I've finally hit a wall with math

[micromass]

Good for you micromass.

I think even non-abstract math works this way. I never really understand the material in a course until probably the day after the final exam. And even then...

-DaveK

In my (limited) experience, it's a very gradual process. If I look back at my knowledge of a few years ago, I am amazed on how little I knew. Even in a final exam. Things that were not obvious back then, are very simple now.
For example, when I took topology, I thought I understood it very well. Then I studied for the final, and I found out that there was a lot that I didn't know. Now I teach the course, and I still find new things or perspectives that I didn't know when I was a student. I am certain that I will keep discovering new insights even in 10 or 20 years. That's how mathematics works. So no: it's not because you don't know abstract algebra (or calculus) well, that you should quit mathematics. Hard work and passion are far more important than raw talent (which also plays a roll, but a minor roll in my opinion).

 

[X89codered89X]

First is to realize that problems in Calc 2 come in only 5 basic forms:

1. U substitution
2. Integration by Parts
3. Partial Fractions
4. Completing the Square
5. Trig Substitution

The most important skill is to recognize which method will solve what type of integral, then apply that method.

Calc 2 also usually includes series, which for many, including myself, was the first time you look at that topic. A few kids apparently touched upon it in high school for some reason. I wish I could have. Study your butt off for series.

On another note, the problems tended to be longer in calc 2 than in calc 1 or calc 3. The techniques theoretically are as simple as in calc 1, but there is a lot more manipulation to do for each problem.

 

[SunnyBoyNY]

Aside from a highly hypothetical scenario where an employer will look at employees A and B, otherwise perfectly matched, and say, "this one has a better GPA," I don't remember ever hearing about an employer asking for grades. Are your experiences different?

-Dave K

I used to work for a former university professor (he decided that having his own R&D company will be more fun) but he never asked for a transcript. When it came to hiring, he looked at the school and GPA and perhaps asked for an explanation when the latter was somewhat low. Grades themselves rarely mattered.

As for the topic originator:: I remember studying hard for a power electronics course in grad school. I went through almost every exercise in the book so I felt well prepared. The midterm exam had a question on one exercise that I did not do. Of course I blew the test. The whole PE field was so... vast and mythical to me (higher math still is...). In any case,
I am a PE engineer and I laugh at the problem I could not solve back then. Knowledge comes gradually and you can do it. If you could get into a college and could pass the first few math courses, then you will do fine. It might just take a while and perhaps a change in your learning strategy.

Good luck!

 

[symbolipoint]

Aside from a highly hypothetical scenario where an employer will look at employees A and B, otherwise perfectly matched, and say, "this one has a better GPA," I don't remember ever hearing about an employer asking for grades. Are your experiences different?

-Dave K

YES.

All employers who employed me for professional positions required my transcripts.

 

[dkotschessaa]

YES.

All employers who employed me for professional positions required my transcripts.

Transcripts, yes. (For GPA (maybe), for what classes you took, your major/minor, to confirm your degree) But the question is to what extent they care about individual grades.

-Dave K

 

[symbolipoint]

Transcripts, yes. (For GPA (maybe), for what classes you took, your major/minor, to confirm your degree) But the question is to what extent they care about individual grades.

-Dave K

The question of what extent caring about individual grades depends on the company/institution's policy, the particular job position, and the administrators who are reviewing the candidates. Knowing to what extent would vary - depends on the employers.

Some employers will directly assess a candidate to find what math skills the candidate has - what can he do with the math that he has retained.

This is moving off the topic of "hit a wall with math".

 

[homeomorphic]

As for "anyone can do math..." well it's not as simple as that. The truth is that anyone can do whatever amount of math they want, provided they are willing to put in the time and effort and that they enjoy it enough to do so. There may come a point where someone says "this is too much work, given my aptitude, so maybe I should do something else." This is not the same sentiment as "I'm no good at math and I should give up." There is no wall. Only hills and humps. Or perhaps walls which require tunneling through.

That's about right. There's never a wall. You can always improve. It's my suspicion that anyone COULD do advanced math if they put enough effort into it. Granted, it might take some people twenty years to learn differential topology, rather than two years for someone with more aptitude, but I suspect it would be possible eventually. I could be wrong--it's unlikely that someone who found it that difficult would go through this experiment--but that's my hunch.

