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.
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.)