You're right that there is a big social aspect to mathematics that has bitten people in the butt many times throughout history.
But to say that an "observation of reality" should have any effect on existing mathematics is silly. Though mathematics might take inspiration from the physical world, it is removed from it by design. When some observation of reality disagrees with mathematics, that usually means the mathematical framework in question needs to be generalized or specialized, not altered.
This has happened over the years, for example, with measure theory, Fourier analysis, Lie theory, computational complexity theory, and many others.
But to say that an "observation of reality" should have any effect on existing mathematics is silly. Though mathematics might take inspiration from the physical world, it is removed from it by design. When some observation of reality disagrees with mathematics, that usually means the mathematical framework in question needs to be generalized or specialized, not altered.
This has happened over the years, for example, with measure theory, Fourier analysis, Lie theory, computational complexity theory, and many others.