Here's something my adviser told me about my thesis: "I don't think there are any mathematical difficulties. There are psychological difficulties and psychology is a much more difficult science that mathematics."

It can be a self-fulfilling prophecy if you start saying that you aren't good enough.

I am somewhat guilty of that myself, lately. There are people who aren't as good at math as I am that succeed where I fail because maybe they have more people skills, fit into the system better, are less rebellious, so they don't have to try so hard to swim against the stream, etc. There are people I used to work with on homework and I had way more ideas than they did on homework, but they graduated and I haven't yet because they were plugging away on their thesis until it got done, but I couldn't restrain myself I was interested in too many other things and couldn't focus on it. But part of it is that I let grad school psych me out too much and shake my confidence. I should have just tried to ignore the pressure and keep pushing through it. I have been doubting lately whether I will graduate at all, but I think I have pulled myself together, and things are moving forward again. But it's just a matter of ignoring the fear of defeat and just trying to focus on the task at hand. I just think of the next little step. I don't think of finishing the thesis, I just think about proving the next case of my theorem each day. One by one the cases are being proven, and I still feel guilty that it is going too slow, but it's getting there. Eventually, math becomes more like a marathon than a 100 m race. Probably the most important thing is just to keep calm under fire and not get overwhelmed by the pressure.

You can't go off of the anecdotal evidence of one person to prove that there are limits to mathematical ability. That's quite obviously not even remotely scientific.

 

[chiro]

I'd imagine that most of the people that stay it for the long haul are probably not seeing it as something that requires any kind of strenous force just to do what they need to do, and don't feel at least in some level, that they are putting in as much effort as the other guy who otherwise feels like he is trying to pull a truck with his teeth.

To someone, you will have them be aware of the difficulties, the failures, and all that comes with this in a particular viewpoint encapsulating these attributes and for others those attributes are seen a completely different way more so as a means where one needs to learn more rather than seeing themselves as being a process of constant barrages of failure and demoralization.

But this happens in many things not just mathematics: one person will see endless instances of torture possibly both physically and mentally and the other will see opportunity to grow, develop, and experience while not focusing on the detrimental aspects as much as the other who feels more demoralized would.

Everyone has their own limits to how important something is them and usually the more important thing will win out in some way (this includes even the fear of failure where some will avoid what they otherwise value to be important but the fear of failure has a much higher priority than overcoming it).

 

[Group_Complex]

That's about right. There's never a wall. You can always improve. It's my suspicion that anyone COULD do advanced math if they put enough effort into it. Granted, it might take some people twenty years to learn differential topology, rather than two years for someone with more aptitude, but I suspect it would be possible eventually. I could be wrong--it's unlikely that someone who found it that difficult would go through this experiment--but that's my hunch.

Here's something my adviser told me about my thesis: "I don't think there are any mathematical difficulties. There are psychological difficulties and psychology is a much more difficult science that mathematics."

It can be a self-fulfilling prophecy if you start saying that you aren't good enough.

I am somewhat guilty of that myself, lately. There are people who aren't as good at math as I am that succeed where I fail because maybe they have more people skills, fit into the system better, are less rebellious, so they don't have to try so hard to swim against the stream, etc. There are people I used to work with on homework and I had way more ideas than they did on homework, but they graduated and I haven't yet because they were plugging away on their thesis until it got done, but I couldn't restrain myself I was interested in too many other things and couldn't focus on it. But part of it is that I let grad school psych me out too much and shake my confidence. I should have just tried to ignore the pressure and keep pushing through it. I have been doubting lately whether I will graduate at all, but I think I have pulled myself together, and things are moving forward again. But it's just a matter of ignoring the fear of defeat and just trying to focus on the task at hand. I just think of the next little step. I don't think of finishing the thesis, I just think about proving the next case of my theorem each day. One by one the cases are being proven, and I still feel guilty that it is going too slow, but it's getting there. Eventually, math becomes more like a marathon than a 100 m race. Probably the most important thing is just to keep calm under fire and not get overwhelmed by the pressure.

