The Trachtenberg Speed System

Who was Trachtenberg?

  • Professor Jakow Trachtenberg was the founder of the Mathematical Institute in Zurich, Switzerland.
  • He was a Russian, born June 17th, 1888 and studied engineering.
  • While still in his early twenties, he became Chief Engineer with 11,000 men under his supervision.
  • After the Czar of Russia was overthrown, he escaped to Germany where he became very critical of Hitler. He was later imprisoned.
  • Most fellow prisoners around him gave up hope and died even before being sent to their death. He realized that if he wanted to stay alive, he had to occupy his mind with something else rather than focus on the hopeless conditions surrounding them. He set his mind on developing methods to perform speed mathematics.
  • With the help of his wife, he escaped from prison and fled to Switzerland.
  • There, he taught his speed math system to young children. It was very successful.

Trachtenberg developed a set of rules (algorithms) to multiply long numbers by numbers from 0 to 12. These rules allow one to dispense with memorizing multiplication tables, if that is desired.
Even better, it gives a way to help memorize them, by allowing one to
work out the answer by rule if one cannot remember it by rote. We
perform each rule starting at the far right. The `number’ is the digit
of the multiplicand just above the place that we are currently
computing. The `neighbour’ is the digit immediately to the right of the
`number’. When there is no neighbour, we assume it is zero. We also
write a zero in front of the multiplicand.

Note that the following rules only use the operations of addition, subtraction, doubling, and `halving’.


Download the file trach.pdf for some examples. Also see the book: Trachtenberg, Jakow (1960). The Trachtenberg Speed System of Basic Mathematics. Doubleday and Company, Inc.
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