Is there a point in maths where, after that, not everyone can grasp it despite studying? I.e. everyone, given the proper books and education can understand calculus or other high school/university stuff. In other words, can anyone without a mental impediment understand everything about maths or not?
>>10718660>everyone, given the proper books and education can understand calculusMost engeneering students would disagree
>>10718699>considering enginiggers as peopleStop right there faggot of course subhumans can’t study up to Calc II, OP you should be excluding engineering majors. Then everyone can study up to maybe Abstract Algebra
Everyone should be able to get through anything computational, it's just following rules. A proper course in analysis is probably going to stop a good number of people.
>>10718709I agree. Those faggots can't understand things like Abstract Algebra (In general, abstract ideas) even with proper text books.
>>10718736If you call it abstract algebra you don't know what it is.
Wow this thread is filled with cringey math undergrads
>>10718741The subject in my pensum it's called abstract algebra. It is ring theory and group theory for undergraduates.
Given enough time the average person could reasonably understand everything in the undergraduate maths curriculum, which in a decent university includes things like basic functional analysis and field theory/intro Galois theory. It's not that hard to grasp. Things in research-level mathematics often seem "hard" to grasp since they're not well organized yet -- for instance, some facts about ODE qualitative theory (i.e. stability theory) have undergone massive change starting in the late 70s/early 80s, and what was once an ugly field that was written in the language of functional analysis can now be presented in terms of basic analysis and linear algebra.
>>10718660that's like asking if everyone can play music. the answer is yes, it just takes practice
>>10718660Well a very good example is the fundamental theorem of homorphisms, though I don't remember it good enough to describe how it requires a lot of working memory to understand, so perhaps someone who knows about it could try ^^
>>1072057996% of the white population cannot use a calculator to find the cost of carpet for a room given the size of the room and the cost of carpet per square foot (Haier 2017). Some people do not have the ability to learn math. I would say that the point where not all people could grasp math with intense study would be basic calculus or high school algebra.
>>10718660IQ is largely genetic, so yes. I'd say the cutoff is around real analysis, Rudin level. A double digit IQ individual will never understand Rudin.
>>10720606Though it's not too hard to think that one can think of some neologisms could help one understand th theorem instead of depending on visual working memory alone. However even then you need some amount of autonomy. But with enough autonomy and a belief that you can improve and actually searching for a way to improve, and you'll realize that there is no such limit
>>10720621Kind of mass that first sentence, but what I meant is that it's not to hard to think that a person can come up with certain neologisms that could aid them understand such complex theorems
>>10718660>orOnly mathematically retarded statements use the word "or", true autist mathematicians speak only in terms of the absolutes approachable from the moment of measurement request.
>>10718660even if you come to the conclusion that "being stupid only means you learn slower" and not acting as an insurmountable gatethere comes a point when you learn so slowly that your lifespan is just too shortgiven infinite time (almost) anyone could learn anythingthat is not a given howevermost people cannot be mathematiciansmost people cannot be physicistsmost people are not smart
>>10720659Yet everyone has a unique seed of genius to gift the world. The trouble when you are that unique is that you have to develop a completely new language to explain your existence/knowledge/awareness to the rest of reality.
>>10718660Hard to say... The problem is most people when introduced to a type of math they need analogies and concrete examples for them to understand it. So doing anything past Proofs or Analysis can be tricky for most because it requires a really unpopular way of thinking. Abstract math isn't impossible to grasp. However in general most people struggle. Like remember when you first introduced to the concept of putting an x with numbers? It was unfamiliar and even daunting to some of those in my class. Once you realized that the x meant something using some example that were "relatable" to something you were familiar with then you could work with it. Now bring this up to undergraduate pure math programs, that x becomes proofs and theorems and generalizations. The difference here is that a proof at least from my experience can't be related to say some object or some specific thing. It is it's own thing so now you need to work with it. If this is something you've been reflecting on yourself, try proofs. Immerse yourself in abstract math and see if you can really understand it. Chances are if you understand what's going on your brain becomes blue and enlightened and the realizations you start to have about math really change your perspective as a whole. If this doesn't work out for you do something for related computationally. Engineering, Bio sciences, Physics or even applied math. Pure Math is the Autist kid that doesn't blend in with the crowd, yet what constitutes pure math even for me is still beyond me in a way where it seems like magic.
>>10720792Where do I start with proofs? Is there a document or book that's just filled with proofs that I can read through? Can you recommend me any good textbooks on proofs?
>>10720617You do realize Rudin wrote multiple books right? It's not clear which one you're referring to (don't bother clarifying because your post is trash anyway).
>>10718660>can anyone without a mental impedimentthere is no discrete line to differentiate normal, intelligent, or stupid people. It's a spectrum.
>>10720607>96% of the white population cannot use a calculator to find the cost of carpet for a room given the size of the room and the cost of carpet per square foot (Haier 2017)That´s a load of horseshit. That task is absolutely trivial; it requires nothing more than calculating the area of the floor and multiplying that by the cost of carpet per unit area.
>>10720913Not that guy, but rudin typically refers to baby rudin, intro. papa rudin is used for real and complex and grandpa rudin for functional.
>>10720792Analogizing is a very important part in pure math as well, but you have to do it in the context of other pieces of pure math. That is, the analogies apply to intuition rather than “this resembles a physical object/phenomenon I know”
>>10718660Maybe, maybe not. I think what’s more the case that people give up long before they exhaust their actual abilities, so I’d say what’s more important is being invested. More often than not, the deciding factor in my advanced classes was engagement and time spent on the material (especially in grad prep analysis)
>>10718682lol pretty much. I'm pretty sure 90% of the population in first world countries are unable/unwilling to make it past calc II.
>>10722096Then provide a source that says otherwise. "That's horseshit" is not an argument. The reason why you think that is because you probably associate with people of similar cognitive ability, and thus have a biased view of the general population's intelligence. It's called cognitive segregation.>That task is absolutely trivialthat's the point.
>>10722279Yeah I agree but again those pure math analogies still have the element of abstraction so regardless the typical individual will struggle.
>>10718660Not everyone can understand calculus or even trig
>>10720911I would say Intro to Mathematical Structures and Proofs by Gerstein isn't a bad option but after that just read multiple Real Analysis and Algebra (Abstract obviously) books.
>>10720911>Where do II can recommend one! Proofs and Refutations, the best book ever on the subject in my opinion, also if you want methods you can go for polya's how to solve it
algebraic number theory
>>10718660average person - calcaverage undergrad - elementary analif you can understand real anal, you probably have the fundamental abstraction needed to understand anything in math you need to (this doesn't mean you will be able to solve any problem/prove any conjecture, however)
>>10718682yeah about much, multivariable calculus (3) ia really where it all picks up
>>10720607Interesting. Ive looked for the source to no avail. Elaborate on Haier 2017