You can't go off of the anecdotal evidence of one person to prove that there are limits to mathematical ability. That's quite obviously not even remotely scientific.

To be honest Homeomorphic, I would say that your friends may have more mathematical ability than you if you are finding it difficult to finish your thesis in the time that they have finished theirs. I also think you overestimate the effect of the "system" on your confidence, when it is much more likely that you have hit the wall in terms of mathematical ability. I would say it is a lack of talent which is your problem, as you have mentioned to me before, you had difficulty in Graduate Classes, I don't think it is that the culture of graduate school is against deep thought, I just think you are unable to think deeply because you have hit the mathematical wall.

 

[micromass]

To be honest Homeomorphic, I would say that your friends may have more mathematical ability than you if you are finding it difficult to finish your thesis in the time that they have finished theirs. I also think you overestimate the effect of the "system" on your confidence, when it is much more likely that you have hit the wall in terms of mathematical ability. I would say it is a lack of talent which is your problem, as you have mentioned to me before, you had difficulty in Graduate Classes, I don't think it is that the culture of graduate school is against deep thought, I just think you are unable to think deeply because you have hit the mathematical wall.

Could you please stop posting rubbish like that unless you have some kind of reference which agrees with you??

 

[chiro]

To be honest Homeomorphic, I would say that your friends may have more mathematical ability than you if you are finding it difficult to finish your thesis in the time that they have finished theirs. I also think you overestimate the effect of the "system" on your confidence, when it is much more likely that you have hit the wall in terms of mathematical ability. I would say it is a lack of talent which is your problem, as you have mentioned to me before, you had difficulty in Graduate Classes, I don't think it is that the culture of graduate school is against deep thought, I just think you are unable to think deeply because you have hit the mathematical wall.

Lack of talent?

Show us what you have done o mighty master of the universe so we can see what kind of talent you have that homeomorphic is "lacking".

Graduate school for pure mathematics is not easy even for the most apt.

Also you should be aware that graduate school does expect you to produce work in some kind of structured way and we all have different personalities of which some can handle some situations better than others regardless of any kind of metric for talent, IQ, or any such thing.

It's the same reason why you get lots of people who hate school and find it boring (and may not meet the barriers grade-wise to be considered socially acceptable) but yet flourish in their lives when they find where their strength is.

You might find that arrogance will hinder you more than it will help: we all get arrogant when things go well for us in our own lives but the difference is that the people that don't see it after being slapped in the face will never ever continue to develop because they miss all the things out there that they think they know when they don't.

Unsurprisingly a lot of experienced people here seem to communicate that thought either directly or indirectly in their comments.

You really have a lot to learn, and hopefully when do you get a slap in the face (like we all do when we get arrogant myself included), then hopefully you'll be aware of this to understand the power of humility.

 

[micromass]

You really have a lot to learn, and hopefully when do you get a slap in the face (like we all do when we get arrogant myself included), then hopefully you'll be aware of this to understand the power of humility.

He already got a slap in the face because he couldn't handle abstract algebra. So now he feels the need to make other people feel bad. Not really the best quality in a person.

 

[SolsticeFire]

To be honest Homeomorphic, I would say that your friends may have more mathematical ability than you if you are finding it difficult to finish your thesis in the time that they have finished theirs. I also think you overestimate the effect of the "system" on your confidence, when it is much more likely that you have hit the wall in terms of mathematical ability. I would say it is a lack of talent which is your problem, as you have mentioned to me before, you had difficulty in Graduate Classes, I don't think it is that the culture of graduate school is against deep thought, I just think you are unable to think deeply because you have hit the mathematical wall.

He can't finish his thesis because he's curious! Others have finished their thesis on time because they have finished it for sake of finishing it. He wants to explore his ideas thoroughly. I understand completely when he says that he's rebellious but unfortunately time is not a thing of luxury in graduate school.

Group you seem to be imposing limit unto others because you have found a limit, within yourself. If you brush off this uncertainty about your "ability" and really try to learn, you'll find that you are without limits. And others as well! :)

Maybe you adhere to this notion of "hitting a wall" because you are shocked that there is something (i.e. Abstract Algebra, in your case) that you don't understand; maybe this is your first failure in life. Don't just give up saying "I have reached my limit". Try again, fail again. Fail better.

