We assume that nature is probabilistic in the sense that it is linear, binary and symmetric (Schrödinger's exact equation is misunderstood as linear but not binary or symmetric)
The numerical derivation of the normal/Gaussian distribution for the probability density has already been explained [1] via the use of the 4D x-t B matrix strings which are linear, binary and symmetric.
The proof, which takes a few minutes, skips the mathematical complications of the central limit theorem and its multipliers.
The question is valid:
Who best illustrates how nature works:
classical math or matrix B strings?
[1] I.Abbas, January 2023, researchgate and IJISRT review.