Zacharias Dase

Cast of 15-year old Dase's head

Full name: Johann Martin Zacharias Dase (Dahse)

Born 23rd June 1824 in Hamburg, Germany. Died 11th September 1861.

Excelled at written arithmetic from an early age, devouring "every book in Hamburg" on the subject. His mental arithmetic developed later and proceeded as it would if written down.

Started giving public demonstrations of his calculating ability at the age of 15. During these he would write on a blackboard the problem proposed by a spectator and then write a provisional solution beneath it. After checking his answer, he would announce it as fact. He was not disturbed by noise and could even hold conversation with spectators while calculating.

Attributed his calculating ability to an early preoccupation with dominoes.

Possessed very vivid mental imagery and excellent spatial awareness.

Claimed to be never fatigued by calculating, which he could continue all day long.

Had epilepsy, suffering attacks since early childhood.

At the age of 16 computed the first 205 digits of pi using the formula pi/4 = tan-1 1/2 + tan-1 1/5 +tan-1 1/8, taking two months.

Calculated the natural logarithms of the first million integers to seven places, a task of three years.

Appears several times in the correspondence between German mathematicians Heinrich Christian Schumacher and Carl Friedrich Gauss, the latter seemingly unimpressed by Dase's feats. Gauss did, however, recommend Dase to a publisher of mathematical tables and Dase set about extending the published tables of factors of numbers up to ten million and, by the time of his death, had completed a substantial part of it.

Calculations performed by Zacharias Dase

354783293 x 5423957 = 1924329325550401 in 1.5 minutes

684028396281753 / 6541325 = 104570312 138353/6541325 in 2.5 minutes

423339075240048565 / 708346795 = 597643807 in 5 minutes

19th root of 7093585369945932256195429028464404423 = 87 in 3 minutes

Extracted the 52nd root from a 97-digit number. This appears to have been misreported in some texts as the much more impressive feat of extracting the square root from a 100-digit number in 52 minutes.

Could count at a glance the number of spots on 10-20 dominoes laid out in a line. Similarly he could scan a bookshelf and give the number of books it held.

Perhaps Dase's best known feats of mental calculation were his multiplications of huge numbers. He could multiply a pair of 12-digit numbers in a little over 2 minutes, a pair of 20-digit numbers in 6-8 minutes and a pair of 60-digit numbers in 3 hours. He once multiplied a pair of 100-digit numbers in 8 3/4 hours. Dase speculated that he could multiply a pair of 300-digit numbers, but that it might take 100 hours.

References/Links

1.  The Anthropological Review 1863, Vol. 1, No. 3, p492

2.  The Phrenological Journal and Magazine of Moral Science 1841, Vol. XIV, No. 67, p153