Good Luck

SolsticeFire

 

[Group_Complex]

Lack of talent?

Show us what you have done o mighty master of the universe so we can see what kind of talent you have that homeomorphic is "lacking".

Graduate school for pure mathematics is not easy even for the most apt.

Also you should be aware that graduate school does expect you to produce work in some kind of structured way and we all have different personalities of which some can handle some situations better than others regardless of any kind of metric for talent, IQ, or any such thing.

It's the same reason why you get lots of people who hate school and find it boring (and may not meet the barriers grade-wise to be considered socially acceptable) but yet flourish in their lives when they find where their strength is.

You might find that arrogance will hinder you more than it will help: we all get arrogant when things go well for us in our own lives but the difference is that the people that don't see it after being slapped in the face will never ever continue to develop because they miss all the things out there that they think they know when they don't.

Unsurprisingly a lot of experienced people here seem to communicate that thought either directly or indirectly in their comments.

You really have a lot to learn, and hopefully when do you get a slap in the face (like we all do when we get arrogant myself included), then hopefully you'll be aware of this to understand the power of humility.

I am not arrogant, Micromass is right, my second course in Algebra has slapped me in the face. In fact it slapped me so hard that I now hope that I can now see reality for what it is, without having my vision clouded by the politically correct nonsense in this thread. If you read some of Homeomorphic's posts you will see he is the one who is quite arrogant about his mathematical ability, but when he speaks about graduate school and his failures there he makes all manner of excuses and ends up blaming the culture of pure mathematics or the inability of the professors to think deeply about mathematics and to grasp his own genius. In fact he believes that the entire discipline of pure mathematics is offtrack and only when mathematicians follow his advice will it be righted. Yet you call me the arrogant one.

Maybe I should be like Homeohmorphic and claim that my failures in Algebra are due to my superior talent in it, that my vision of algebra is so perfect that the professor's mundane exam questions are beneath me and that is why I am only going to get a B. Or I can be a man and admit that my mathematical ability has reached a limit and no amount of hard work will change that.

 

[micromass]

I am not arrogant, Micromass is right, my second course in Algebra has slapped me in the face. In fact it slapped me so hard that I now hope that I can now see reality for what it is, without having my vision clouded by the politically correct nonsense in this thread. If you read some of Homeomorphic's posts you will see he is the one who is quite arrogant about his mathematical ability, but when he speaks about graduate school and his failures there he makes all manner of excuses and ends up blaming the culture of pure mathematics or the inability of the professors to think deeply about mathematics and to grasp his own genius. In fact he believes that the entire discipline of pure mathematics is offtrack and only when mathematicians follow his advice will it be righted. Yet you call me the arrogant one.

Maybe I should be like Homeohmorphic and claim that my failures in Algebra are due to my superior talent in it, that my vision of algebra is so perfect that the professor's mundane exam questions are beneath me and that is why I am only going to get a B. Or I can be a man and admit that my mathematical ability has reached a limit and no amount of hard work will change that.

If you fail a course, then there are two options that you can take: you can give up and you can say that you will never understand it, and that is what you are doing now. Or you can say to yourself that you will do everything you can to understand it. And guess what? You WILL!

Hitting a wall is very common in science. I don't think there is any mathematician or scientist out there who hasn't hit a wall somewhere in his career. It is how you handle the wall that determines how good of a scientist you will be. If you work hard and give it time, you will conquer the wall if you want to. Scientists are exactly those people who ADORE walls and obstacles. Nothing is more fun than to encounter a topic that you don't understand at all at first, but that makes perfect sense after you studied it. The "high" you experience then is what makes it all worth it. If it were all so easy to understand, then I wouldn't do math in the first place.

If you're going to allow yourself from being discouraged because of the abstract algebra failure, then you're right: you're not cut out to be a mathematician. Why? Because mathematicians know how to handle obstacles and walls. You obviously don't.

