William Shanks

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William Shanks (January 25, 1812 -- 1882 in Houghton-le-Spring, Durham, England) was a British amateur mathematician.

Shanks is famous for his calculation of π to 707 places, accomplished in the year 1873, which, however, was only correct up to the first 527 places. This error was highlighted in 1944 by Ferguson (using a mechanical desk calculator).

Shanks earned his living by owning a boarding school at Houghton-le-Spring, which left him enough time to spend on his hobby of calculating mathematical constants. His routine was as follows: he would calculate new digits all morning; and then he would spend all afternoon checking his morning's work. To calculate π, Shanks used Machin's formula:

$\frac{\pi}{4} = 4 \arctan \left(\frac{1}{5} \right) - \arctan \left(\frac{1}{239} \right)$

Shank's approximation was the longest expansion of π until the advent of the electronic digital computer about one century later.

Shanks also calculated e and the Euler-Mascheroni constant γ to many decimal places. He published a table of primes up to 60 000 and found the natural logarithms of 2, 3, 5 and 10 to 137 places.