Why is it that finding out more digits down the line of the pi number is such an accomplishment in ancient times? There are many notable, especially Chinese mathematicians, that are famous because they found a closer approximation for pi, more of the digits down the line.

It's still considered an accomplishment now...as trillions of digits have been calculated. How Much Pi Do You Need

Because it takes ever increasing advanced algorithms to compute more and more digits. It's not about having a more accurate approximation, it is about computational prowess.

As a student, I wrote a program in C that could calculate pi to 65536 places, and it took my 386 based PC about 19 hours to do so...I used a formula discovered by Euler using the inverse tangent function. But that was nothing compared to what the pros do.