 

[chiro]

I am not arrogant, Micromass is right, my second course in Algebra has slapped me in the face. In fact it slapped me so hard that I now hope that I can now see reality for what it is, without having my vision clouded by the politically correct nonsense in this thread. If you read some of Homeomorphic's posts you will see he is the one who is quite arrogant about his mathematical ability, but when he speaks about graduate school and his failures there he makes all manner of excuses and ends up blaming the culture of pure mathematics or the inability of the professors to think deeply about mathematics and to grasp his own genius. In fact he believes that the entire discipline of pure mathematics is offtrack and only when mathematicians follow his advice will it be righted. Yet you call me the arrogant one.

Maybe I should be like Homeohmorphic and claim that my failures in Algebra are due to my superior talent in it, that my vision of algebra is so perfect that the professor's mundane exam questions are beneath me and that is why I am only going to get a B. Or I can be a man and admit that my mathematical ability has reached a limit and no amount of hard work will change that.

The response you gave was an arrogant one: suggesting someone doesn't have the talent for something is not humble any means and it incites the kind of response that I (and others) gave.

Also graduate school is a real grind and like all things, people can feel the pressure: everyone deals with in their own unique way and some have different ways of venting and mathematics scares most people off before university even starts let alone for graduate school.

I have also seen Homeomorphic describe his feelings towards mathematics and I have seen comments that reflect his acknowledgment of both not getting out of mathematics what he thought (i.e. what he thought pure mathematics was turned out not to be what he had in mind) and also acknowledging that there are other people better than him at it which is counter to your own statement.

He may have made the comments you made, but I have seen him make the kinds of comments I illustrated above and take those into consideration.

But regardless, coming out with a statement like that shows a lot about the personalities of someone that feels like they have been defeated themselves, and this is not a forum that really wants to promote that kind of attitude especially towards others.

Homeomorphic is dealing with his life like we all deal with our life, the decisions we make, the thoughts we think, and the consequences they have but regardless of all that, having a defeatist attitude is one of the worst ways to not only deal with a situation, but also to project on other people.

 

[homeomorphic]

To be honest Homeomorphic, I would say that your friends may have more mathematical ability than you if you are finding it difficult to finish your thesis in the time that they have finished theirs. I also think you overestimate the effect of the "system" on your confidence, when it is much more likely that you have hit the wall in terms of mathematical ability. I would say it is a lack of talent which is your problem, as you have mentioned to me before, you had difficulty in Graduate Classes, I don't think it is that the culture of graduate school is against deep thought, I just think you are unable to think deeply because you have hit the mathematical wall.

Ouch. I did very well in some of my graduate classes, actually. But in some, I just couldn't take the way it was taught. The culture is not really AGAINST any particular kind of thought per se, it just doesn't value motivation and intuition enough. It is not me who says this, it is great mathematicians, like Arnold or Thurston, who have both very recently passed away. You don't need me to say the mathematical community is off track.

No, it is the textbooks and the profs. Why is it that when I read Baez, Penrose, Arnold, Thurston, or one of those big shots, their math is interesting, but 90% of the other guys' math is boring? You can't accuse THOSE guys for their lack of ability. No, I take the masters as my example. I am not saying that the mathematical community is off track because they are not like me; I am saying it because they are not like those guys. It doesn't really have to do with ability or talent. I am not exactly accusing mathematicians of being stupid, I am accusing SOME of them of being boring. And yes, maybe being boring makes them less competent because interesting math sticks better in your mind and is easier to think about.

Even mathematicians like Atiyah and Singer have complained about how there is too much pressure on young mathematicians to show early promise.

See, there are a lot of people who have succeeded in the system, up to the very highest levels in math, who are saying the same things that I am saying.

Take Morris Kline--I don't know what level of mathematician he was, but he was a professor, at least:

http://www.marco-learningsystems.com/pages/kline/prof/profchap2.html

I independently arrived at many of the same conclusions that Morris Kline did, and recently discovered his writing.

Also, as I said, those people who graduated--I used to kick their butts when we did homework together, some of them. SOME of them kicked my butt, but not all of the ones who graduated. I know for a fact some people succeed in the system that have less ability than I do. I think my ability is average by mathematicians' standards. But my level of rebelliousness is way above average. Only a genius like Arnold can get away with doing the kind of thing I am doing and succeed. I DO think I lack ability in that sense. But I have more ability than some people who manage to succeed.

