Or can you actually study enough to get good grades in any math class?
I think there is some innate reasoning skills that may allow certain people to excel in upper division math classes with relative ease but I don’t think that other people just “hit a wall” when it comes to math. If you’re dedicated to something enough, you’ll most likely do well.
I partially disagree with preamble. I think that some people do hit a wall. Scientifically speaking there are 2 (at it’s most basic) types of brains. Those which can process logic and math and those which are more visual and detail oriented
http://www.ucmas.ca/wp-content/uploads/2011/04/Left_Vs_Right_Brain.gif
[Researchers Debunk Myth of “Right-brain” and “Left-brain” Personality Traits](News stories by month | University of Utah Health | University of Utah Health)
Yeah, this is not a thing. Science doesn’t acknowledge the existence of two “types” of brains. Those are just the sides of your brain that process different things, but it doesn’t mean that one side of your brain because more developed than the other. The connections between areas are what counts, and science has even shown that when connections on one side of the brain are damaged, the brain can form new connections to make up for them.
That said, forming connections in the brain is about encountering things repeatedly - so it follows that the way to get better at math is to practice a lot, and continually expose yourself to math. I think the “wall” is mostly desire + time - how much do you want it, and how much time are you willing to sink into it?
The “best” people at math I have found are people that are diligent, practice, and do their work. There are people that understand things easier, but for better or worse, they may get deducted points for reasoning because they fail to show their work or don’t practice enough compared to someone who decides to do more practice problems. Homework in college is often optional, so how much effort you put into it, especially in something like mathematics, is how much you get out of it
Definitely agree with @shawnspencer. It is very practice and work intensive.
My brother, for example, is one of those kids that excels in math and science. He built a computer for fun when he was a high school sophomore, and built a nuclear probe for his engineering class as a college freshman. A nuclear probe that is now slightly radioactive and sitting in his dorm room, but alas.
In high school, though, he almost made a C in AP Calculus and made a 30 on his first calc exam in college. Why? He never shows his work, or doesn’t show it the way the teacher wants him to, and often that leads him to make silly mistakes.
He eventually got his act together, but it really is a lot about what you put into it.
Thank you all for the responses. I guess effort applies even in higher level mathematics. Like Mynaaa’s brother, I never put in too much work in any class in middle and high school, but I also never “got” math so I was worried that maybe effort would not be enough to overcome not “getting” it.
While some people can study a lot in math and do well in it, I’ve come to learn through the years that math just isn’t for me. No matter how much I studied, no matter how many extra practice problems I did, no matter what tutoring I got, math never really clicked with me. The last math class I took was an online Intro to Statistics course, and I was only able to pass it with a B because we were allowed to bring one sheet of paper with all the formulas written on it. If we weren’t allowed to use our notes on the tests, I probably would have flunked. I think I may have dyscalculia, but I haven’t been properly tested for it. I do know that I have trouble with numbers in general, though. To this day, I still have to count slowly with my fingers while everyone else around me can do it mentally in their heads. Even when counting change, I have to count them slowly and out loud so I don’t lose track or miscount.
Not everybody is smart enough to get a PhD in Math. Most people aren’t. The more advanced/“harder” the math course, the fewer the people will be able to comprehend it. I’d say probably most people can handle more math than they think, but all but the very brightest will have some limit.
I would say a lot of it depends. There is some of math that you can get through pure elbow grease and putting your mind to it, but the really abstract parts either make sense or don’t. IMO that’s what determines a Math PhD candidate from a businessperson. If the non-practical stuff has you floundering, a job in finance where it’s more applied math might be better.
I’ve never heard of a fetus passing any math class (let alone the highest) so yeah, I’d assume you have to be born first in order to pass the highest math classes.
It’s never too soon to start reading the Principia to a developing child in the womb. Start right away, and they might manage to make it to complex analysis or something before being born.