my goal to learn everything there is to learn in the entire branch of mathematics

[Brutha]

And that is how my textbook taught me to use the epsilon-delta definition of limit to prove the limit of a linear function.

You can memorize the method that your textbook teaches you to solve a given problem.
There's however the different ability of being able to find your own way to solve a problem. That way requires understanding.

In the end computers can do the work of taking a predefined way to solve a problem a lot better than humans. The ability that computers lack is that they aren't able to come up with their own way of solving new problems.

Part of the ability of being a good mathematican is to develop proofs on your own when you just have definition of axioms and theorems.

About memorization. A lot of people are echoing the sentiment, "rote memorization is bad". I believe this is a rare example of mathematical dogma.

The dogma lies in the fact that you don't use a mathematical formula without proof.
Either your professor did the proof during the course do the prove yourself in the exam.
It not just about finding the right answer but also about proving that the answer is right.

[andrew112]

Originally Posted by Brutha

You can memorize the method that your textbook teaches you to solve a given problem.
There's however the different ability of being able to find your own way to solve a problem. That way requires understanding.

In the end computers can do the work of taking a predefined way to solve a problem a lot better than humans. The ability that computers lack is that they aren't able to come up with their own way of solving new problems.

Part of the ability of being a good mathematican is to develop proofs on your own when you just have definition of axioms and theorems.
The dogma lies in the fact that you don't use a mathematical formula without proof.
Either your professor did the proof during the course do the prove yourself in the exam.
It not just about finding the right answer but also about proving that the answer is right.

yes, figuring out how to solve problems on my own rather than learning how to solve problems from other sources is something that I am lacking right now, but I would like to learn how to develop that area so that I will be able to take any problem and figure out how to solve it on my own. however, it might take more discipline to learn other ways of solving problems rather than just resorting to the way that you think the problem should be solved.

[ballhit2]

Dude Andrew if you want to learn everything there is to possibly know about mathematics ('bleedin everything about sod all' you could say in England) you should begin by calculating how many hours that would take, and how that would affect the rest of your life.

Not having done the math myself, I'm guessing it's over 8 hours a day. Do you really want to cut that much out of the rest of your life?

But hey, more power to you, better than memorizing bible verses for that amount of time.

[andrew112]

Originally Posted by ballhit2

But hey, more power to you, better than memorizing bible verses for that amount of time.

It's funny you should say that, because I also have an interest in memorizing bible verses as well; I already have some memorized, and yes, it is boring and takes discipline in doing so.

[shivraj]

I think this is a goal for lifetime. Ask any senior mathematician, how long it took them to master math. Also some professional trainning is required IMO.

[Trustme]

I think you will need to specialize at one point or another. There are people who devote a lifetime to one area of mathematics. Of course this specialization happens after they acquired a very good general understanding of all fields.

[Brutha]

however, it might take more discipline to learn other ways of solving problems rather than just resorting to the way that you think the problem should be solved.

The beauty about math is that either your solution is right or it isn't.
That one of the reason why college is good because you have a teacher who will tell you when you have made an error somewhere.
Often multiple right ways to solve a problem and the goal is to find one of them.

That what mathematicians are for:
Finding ways to solve mathematical problems of other people (well sometimes the other people are mathematicians as well ).

When a mathematican produces a forumla a chemist might use that formula in his work.
Most chemists aren't good enough in math to create the mathematical toolkit that they use themselves.
And when the mathematican proved that the formula works the chemist doesn't have to brother about the math and can concentrate himself on chemistry.

The chemist can get away if he simply memorizes the forumlas.