My hunch on the difficulty of higher math

[bobsmith76]

Just about all of the problems in my calculus textbook range on average range between 4 and 8 steps. Once you know the algorithm the problems are usually easy and routine. It is simply a matter of understanding what the algorithm requires. Ironically the hardest part about math is understanding the vocabulary and the special language that it is written in. As everyone know, all math builds on other math. I have a feeling that higher math problems will continue to range between 4 and 8 steps, it's just a matter learning all the algorithms and learning all the prerequisite math. Is this true? Adding new knowledge to math, that of course is hard, but learning something else that someone has discovered is easy. To illustrate this is easy. Think of how easy it is to understand that F = MA, yet it took centuries for man to discover.

 

[Number Nine]

Higher math bears no resemblance to the math you're doing right now. In particular, you will rarely be performing calculations, and there will almost never be an algorithm for you to follow. Most of the time, you won't even be working with numbers.

 

[yenchin]

It will get to a point when the whole lecture is spent on proving a *single* theorem, and the homework takes days to *think* about, with a single question taking pages to write down its proof.

 

[pwsnafu]

learning something else that someone has discovered is easy.

Ha ha, no. Easier sure. But easy? The amount of required reading you need for, say, K-theory will send you back months, if not years.

 

[bobsmith76]

Guess, I was wrong. I am aware of the difficulty of the theorem for finite simple groups:

one cannot command a clear view of the classification theorem for finite simple groups. Though the statement of the theorem requires but half a page, its proof required 10,000 pages and employed the joint effort of hundreds of mathematicians spanning several decades. The mathematical community considers the theorem proven, but no one mathematician is able to survey the entire proof. - William Dembski