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.