Jakow Trachtenberg

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Jakow Trachtenberg (17 June 1888 – 1953) was a Russian mathematician who developed the mental calculation techniques called the Trachtenberg system. He was born in Odessa, in the Russian Empire (today Ukraine). He graduated with highest honors from the Mining Engineering Institute in St. Petersburg and later worked as an engineer in the Obukhov arms factory. While still in his early twenties, he became Chief Engineer with 11,000 men under his supervision. The Tsarist government gave him the responsibility of supervising the formation of a well-developed navy.

After the Russian Revolutions of 1917, Trachtenberg fled to Germany where he became critical of Nazi policies. He was imprisoned in a Nazi concentration camp during World War II. He developed his system of mental arithmetic during his imprisonment. He later fled to Switzerland.

Early life[edit]

Trachtenberg was a dedicated pacifist. When war broke out in 1914 he was instrumental in organising a society known as the Society of Good Samaritans. The idea was to train Russian students to take care of the wounded. This also had a special recognition from the Czar. He was against violence of any sort, despite having a leading position in Tsarist arms production. He refused to accept defeat even under trying conditions.

Life in Germany and World War II[edit]

His successful professional life ended with the Russian Revolutions of 1917. In 1918, when the Bolshevik government was in power, the ex-Tsar (who had been deposed in the February Revolution) and some of his family were executed. Trachtenberg was very critical of the new government, and felt that he was in danger.

Disguising himself he escaped to Berlin which became his new home. He worked as an editor for a magazine publishing company advocating a peaceful future. He was regarded as an expert on Russian affairs and wrote a book on Russian industry. When fascism came to power under Hitler, Trachtenberg criticized the Nazis from a pacifist perspective. Fearing that the regime was after him he escaped with his wife to Vienna in Austria. There he worked for a scientific magazine.

After the Anschluss, Trachtenberg was captured and sent to prison. From there he escaped and fled with his wife to what became Yugoslavia where he lived incognito. This was only short-lived as the Nazis caught him and transported him to a concentration camp.

He diverted his attention to think on manipulation of numbers to forget the ruthlessness he witnessed in the concentration camp. Without any paper or pencil he worked mentally and only scribbled the final results on any bit of paper he could lay hands on.

In 1944, after almost seven years in prison, when he learned that he was to be executed, his wife bribed the guards and got him transferred to another prison from where he escaped and fled with his wife. Again he was caught and sent to another prison from where he escaped to Switzerland with the help of his wife who pawned her jewelry to bribe the guards.

Life after the war[edit]

In Switzerland he started teaching his mental manipulation of numbers, and won some renown. He was especially successful with children who had problems with ordinary mathematical teaching.[citation needed]


  • Jakow Trachtenberg, adapted by Ann Cutler and Rudolph McShane (1965). The Speed System of Basic Mathematics. London: Pan Books Ltd.