What blew my mind is that it hasn’t been proven that pi contains an infinte number of ones, for instance. It’s not out of the question that there is a decimal place where the last 1 appears and there are none from then on.
It’s not really likely, but we simply don’t know and it is possible. It sounds weird given how many decimals of pi we’ve calculated, until you realise we’ve literally calculated 0% of them.