It's clear that you are just depressed now and lashing out. Very much like me, except I don't lash out, I just lash in at myself.

 

[symbolipoint]

micromass wrote:

If you're going to allow yourself from being discouraged because of the abstract algebra failure, then you're right: you're not cut out to be a mathematician. Why? Because mathematicians know how to handle obstacles and walls. You obviously don't.
__________________

If we may do without the metaphor a bit, we have the obstacle: Learn and earn a good grade in this difficult course by the end of the current term, and if you repeat any course more than three times, or if you need to repeat too many courses, then you are doing something wrong - Find out yourself what you are doing wrong that you do not yet understand the courses materials.

Some wish they were better at Mathematics than they've been. What were they doing wrong? Imagine: Three semesters of progressive undergraduate lower level Calculus took took long to learn successfully, and done with the hardest studying one could do. One simply could not learn as fast enough. Course repetition was the way to go. The other option would have been surrender. Should such a person continue with more Math, maybe more advanced courses or other intermediate level course?

 

[chiro]

Ouch. I did very well in some of my graduate classes, actually. But in some, I just couldn't take the way it was taught. The culture is not really AGAINST any particular kind of thought per se, it just doesn't value motivation and intuition enough. It is not me who says this, it is great mathematicians, like Arnold or Thurston, who have both very recently passed away. You don't need me to say the mathematical community is off track.

No, it is the textbooks and the profs. Why is it that when I read Baez, Penrose, Arnold, Thurston, or one of those big shots, their math is interesting, but 90% of the other guys' math is boring? You can't accuse THOSE guys for their lack of ability. No, I take the masters as my example. I am not saying that the mathematical community is off track because they are not like me; I am saying it because they are not like those guys. It doesn't really have to do with ability or talent. I am not exactly accusing mathematicians of being stupid, I am accusing SOME of them of being boring. And yes, maybe being boring makes them less competent because interesting math sticks better in your mind and is easier to think about.

Even mathematicians like Atiyah and Singer have complained about how there is too much pressure on young mathematicians to show early promise.

See, there are a lot of people who have succeeded in the system, up to the very highest levels in math, who are saying the same things that I am saying.

Take Morris Kline--I don't know what level of mathematician he was, but he was a professor, at least:

http://www.marco-learningsystems.com/pages/kline/prof/profchap2.html

I independently arrived at many of the same conclusions that Morris Kline did, and recently discovered his writing.

Also, as I said, those people who graduated--I used to kick their butts when we did homework together, some of them. SOME of them kicked my butt, but not all of the ones who graduated. I know for a fact some people succeed in the system that have less ability than I do. I think my ability is average by mathematicians' standards. But my level of rebelliousness is way above average. Only a genius like Arnold can get away with doing the kind of thing I am doing and succeed. I DO think I lack ability in that sense. But I have more ability than some people who manage to succeed.

It's clear that you are just depressed now and lashing out. Very much like me, except I don't lash out, I just lash in at myself.

One also has to look at the incentives, especially for research-geared universities that are expected to publish at some de-facto rate.

The other thing (and this is important) is that creativity is not something that can easily be pumped out and it depends on the person.

The other thing (and to me its ironic) is that creative people don't work well in a structured and highly rigid environment meaning that you get this complete oxymoron of a system that discourages highly creative people from doing those things in environments like mathematics. I'm not saying all highly creative people will be discouraged, but the nature of creativity is not suited to the way things are currently structured.

One other thing is the incentive structure: do people publish papers just so they can say they've published 50 or 100 papers or do they publish a paper because they don't care as much about getting another "stamp" for their career and care more about the act of discovery and sharing what they found?

Now we need both kinds of people: we need the people that are rigid, can stick to protocol and are pretty much inflexible along with the people that are crazy, wild, rebellious, all over the place, but provide the kinds of creative suggestion that the first group don't.

But ultimately where does the incentive lie currently for professional researchers? What are they obligated to do or pressured to do career-wise?

Also, are we as a society able to tolerate any kind of uncertainty at all when it comes to risk-taking for any kind of project in the mathematics community and if so, roughly how much?

