For example my birthdate, 12-18-1983, written as 12181983, seems like a fairly meaningless numerical sequence, but it's most likely in pi somewhere.
The string 12181983 occurs 3 times in the first 200 Million digits of Pi.
The expected value for the number of times that string (or any other eight digit sequence) to occur in the first 200 million digits would just barely under 2 (it would be exactly 2 for the first 200,000,007) if the sequence of the decimal digits of pi were effectively equivalent to a random sequence of digits. But 3 is certainly close enough to make it plausible. However, whether pi or e have this property (which would make them a normal number for base 10) is currently unknown. There are only a few classes of numbers for which it has been shown that they definitely are normal to a specific base, and fewer still for which it has been shown that they are absolutely normal (normal numbers for any base), but none of the fundamental irrational mathematical constants have been shown to have that property.
Yes, better to call it the infinite pi conjecture.