Someone who is tone deaf will never be proficient with a violin, or a theremin.
No amount of hard work would have allowed Stephen Hawking to succeed at sports.
Some pursuits are simply unavailable to those without the requisite immutable attributes. This is not politically comfortable, but it is true. I think the only legitimate question is whether mathematics is such a pursuit, and I'd like to be proved wrong on that point, but trying to convince me that anyone can do anything they put their mind to is wasted effort as it is so plainly contradicted by the available evidence.
Note that the contradictions you mention are _physical_ in nature; it is true that there are some functions that some bodies can perform that others cannot. Mathematics is not one of those things.
Is the brain not a physical thing? Do you believe that all human brains are physically and functionally equivalent such that one brain should be able to learn to do anything that another can?
What about those people in this world with genetic abnormalities that affect brain function? Would you expect someone with Prader-Willi syndrome to be able to become competent at mathematics if they only worked hard enough at it? At what point does “hard enough” become “virtually impossible” or even “definitely impossible”?
Why, sure - from the physics standpoint all the human brains are essentially the same, they all consist of the same protons, neutrons, electrons... (Also, they are close enough to being spherical.)
While I feel your point is incredibly pedantic, perhaps I should have qualified with some form of "at least X% of people that do not have rare genetic disorders can learn math, X >> 50". However, I think such statements are usually implicit when talking in generalities.
Got it. Your previous statement didn't really seem like you were speaking in broad generalities and instead seemed more absolute, like math is something that could always be learned by any human brain. Clearly that's not the case, which was the point of gpp, I think.
No amount of hard work would have allowed Stephen Hawking to succeed at sports.
Some pursuits are simply unavailable to those without the requisite immutable attributes. This is not politically comfortable, but it is true. I think the only legitimate question is whether mathematics is such a pursuit, and I'd like to be proved wrong on that point, but trying to convince me that anyone can do anything they put their mind to is wasted effort as it is so plainly contradicted by the available evidence.