Mathematics ironically is a highly creative endeavor (especially when it comes to creating the new mathematics and this is the stuff that tends to solve the problems of yesterday) so I find it a little amusing in a sense to denigrate and decentivize people with those creative tendencies and push them away from mathematics.

It's definitely not good when most of the population see mathematics as un-creative when in fact it the opposite, and driving away these potential newcomers that have a lot to offer who are highly creative is a detriment to the future of the entire field itself IMO.

 

[homeomorphic]

I am not arrogant, Micromass is right, my second course in Algebra has slapped me in the face. In fact it slapped me so hard that I now hope that I can now see reality for what it is, without having my vision clouded by the politically correct nonsense in this thread.

It's quite obvious that you can't think very objectively about this. You got owned when I said you can't use your one anecdotal example to prove your silliness about how everyone hits a wall. The fact is that it is not proven what anyone's limits are. Therefore, we should be agnostic, rather than claim that so and so is or is not going to succeed based on their record so far.

It is very easy to provide counter-examples to your ridiculous claims. My dad is an EE prof. He said he got off to a really bad start in research. Very bad publication record, didn't publish thesis. But eventually, he did okay. Almost 200 publications, 15 in top journals. My analysis prof failed calculus. I keep waving these examples in front of you, but you don't seem to be interested in the evidence. Almost as if you are a creationist or something. It's really weird--you need to snap out of it, ASAP.

Here's the ultimate death blow to your claims: Stephen Smale.

http://en.wikipedia.org/wiki/Stephen_Smale

That's not to say that ability might not play a role, but it clearly demonstrates that your black and white reasoning is completely inaccurate. You can't say, you had trouble with graduate classes, therefore you are hitting a wall. That's just in complete conflict with reality.

If you read some of Homeomorphic's posts you will see he is the one who is quite arrogant about his mathematical ability,

Yes, like when I say I feel so dumb in grad school, I can't function. I am NOT blaming it ALL on grad school. Some of it is that I'm not that great, but some of it is that I like to think things through deeply, where grad school just wants me to accept it and move on. If you ever go to grad school, you will learn that they want you to accept it and move on, not to think about it. I am in grad school, I know. You are not. You don't know. Unless you go to grad school, you don't know what you are talking about. End of discussion. I mean, this is just obvious to someone who has done it. You're surrounded by it.

but when he speaks about graduate school and his failures there he makes all manner of excuses and ends up blaming the culture of pure mathematics or the inability of the professors to think deeply about mathematics and to grasp his own genius.

Now, you are really contorting the things that I have said in the past. That is a far cry from what I have been saying. Grasp my genius? I never said I had any genius, for one. I said I feel like a complete idiot. You're just looking at it from a perspective of complete misunderstanding. I never said I had anything to offer in terms of new mathematical results, except my paltry little crappy thesis. I do think I have something to offer in terms of motivating and thinking about old results, and that I believe that that is more valuable than most new results would be. The reason is simple. Most applications rely on very simple math. Research mathematicians are talking to a VERY small audience when they write papers most of the time. And there may be no concern for applications. What I want to do is focus on USEFUL math and how to make it more interesting for people like myself. I want to create that library of intuition that I always wish was there to ease the suffering of poor students, such as myself who always wanted a more intuitive grasp of things. Am I asking that MATHEMATICIANS should care about this? Well, maybe to SOME degree, but actually, what makes what I want to do significant is precisely that it isn't mathematicians that I want to recognize my work. It's that student who is suffering at the hands of boring classes. That's who I want to recognize my "genius". Mathematicians? I could care less about them.

Infact he believes that the entire discipline of pure mathematics is offtrack and only when mathematicians follow his advice will it be righted.

I never said it was the entire discipline. But yes, the general mathematical culture, I find very bizarre. Again, it is not my advise, it is the advice of some of the top mathematicians, at least as far as the pedagogical side of things goes. The other part of it is that we need more applied stuff, but who can really argue with that when applications are, to my mind, the whole point, otherwise, why are we working our butts off on something that doesn't contribute much to society. If you claim that we don't need applications, that's just pleading guilty. I'm all for the trickle down math argument where the applications are eventually found, but maybe people don't have them in mind--however, if there are to be applications, there has to be someone trying to bridge the gap and go out and find them and I don't see enough of it. I see a lot of grad students, even ones that graduate, unable to say how their work is going to help anyone, and sometimes they don't care, but sometimes, it bugs them.

