians.).)

And again, there are always exceptions to the rule, but the number of triple-major graduates I know from US universities, who freely admit that they aren't the next Einstein, compared with what someone would need to do to get three degrees in the UK, makes it clear that the US degree isn't as deep as a British one (or indeed, many of the European degrees).

Oh and

"I am merely saying, anything you can do anyone else on this forum can as well. Your position that they can't is non-falsifiable so you no longer have a case my friend."

If this were true, then I should be able to at least understand what Deligne and Lusztig are talking about. After all, it's not talent, so it must just be hard work. But if it takes me longer to understand it that it does for them to originally come up with it, I'm confused...

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Re: How do these punks do it?

Postby 3.14159265... » Sat Aug 16, 2008 2:16 am UTC

Haven't you ever known anyone who gets amazing grades in all their classes without seeming to do much work? What's your explanation for this, if not talent?
I did not take a single page of notes, nor studied for a minute outside of class for number theory. I got perfect on my final.

You see though, when I was stoned and drunk I was telling my friends about this beautiful theorem that Dirichlet proved.

I don't think "work" or "effort" is measurable, what we don't understand of it we call talent.

Skeptical if there is such a thing as "talent" we should be able to measure it. Can you measure my "talent" in math? Suppose I do better than you thought I could using sheer will power, then what? you "measure" was wrong?

Suppose there was no such a thing as talent, how could you prove it to not exist?

DavCrav it takes me longer to learn a move than it takes Ronaldinho to come up with it. Damn, there must be a "soccer coming up with gene".
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Re: How do these punks do it?

Postby skeptical scientist » Sat Aug 16, 2008 7:08 am UTC

3.14159265... wrote:Skeptical if there is such a thing as "talent" we should be able to measure it. Can you measure my "talent" in math?
Not directly, because all ways of measuring talent (e.g. long lists of IMO type questions, speed of picking up new concepts) will also measure amount of general mathematics knowledge and experience with similar questions and/or related concepts. This is no different from other situations where there are many contributory factors - teasing out the effect of a single factor can be very difficult. That doesn't mean it doesn't exist, and certain tools (e.g. econometrics) could probably be employed to estimate it (albeit likely with significant error bars).
Suppose I do better than you thought I could using sheer will power, then what? you "measure" was wrong?
Right, I'd have to readjust the estimate based on the new data, and hopefully shrink the error bars a bit.
Suppose there was no such a thing as talent, how could you prove it to not exist?
You couldn't ever conclusively prove it, but you could set progressively smaller limits on the maximum effect size. This is just like anything else - you can't ever conclusively prove that (for example) a purported medical treatment has no effect on illness X, but after many double-blind controlled statistical trials, you can put progressively smaller upper bounds on the effect size. So if many studies of different people show that you can consistently and accurately predict their performance on mathematics tests based solely on time spent reviewing the material, you can show that the effect of some unknown quantity has to be small.
DavCrav it takes me longer to learn a move than it takes Ronaldinho to come up with it. Damn, there must be a "soccer coming up with gene".
Nice straw man.

DavCrav wrote:Right, I'm a little drunk now, but I will say that I was not saying that all courses on offer at a university the other side of the Atlantic were crap, I was merely saying (and this is backed up by various American-trained mathematicians I know) that to get 'a math degree' in the States (for example) requires not a lot of actual mathematics...

And again, there are always exceptions to the rule, but the number of triple-major graduates I know from US universities, who freely admit that they aren't the next Einstein, compared with what someone would need to do to get three degrees in the UK, makes it clear that the US degree isn't as deep as a British one (or indeed, many of the European degrees).
It may be true that a the requirements for an undergraduate math major are much less rigorous at a typical american university, as compared to a european one; I wouldn't know. I had no idea what my undergraduate major requirements were, but looking back all they required was the linear algebra/multivariable calculus sequence, one semester of analysis, one semester of algebra, taking (or testing out of) the proofs class, and four semesters of electives. Even getting an honors math major isn't much harder. Even at the University of Chicago (which is a damned good university), you can fulfill all the concentration requirements for a degree in mathematics in three years of one math class per quarter.

