Question

Is it just me, or is mathematics never self-fulfilling?

Don't get me wrong: I treasure it with my whole soul, I can't resist a good puzzle and I want to study it for many more years to come. But does it always feel as though you never know enough?

For example, when I first took calculus, I felt proud of being there. However, a month later, it was embarrassing: I had to know more complex, more “grown up” things.

Answer 1

I'm helping TA an ODE course, and when I find myself dusting off and reviewing its concepts, I hide in the library in hopes that my colleagues won't ever find me.

I’m always seeking to know more about it akin to a girl trying to quench her thirst whilst dreaming—it can’t be done.

Is it just me?

Answer 2

Ain't never been a single man whose known everything there is to know in mathematics. Even Newton or Taylor could never have hoped to be as knowledgeable about the subject as we (as a collective group) currently are. Trying learn everything ever in mathematics is akin to saying you want to understand the origins of the universe. Rather pointless if you ask me.

Answer 3

you should try playing chess if you want to be frustrated

Answer 4

I don't want to know it all... I understand the vastness within.

But what I find depressing is how unfulfilled I feel at times.

Answer 5

As a TA for and ODE class you know more about math than pretty much everyone. I'd find fulfillment in being able to help essentially everyone, but that's just me. Furthermore, I'd be able to contribute to almost any mathematics-related research. I suppose I'd find some fulfillment there as well. I guess this is more philosophically geared towards what makes YOU happy.

Answer 6

Most of my college friends, who graduated with engineering degrees, never cease to comment on how proud they are of themselves. They brushed grad school aside and began working for their "dream companies."

I want to become a professor, so I still have a long way to go.

Anyway... perhaps I'm just being a girl and over reacting...

Answer 7

You're lucky if mathematics is the only area where you think you don't know enough.
I feel like that about everything in life :)

Answer 8

"Anyway... perhaps I'm just being a girl and over reacting..."
Bingo!

Answer 9

lol

Answer 10

No, you're not "just being a girl and over reacting."

The thing you are experiencing is akin to that which is experienced by every great mathematician. Have you read of Kurt Gödel? He's a very fascinating figure who inevitably killed himself. He experienced such psychological stress because he could not formalize his ideologies into his mathematics. More specifically, his incompleteness theorems contradicted his notion of the existence of intuition. He spent the majority of his life trying to formalize mathematically the idea of "intuition" so that he could somehow rigorously explain how humans are not susceptible to the issues found in his incompleteness theorems.

His friend, Einstein (though not a mathematician), had a very similar issue. Einstein was so irked by the conclusions in quantum mechanics that he spent the majority of his life searching for a grand unified field theory. He never succeeded in this task, despite spending around 30 or more years on it. The biggest road block was the fact that he would not even touch any of the results in quantum mechanics because he outright rejected quantum mechanics.

And then there's Georg Cantor. He was driven insane by his desire to know. Georg changed the fundamentals of set theory entirely with his ground breaking ideas. The mathematical community found him disturbing and intellectually cancerous because they could not and would not accept the fundamental implications of his great discoveries. They simply hated his work. But this alone was something that Cantor could contend with psychologically. What drove him insane, actually, was the continuum hypothesis. He spent the vast majority of his life struggling to prove or disprove this hypothesis. He never succeeded due to the fact that the continuum hypothesis is neither provable nor disprovable (I excluded the other clarifying conditions here).

And these are just a few. All of these people were driven insane by their desire for knowledge.

Mathematics is just not self-fulfilling due to the fact it is incomprehensibly vast. Life is but a continuous struggle of will on behalf of the living; it is an eternal question, "Will you know? Must you know?"

Answer 11

^ Told you, Across. He is a genius, right?

Answer 12

And that is exactly what I feel. I am currently being challenged by proofs.

Whenever I have to encounter a new one, I can't find new ways to do it. Everything seems strange to me -- but that is what I felt when I was learning the English Alphabet.

You need memorization on some parts of that journey. I seriously am in the need to do proofs by contradiction, and direct proofs.

Another thing is challenging me - Trigonometry. Seems all like a chicken scratch to me.
It makes me feel like a dyslexic kid with no abilities. I feel ashamed of that.

But, fortunately, I haven't lost my hope to learn new things - and there is what I admit.. I have stalked all of the five people listed on my profile more than a thousand times in search of inspiration.

But this attitude still doesn't seem right to me. There are a lot of things I haven't learned and I have encountered a lot of times on OpenStudy.

1) Trigonometry
2) Calculus
3) Modular arithmetic(especially that Chinese Remainder Theorem)
4) Programming the questions that can't be written out by hand(Cryptography)
5) Biology
6) Chemistry
7) Physics
8) Writing

I'd be satisfied by myself when I become great at these(no one is perfect).

^_^

Answer 13

Additional note: I keep in contact[or at least I want to] with the super-five on my profile.
I am a beginner's mind. Well, that is what I consider myself on OpenStudy.
Gotta lot to learn. Heh.