Johann Jakob Winkler

Johann Jakob Winkler (born February 23, 1831 in Wermatswil ; † August 25, 1893 in Stans ) was a Swiss arithmetic artist .

He was the second of ten children of Ulrich Winkler and Elizabeth Enderlig. His grandfather came from Zell ZH and became a citizen of Uster in 1829 . He married Amalie Karoline Forstinger from Karlsruhe. The couple had no children.

Zell earned his living doing mental arithmetic . He had an excellent memory for numbers, did not take notes or read anything during demonstrations, as he was very short-sighted. As a rule, he had tasks read aloud to him twice, and he often had the solution before reading the second time. Like the arithmetic artist Jacques Inaudi , he first calculated an approximate solution and then interpolated. He calculated logarithms to seven places and vice versa the numbers for given logarithms with equal ease. He also solved physical problems.

He visited England and then went to Paris, where he met Hermann Laurent , who thought he was English and reported about him in the Grande Encyclopédie of Larousse (article " mental arithmetic", Calcul Mental ). He was able to recite 5,000 numbers that were read to him twice after a fortnight. He was given the task of breaking a five-digit number into four squares, and after three minutes he gave different solutions.

Usually he split a number into products:

${\displaystyle x=a\prod _{i}(1+{\frac {p_{i}}{q_{i}}})}$

and then used logarithms that he knew by heart from 1 to 100 and, for most of them, from 100 to 1000 (plus many other logarithms of the numbers 100p, 1000p, etc.). In addition to logarithms, he used memorized interest tables for pension and interest calculations. He also knew and used all common quick calculation rules.

In contrast to other mental calculators of the time, he was educated and understood something of higher mathematics ( analysis ). He was also interested in literature and philosophy. He had a perfectly normal memory for writing (according to his own account, he had normal problems memorizing a story).

He had his methods published by G. von Tobel in Zurich in 1883. In Paris in the 1860s he offered to disclose his method for 100,000 francs. He gave public performances of his art in Switzerland, for example in Solothurn and other cities. Winkler died completely impoverished in the canton hospital in Stans.

Fonts

• Collection of very valuable calculation formulas, tasks and tables, easy to understand for everyone, especially for mental arithmetic. Meyer and Zeller, Zurich 1889 (publisher G. von Tobel).

literature

• Arnold Emch : The mathematician Winkler and his methods. ICM, Rome 1908, digitized version (PDF; 325 kB).