However, you are making a huge and unjustified leap when you make comments like "US degrees aren't worth the paper they are written on" or "your entire undergrad degree is what most people here do in their first year anyway." Many people go well beyond the major requirements when getting the major, and it's pretty typical for a student interested in mathematics to exhaust most of the undergraduate curriculum and start taking graduate classes. Personally, after taking linear algebra and multivariable calculus, I took a year and a half of undergraduate analysis (full year real analysis sequence plus a semester of complex), a full year of undergraduate algebra, a full year of graduate analysis, a graduate manifolds class, and 5 semesters of mathematics electives. That's 15 semesters of mathematics courses to get a degree I could have had with 8 semesters. I imagine Yakk and ~pi had (have? ~pi, I forget whether you're still in school) similar undergraduate programs, and I bet that's pretty comparable with the requirements for a maths :P degree at the best schools in the UK.
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Re: How do these punks do it?

Postby Pathway » Sat Aug 16, 2008 7:14 am UTC

3.14159265... wrote:Skeptical if there is such a thing as "talent" we should be able to measure it. Can you measure my "talent" in math? Suppose I do better than you thought I could using sheer will power, then what? you "measure" was wrong?


That's naive. Does there exist such a thing as love? Can you measure it?

"Talent" is a broadly-defined word, and I think that's part of the problem here. I love Nietzche's words for this: "As if all words were not pockets into which now this and now that has been put, and now many things at once!"

Suppose we rephrase it this way: "There are certain heritable characteristics, not shared by a majority of human beings, which can cause a greater than normal ability to understand and develop mathematics." (<=> "Mathematical talent exists.") Do you also contest this statement?
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Re: How do these punks do it?

Postby DavCrav » Sat Aug 16, 2008 4:06 pm UTC

skeptical scientist wrote:It may be true that a the requirements for an undergraduate math major are much less rigorous at a typical american university, as compared to a european one; I wouldn't know. I had no idea what my undergraduate major requirements were, but looking back all they required was the linear algebra/multivariable calculus sequence, one semester of analysis, one semester of algebra, taking (or testing out of) the proofs class, and four semesters of electives. Even getting an honors math major isn't much harder. Even at the University of Chicago (which is a damned good university), you can fulfill all the concentration requirements for a degree in mathematics in three years of one math class per quarter.

However, you are making a huge and unjustified leap when you make comments like "US degrees aren't worth the paper they are written on" or "your entire undergrad degree is what most people here do in their first year anyway." Many people go well beyond the major requirements when getting the major, and it's pretty typical for a student interested in mathematics to exhaust most of the undergraduate curriculum and start taking graduate classes. Personally, after taking linear algebra and multivariable calculus, I took a year and a half of undergraduate analysis (full year real analysis sequence plus a semester of complex), a full year of undergraduate algebra, a full year of graduate analysis, a graduate manifolds class, and 5 semesters of mathematics electives. That's 15 semesters of mathematics courses to get a degree I could have had with 8 semesters. I imagine Yakk and ~pi had (have? ~pi, I forget whether you're still in school) similar undergraduate programs, and I bet that's pretty comparable with the requirements for a maths :P degree at the best schools in the UK.


Yes! This is exactly my point! You CAN do lots of courses, and have a very good education, but to have 'a major' in a subject doesn't mean anything. The average person coming out with a major in mathematics has not done tonnes of extra courses, I would wager. I've known some people come out of non-Ivy League universities with a very good and thorough background in mathematics, but they've done at least twice as many courses as they HAVE to.

To know whether a US degree is good, you have to look beyond the major and look at the quantity and quality of courses taken; this is true to a much lesser extent in the UK. (There are still hard and easy courses, but you are forced to take some hard courses in the UK.)

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Re: How do these punks do it?

Postby 3.14159265... » Sat Aug 16, 2008 8:00 pm UTC

SS that was not a straw man it was an analogy to his Deligne and Lusztig example. That I used "gene" perhaps was, but that was not my intent.

Pi is going into his third year now, and off to study biology :cry:

That doesn't mean it doesn't exist, and certain tools (e.g. econometrics) could probably be employed to estimate it (albeit likely with significant error bars).
How big can your errors bars before you can say, this is useless?

