Whilst attending a wedding in a country manor in Essex, England an acquaintance of mine from India (a liquidity trader at Citibank by trade) nonchalantly dropped into passing conversation the term Trachtenberg mathematical modelling. A few questions later this intriguing statement was firmly lodged to memory - or more correctly the trusty iPhone notes memory. Upon further investigation it appeared that the Tale of the late Jakow Trachtenberg, founder of the Mathematical institute in Switzerland, is a story worthy of an Oscar winning Hollywood blockbuster. Sprinkled with heroics, despair, tragedy and revolutionary ideas this tale had everything. However ask the average individual on the street and they won’t have a clue as to the previous existence or influential ideas of the late Jakow Trachtenberg.
A Russian, born in Odessa, June 17, 1888, Jakow Trachtenberg excelled in education graduating from the famous Mining engineering institute Berginstitut with the highest honours. In his early twenties he was named Chief Engineer at the World-renowned Obuschoff shipyards on a project overseeing 11,000 men to create a superlative navy. Trachtenberg was a dedicated pacifist though – so much so that during the outbreak of World War I he organised the society of Good Samaritans which trained Russian students to care for the wounded. The murder of the imperial family gave rise to a savagery and lawless communist party who Trachtenberg spoke out against. As a result of the criticism in 1919 the Communist Party attempted to have Trachtenberg murdered. Hearing of this he dressed as a peasant walking at night and hiding out through the day, until he made it to Berlin, Germany.
In Berlin Jakow Trachtenberg married became the editor of Magazine where he received praise for his critical work on Russian industry. He was considered one of Europe’s leaders in Russian affairs. In addition to being a leader in Russian affairs Trachtenberg devised a method for teaching foreign languages which is still used in many German schools today. In addition to his career success Jakow met and married his beautiful wife in Germany – a woman of the aristocracy. However with the rise of Hitler in Germany and Trachtenberg’s outspoken temperament, in 1934 Jakow and his wife fled to Vienna for safety reasons.
The Germans marched on Austria and soon Trachtenberg was arrested and thrown into prison. He managed to escape, taking his wife Countess Alice, to Yugoslavia (Bosnia and Herzegovina as known today). His freedom was brief and the Gestapo had soon caught up with him. He was shipped in a cattle car to a concentration camp. Whilst his body grew weak his mind found solitude in logic and mathematics. Out of the pit of darkness something truly beautiful was born. Manipulating large numbers Trachtenberg devised a set of fool proof formulas which completely simplified arithmetic. The years spent in the concentration camp and all of the atrocities he bore witness to faded out as he escaped into the refinement of these mathematical models. He scribbled these methods onto any form of paper possible be it envelopes or wrapping paper. In 1944 Trachtenberg entrusted all of his secrets to a cellmate after he found out that he was to be executed. Mrs Trachtenberg, who had lived within close proximity of the prison since her husband’s arrest, hearing of her husband’s imminent execution used the last of her money and jewels to bribe officials to transfer Jakow to a different concentration camp just before the sentence was to be carried out.
He was transferred to Leipzig where the facilities were so bad and morale so low that Trachtenberg successfully managed to escape to meet his wife late one night. With no passport or papers he was soon taken back into custody and sent to a labour camp in Trieste. Again Mrs Trachtenberg got to work bribing officials to send messages to her husband and to arrange an escape. After climbing a wire fence and being shot at by guards early 1945 was the most dangerous but last escape. Jakow and his wife made their way across the border into Switzerland where they regained strength.
Jakow Trachtenberg was of the opinion that everyone comes into the world with ‘phenomenal calculation possibilities’. It was in Switzerland that he used his simplified mathematical modelling to teach poorly performing children how to do arithmetic more easily. This model didn’t just improve children’s grades but gave them confidence and changed their lives for the better. In 1950, Trachtenberg founded the Mathematical Institute of Zurich, the only school of its kind. The Trachtenberg system is based on procedures which are radically different from conventional methods. Here are a few to wet your whistle:
Multiplication of 11:
Rules
1. The number on the far right of the multiplicand remains the same
2. Each successive number of the multiplicand is added to its neighbour on the right
3. The first number of the multiplicand remains on the left side
SUM
521 * 11
First rule:
***1
Second Rule:
2 + 1
**31
5 + 2
*731
Third Rule:
5 remains
5731
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