I know two opinions:

1. "Central" means "very important" (as it was central problem in probability for many decades), and CLT is a statement about Gaussian limit distribution. If the limit distribution of fluctuations is not Gaussia, we should not call such statement CLT.

2. "Central" comes from "fluctuations around centre (=average)", and any theorem about limit distribution of such fluctuations is called CLT.

Which is correct?

I know two opinions:

1. "Central" means "very important" (as it was central problem in probability for many decades), and CLT is a statement about Gaussian limit distribution. If the limit distribution of fluctuations is not Gaussian, we should not call such statement CLT.

2. "Central" comes from "fluctuations around centre (=average)", and any theorem about limit distribution of such fluctuations is called CLT.

Which is correct?