What's more important in math? >Conceptually understanding

>>9086400
2=4>3>1

>>9086480
Wait, switch 3 and 1 and that's it.

>>9086400
3 and 4 are very important, but are not very useful if you dont have 1 and 2.

Similarly you can't go very far if all you have are 1 and 2

In academic Math? 4.
In profitable Math? 3.
1 and 2 are things that only matter when you don't have them. Vague as hell, but that's life.

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Six6six6

Definitely all are very important.
Modular arithmetic for example, important to understand on a symbolic and visual level, using that to prove some useful rule, applying that rule to compute something, and using all of the above to note relations.

I'd say that you need to understand how math concepts relate to build new theories. Being able to prove = being able to do mathematics. Symbolic/visual doesn't really matter, you need abstract thinking. Computations are garbage, I sometimes have hard times adding 15 and 25

>>9086683
>Computations are garbage, I sometimes have hard times adding 15 and 25

>>Har harh, yep well that dun 'bout says it all 'bout yer higher learnin' there dunnit son? Simple man lak' me can tell ya righ' now that tha' sum is equal tuh 35, guess that's what ya get with common sense schoolin' 'stead uh this liberal nonsense they teachin' nowadays at your wussy school. Son you sign' up fuh football yet? That what makes a man a man I tell ya as much, if a man can't tell yuh tha' I don' know what he can tell yuh these days

When you say you study math, people not in STEM either think you add bigger numbers or find the missing side for higher n-sided polygons.

>>9086400
None of the above
>being able to remember every math problem known and becoming a human calculator

>>9086400
First: being able to prove math concepts. This is because even if you are a supreme genius with great intuition but cannot prove your results and write concise papers to expose your results then no one will ever care about you.

Second: conceptually understanding math at a symbolic and visual level. This is because before you can publish a result you must actually obtain a result. You must be able to explore and find new things.

Third: understanding how math concepts relate to each other. I put this in third because even though it is fundamental to have an overview of all mathematics to become a mathematician, once you are a mathematician you can build a career by completely focusing on one single and isolated concept. Many people have done this, many people have obtained fields medal and other accomplishments by doing this. But it is important that you at least know the core of algebra, topology, and analysis so that you can get that degree and then start exploring the waters because you cannot sail without a boat.

Fourth: Being able to manually work out computations based on math concepts. This is clearly the least important thing because computation is the most trivial aspect of mathematics. It is still necessary because our ultra generalized theorems can only go so far and eventually you will need to compute something in order to advance your understanding. No one would have proven the prime number theorem if it had not been famously conjectured because some guy unironically did a graph for x up to 10000 of [math] \pi(x) [/math] and saw that it kinda looked [math] \frac{x}{log x} [/math]. Fun times.