The reason I take such strong offense to the idea of "talent" is the stereotype threat which by the way has been conclusively proven to exist.

You couldn't ever conclusively prove it, but you could set progressively smaller limits on the maximum effect size.
What effect size is too small to consider? specially given that there is an effect size that dwarfs all other effects? namely the desire to learn?

That's naive. Does there exist such a thing as love? Can you measure it?
Yes, and yes. I don't however view it as an empirical idea, not all things need be scientific. However once the claim is made that something is scientific it should be upheld to scientific standards.

"There are certain heritable characteristics, not shared by a majority of human beings, which can cause a greater than normal ability to understand and develop mathematics." (<=> "Mathematical talent exists.")
I do not contest this statement.

Do you contest the following statement. All members of this forum have the ability to do as great mathematics as any other member, and althought some are "advantaged", that effect is negligible given the amount of effort any of us will really put into math.

Seriously, if I spent all the time that I get stoned and/or durnk doing math, I could have published a couple by now. Sadly I can not love math that much even though it is the great love of my life.
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Re: How do these punks do it?

Postby Buttons » Sun Aug 17, 2008 12:03 am UTC

3.14159265... wrote:Seriously, if I spent all the time that I get stoned and/or durnk doing math....

You mean you don't? Weird.

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Re: How do these punks do it?

Postby 3.14159265... » Sun Aug 17, 2008 2:12 am UTC

i thought so too when i stopped thinking about math as much, and in fact when i started thinking about it that much...

life eh?
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Re: How do these punks do it?

Postby AnotherUser » Sun Aug 17, 2008 5:37 am UTC

skeptical scientist wrote:Haven't you ever known anyone who gets amazing grades in all their classes without seeming to do much work? What's your explanation for this, if not talent?

I strongly disagree with this having anything to do with talent, at least not necessarily. I didn't take many notes and did almost no homework this year for my calculus class (and yes I did well). The reason that happened wasn't because of some innate talent, it was because I had spent the last half of my previous school year reading an introductory book on calculus, and gradually learning more over the summer, enough that not much was new by the time the course rolled around.

My experience with those kinds of people is the same as mine: they're doing well because they've seen some (or all) of this before, because they were interested.

I think the general finding is that the students who don't do much work either begin to do more work or have a rude awakening at some point in college.

Maybe there is such a thing as a natural talent for math, maybe there is little to none and the main factors are interest and dedication. I'll grant that people who win awards such as the Fields medals tend to be very exceptional people, and not just for their math accomplishments. But I can't help but think that luck is as big a factor as any when it comes to things like this.

Consider Andrew Wiles: He first got interested in Fermat's Last Theorem when he was 16. He shelved it, and became a mathematician with an interest in elliptic curves. Along comes a piece of work that conveniently gives elliptic curves a chance to prove Fermat's Last Theorem. So here's a problem that he had an interest in, and he finds himself very qualified to attempt to solve it. That doesn't seem like it was influenced by any kind of innate talent. (I don't mean to say that Wiles had it easy or anything; I'm just saying that he was very qualified to do what he did. That he did manage to prove it is a testament to his persistence and ability.)

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Re: How do these punks do it?

Postby skeptical scientist » Sun Aug 17, 2008 8:37 am UTC

I think to win a Fields medal or any great accomplishment it takes a combination of talent and perseverence and luck. Andrew Wiles is a great example of this. He was clearly talented in mathematics from an early age. He had the luck to be interested in Fermat's last theorem at an early age and then as an adult work with elliptic curves, which turned out (probably to Wiles great surprise) to have something to do with Fermat's last theorem. Finally he had the dedication to work almost exclusively on Fermat's last theorem for the seven-plus years it took to produce the proof.

Another good contemporary example is Michael Phelps. In this case, at least part of his talent is due to directly measurable physical attributes, namely his tremendous wingspan, long torso, short legs, big feet, and flexible joints, all of which are excellent attributes for a swimmer. He had the mindset to dedicate himself to hours of practice every day. And finally, he couldn't have won his eight gold medals without a great deal of luck - most notably, his .01 second photo finish in the 100 meter fly, and also Jason Lezak pulling an amazing last relay leg to beat out Alain Bernard. So to do well, you can make do with one or two of the three, but to be truly great you need all three.
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Re: How do these punks do it?

