100,000 Digits of Pi: How the IBM 7090 First Conquered Infinity in 1961

The Summer That Changed Pi Computation History

Summer, 1961. Two mathematicians — Daniel Shanks and John Wrench — launch a calculation that will go down in history. On a massive IBM 7090 computer, occupying half a room and humming like a jet engine, they become the first people in the world to compute 100,000 digits of pi.

8 hours and 43 minutes. That is how long the calculation took. The previous record stood at 10,000 digits, set just three years earlier. Few believed a computer could correctly produce so many digits. But it could.

The Formula Behind 100,000 Digits of Pi

They used Machin’s formula:

π/4 = 6 arctan(1/8) + 2 arctan(1/57) + arctan(1/239)

and ran two independent versions of the computation as a cross-check — to confirm the result was no accident.

The output was a stack of 20 pages, each printed with 5,000 digits. Shanks and Wrench donated that printout to the Smithsonian Institution. Today, it can be seen in the museum.

Why This Milestone in Pi Digits Computation Matters

This was the first time a machine surpassed human limits — not merely in speed, but in accuracy over a genuinely large scale. The record has since been broken many times over; today, more than 100 trillion digits of pi have been computed. But the 100,000-digit mark became a psychological watershed: the beginning of a grand story that we are still living through, and one that continues to unfold.