Jacow Trachtenberg and mental arithmetic --------------------------------------
Jacow Trachtenberg was born in 1883 in Odessa, in tsarist Russia. He studied engineering in Saint Petersburg. At risk of arrest following the October Revolution, he moved to Berlin and became an engineer at Siemens. A committed pacifist, he criticized the rise of Nazism; as a Jew, he was forced to leave Germany and moved to Vienna, Austria. When the Anschluss took place, he was unable to escape in time and was deported to the Sachsenhausen concentration camp in Oranienburg, Germany. To keep himself from succumbing to despair, he turned to mental arithmetic. He sought to devise methods for multiplying a number by the first few positive integers using only operations on its digits. Everyone knows how to multiply by 10: simply add a zero on the right. Multiplying by 3 or 7, however, is not so straightforward. With his wife's help, he managed to escape in 1944 and settled in Zurich, Switzerland. There he refined his method and tested it on children who struggled with conventional teaching methods. He died in Zurich in 1953.
The Trachtenberg method: an example --------------------------------------