William Shanks and 707 Digits of Pi: The Greatest Manual Calculation in History

With May Day still fresh in mind, let’s take a moment to appreciate a different kind of labor — the mathematical kind.

The Man Behind the Most Ambitious Pi Calculation in History

William Shanks, an English amateur mathematician, devoted a significant portion of his life to computing the digits of π — entirely by hand, without any calculators.

Shanks relied on strict discipline: every morning he would calculate new digits, and every afternoon he would spend checking his work.

For his calculations, he used John Machin’s formula:

π/4 = 4·arctan(1/5) − arctan(1/239)

From 530 to 707 Digits: A Twenty-Year Journey Through Pi Calculation History

He began his calculations in 1850. Just three years later, he published his first major result — 530 decimal places. Later that same year, he extended the computation to 607 digits.

Then, after two more decades of painstaking work, in 1873, he published his crowning achievement: 707 digits of π.

The Error Hidden in Plain Sight

But there’s a twist.

Seventy-one years later, an error was discovered at the 528th decimal place — traced back to his 1853 work — which meant all 180 subsequent digits were incorrect.

Still, the 527 correct digits he calculated by hand remain forever the record for manual computation of π.

Pi Calculation Today: From Human Limits to 314 Trillion Digits

With the advent of computers, calculating 527 digits of π takes a child just a few seconds. Today, π has been computed to 314 trillion decimal places.

But Shanks’ work will always stand as a pinnacle of human effort — he at least tried to compute something that has no end.

A Saturday Puzzle

And since today is Saturday, here’s a small problem to think about.

Given that the sum 1/1² + 1/2² + 1/3² + … equals π²/6, what does this sum equal:
1/1² + 1/3² + 1/5² + 1/7² + 1/9² + …?

Answer: π²/8