Postby DavCrav » Sun Aug 17, 2008 11:23 am UTC

skeptical scientist wrote:I think to win a Fields medal or any great accomplishment it takes a combination of talent and perseverence and luck. Andrew Wiles is a great example of this. He was clearly talented in mathematics from an early age. He had the luck to be interested in Fermat's last theorem at an early age and then as an adult work with elliptic curves, which turned out (probably to Wiles great surprise) to have something to do with Fermat's last theorem. Finally he had the dedication to work almost exclusively on Fermat's last theorem for the seven-plus years it took to produce the proof.


I should also point out that I know Wiles' tutorial partner here in Oxford, and he said that Wiles was absolutely amazing at mathematics and far better than him. (This guy is himself a professor in Oxford.)

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Re: How do these punks do it?

Postby 3.14159265... » Sun Aug 17, 2008 8:54 pm UTC

AnotherUser, I enjoyed reading your post and not because you were agreeing with me. You have really good prose.

SS I clearly accept physical attributes having "talent", but then there is also the factor of you working at it.

I can either say that also applies to knowledge or I can say it doesn't, I choose that it does not. Due to personal preference. I do concede that I can not prove "talent" does not exist, and I also concede that intuitively one thinks that it does. However, since it could go either way I choose that I can be Gauss.

DavCrav, suppose for a second that "talent" did not exist. Does that discomfort you? is it then possible that you are using confirmation bias to prove your point to yourself? Please suppose the premise before answering the question.
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Re: How do these punks do it?

Postby Buttons » Sun Aug 17, 2008 11:51 pm UTC

3.14159265... wrote:I can either say that also applies to knowledge or I can say it doesn't, I choose that it does not.

You're not alone in this matter. When discussing "the myth of talent" in Out of the Labyrinth: Setting Mathematics Free,

Bob and Ellen Kaplan wrote:However you decide about talent on the basis of your own experience and inclinations, you will likely agree that it is best to act as if it were a myth—rather in the spirit, though with the opposite polarity, of what's called Pascal's Wager (act as if God exists; for if he does you may be saved, and if he doesn't, nothing is lost). If there is no such thing as a talent for mathematics, then you do well to proceed as if everyone could be led to its delights; while if such a talent exists, your actions won't harm those who have it and may give a spectator's informed appreciation to those who haven't.

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Re: How do these punks do it?

Postby Pathway » Mon Aug 18, 2008 12:54 am UTC

I find it's better to act as if talent does exist--as if there are people who will surpass me if I work exactly as hard as they do. That makes me work harder than they do, because I hate to lose.
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Re: How do these punks do it?

Postby samspotting » Wed Aug 20, 2008 2:00 am UTC

I believe some people have a genetic disposition to the field, but I don't think that it has that big of a role in determining success. The main thing I am trying to catch up on is that the best in the field will be the people that have a natural feel of math, having tried hard in maths since grade school.

I have come up with a reading list after reading the thread and consulting professors.

1) How to Prove It
2) How to Solve It
3) Rudin's Principles of Mathematical Analysis
4) Gilbert Strang's Linear Algebra
5) Numbers and Geometry (John Stillwell)

and for looking at some of the big questions in math

1) A Mathematician's Apology
2) Prime Obsession/Riemann Zeta Function depending on which one I like best
3) American Mathematical Monthly and/or Mathematics Magazine

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Re: How do these punks do it?

Postby spipper » Mon Aug 25, 2008 2:00 am UTC

Start with the Riemann Hypothesis! I'm just kidding. I would say Just improve what you know, and when you are great with that just browse the internet and take classes when they come up. mathworld.wolfram.com is a cool place to look things up.

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Re: How do these punks do it?

Postby moomin » Tue Sep 02, 2008 3:35 pm UTC

Yakk wrote:DavCrav, 'maths' is British English, and not at all standard in the rest of the English-speaking world.

From http://en.wikipedia.org/wiki/Mathematics
http://en.wikipedia.org/wiki/Mathematics#Etymology wrote:In English, however, the noun mathematics takes singular verb forms. It is often shortened to math in English-speaking North America and maths elsewhere.


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