Do We Need the Digits of $\pi$?

Not for any real-life calculations according to wikipedia

Practically, one needs only 39 digits of π to make a circle the size of the observable universe accurate to the size of a hydrogen atom.

It is however useful to test supercomputers for accuracy and as a memory intensive number-crunching benchmark.

Today the high precision calculation of $\pi$ finds practical use in testing the "global integrity" of a supercomputer. "A large scale calculation of pi is entirely unforgiving; it soaks into all parts of the machine and a single bit awry leaves detectable consequences.

A less mathematical reason for calculating more and more decimal places is because we know they are there. Man is inherently curious and always wants to see what's over the next hill, round the next bend etc.

Knowing more and more digits of $\pi$ has absolutely no value to anybody. Digits of $\pi$, beyond the twentieth or so, are completely worthless. The only value in this enterprise, if any, lies in the process by which the digits are generated, not the digits themselves.