I never claimed to know how things should be done. I just know that how they are being done right now falls short in many ways, not "how it should be done". I claim to have some missing pieces to the puzzle, yes. But I don't claim to have all the answers. I don't know how to handle math. It's huge and unmanagable. I would be the last person to claim I know how to handle it.

What you see as arrogance is just non-conformity. It's not arrogance, it's just not being a sheep. I am a big non-conformist. If I disagree with something that is popular, it becomes a target. It's like waving red in front of a bull. That's just my nature. I hate conformity and I am hyper-vigilant against sheep-like behavior. In experiments, people's answers to questions are influenced if they see other people's answers. They are asked which line is longer and they will give the wrong answer just because they see other people doing it, even though it is OBVIOUS that they are giving the shorter line. You can't eliminate these kinds of psychological biases, but you can try to fight them. That's what I do. I think people in the math community copy what they see, even though it's silly, and it can be PROVEN that it is silly. They copy the culture. They aren't immune from these kinds of things.

Maybe I should be like Homeohmorphic and claim that my failures in Algebra are due to my superior talent in it,

Did I claim that? Nope. Strawman, as usual.

that my vision of algebra is so perfect that the professor's mundane exam questions are beneath me and that is why I am only going to get a B.

Beneath you? Well, if you were like me, you would say his exam questions are all very well, but you are curious about other things. I don't really think I have ever seriously thought that someone gave me bad problems that weren't worth doing. That was never my accusation. Maybe there were some excessive calculations that I didn't learn that much from, but you know what, I am okay with that because you should be aware of how stuff like that can come up. Part of understanding differential geometry is knowing that calculations can get ridiculous if you don't stick to the simplest examples.

Or I can be a man and admit that my mathematical ability has reached a limit and no amount of hard work will change that.

Well, to be fair, we don't have as much information about you as you do yourself, but maybe you could think a little bit more objectively and rather than being a defeatist, you could take a look at all the examples of people who struggled, but eventually did okay. I can guarantee you, it hasn't reached a "limit". That is absurd. There are no "limits". There is always room for improvement. The question is just how fast can you improve. That's it. If you did well in analysis, that suggests that maybe you do have some ability, but you don't know how to think about algebra. Often, it turns out that people are not good at something just because they missed something. Once that is filled in, they can do okay.

 

[Best Pokemon]

Hitting a wall is very common in science.

Math is not a science.

 

[micromass]

Math is not a science.

Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.

See, I can do one-liners without justification too. I'll credit the above quote to V.I. Arnold by the way: http://pauli.uni-muenster.de/~munsteg/arnold.html

 

[DarrenM]

This thread got real silly, real fast. I can't tell if we're being trolled or not. I will say this:

No one is denying the existence of talent; almost everyone is denying that it is the most important factor in one's success in mathematics. There is a substantial body of anecdotal evidence that supports the claim that hard work, not innate talent, is the most important attribute. This body of evidence continues to accrue, from giants in the field and from unknowns. The only argument opposed to this is also supported by anecdotal evidence. However, that evidence is substantially less than that in favor of the previous claim.

The claim that people have a "mathematical limit" is just not substantiated by anything mentioned in this thread. What form does this limit take? How is it determined? How is it measured?

It's an arbitrary restriction with little or no grounding in reality. It's also conflating difficulty in a subject with an inability to do a subject. Terry Tao links to an interesting article about "gifted" students that discusses something similar; the main point of the article suggests that students told that they are intelligent are much more likely to give up, or get depressed, when they don't immediately grasp a concept. They equate it with being unintelligent and because intelligence is linked with their identity, it's a staggering blow. Students praised for their effort instead approach it as simply another obstacle, not as a reflection of their innate worth or value.

The premise that people have a mathematical limit seems to be based on the idea that people that don't have such limits will breeze through every undergraduate and graduate math class without batting an eyelash. I'd like to meet such a person. They can sign my autograph book, right next to Iron Man and the Scarlet Pimpernel.