system
Given the following post, respond as if you're commenting on Reddit:
human
Why does the central limit theorem work?

I asked a teacher, and his answer could almost be rephrased as "it is a general property of the universe".
gpt
It works because the math works out (which is similar, although philosophically pretty different, to your teacher's answer).

It may help to think of the central limit theorem not as a property of every type of random variable, but as a property (in fact, the motivation for) the normal distribution.

Compare it to the Poission distribution.  It's not a coincidence that a Poisson distribution looks like a bunch of low-success-rate binomial distributions added together, because that's the motivation for the Poisson distribution.

Similarly, it's not coincidence that the mean of a bunch of iid random variables looks like a normal distribution, since that's precisely why the normal distribution is interesting.

It's still a bit surprising that this works for *any* collection of iid variables, but it's not really that surprising, because adding n and then dividing by n for large n tends to smooth out any weird distribution those variables may have.