Strange Question Regarding Pi

[Izzhov]

Is there a proof or disproof that any given finite string of digits will occur somewhere in Pi?

[HallsofIvy]

No, there isn't. That would be equivalent, I think, to saying that \pi is a "normal number" and that has not been proved or disproved.

[arildno]

It smells equivalent to the property of normalness, but I'm not sure if it is easy to prove..