Multi-variable calculus is trivial and does not constitute mathematical ability. Solving anything beyond trivial problems requires mathematical reasoning and tools (learned theorems, ideas which were proposed and proven by the great minds of math). Math majors learn these tools throughout undergrad and graduate school. Without these tools, don't expect any musical child to contribute to the field of mathematics within the next 10 years.
Like I said, very few people have the ability to do higher mathematics without training. The same cannot be said for general puzzles. Some people analyze and process information faster than others.
The opportunity is not there. They don't do physics.
Likewise, how many great mathematicians have the great tribes of Africa produced? They have great music, don't get me wrong, but this does not produce mathematical understanding or the ability to navigate through logic puzzles.
You seem to think I equate mathematical ability with musicality, I don't. I only said innate talents exist for both. Yes it is much easier to find the resources for creating instruments than to derive higher mathematics. As for your implication that a higher education is required to learn and understand math, I would say in most cases, probably. But mathematics is called a basic science for a reason, all of it's principles can and are derived from ancient philosophical principles. Though I don't really know what this has to do with the nature vs nurture argument. Some people process information better and faster than others. I haven't seen you address this argument yet. If you are trying to prove to me that a higher education is required to be successful, and that successful people are only "smart" and successful because of the schools they went to and the environment they grew up in, then you are objectively wrong (see last paragraph.)
You are not going to discover linear algebra. Period. Linear algebra is a field of mathematics that was developed by many minds and the discovery of a whole field is not a one-man pursuit. It occurs over lifetimes.
Secondly, the tools of linear algebra that you learned in first-year were proposed by people like Gauss in the 1800s. These are old tools that you learn to use, but getting an A in this course tells me nothing about your ability to solve mathematical problems. Beyond the trivial, previously solved cases, you won't be solving anything. You also won't be discovering any new tools for others to use.
If you want to make an argument, don't give trivial cases.
I'm not sure what your point is, my statement was clearly hyperbolic. People differ in their ability to analyze and process information. I'm starting to sound like a broken record. Yes, some things are so intellectually "heavy" that one mind is likely not enough. You are not going to make slow minds fast by registering them in difficult classes.
There are plenty of child musicians that produce great music, but they are incapable of contributing to the field of mathematics. Taste for music/musical fame is also subjective, mathematics is not. They are completely different things.
Ahh see here is what I addressed in my previous post. Scientists are finding that music obeys certain laws, so no it is not completely subjective. As I said, music is certainly
more subjective than math. But if I like classical rock and you like jazz that may be due less to environment than you think.
We are going in circles here so let me wrap this up. You originally contended that environment plays a greater role than intelligence (and lets define "intelligence" as innate intelligence) in life. If we measure success in life by education level and income level, then you are wrong.
IQ has a greater predictive power for success in life than race, sex, SES, education (primary education), etc. Then we pivoted and you began to argue that intelligence is not really innate, or at the very least not largely genetic and heritable. This, also, is false.
Intelligence is, at the very least, 40-70% heritable (meaning directly heritable from one's parents.) That doesn't even account for whatever cognitive faculties you carry that were not inherited but are no less innate. Neither of the two bold statements are arguable, it is simply what the evidence shows. Which is why people who attack IQ studies say that the tests are biased, or that there are insanely complex reasons that IQ can predict life outcomes, or that scientists are racist/sexist/whateverist. Anyway, it's been real, I'm going to bow out now.
