The Trachtenberg Speed System Of Basic Mathematics translated and adapted by Ann Cutler and Rudolph McShane (book review).

Jakow Trachtenberg was born in Russia and a pacifist who married a German woman, stayed in Germany but with the on-set of war, they fled to Yugoslavia where he was later interned in a concentration camp. A author and engineer, he spent his days there manipulating numbers, understanding their relationships and developing a system of calculating, His wife succeeded in bribing his jailers and eventually they escaped to Switzerland, founded a maths school and eventually the material that became this book, ‘The Trachtenberg Speed System Of Basic Mathematics’. This is its 26th release since 1960, although I have to confess this is the first time I came across it.


Interestingly, as you learn his techniques, Trachtenberg does not deny you a pencil and paper as you learn to manipulate large numbers, pointing out the sums contributing to the final answer as being quite simple. Getting into the swing of things from the beginning gave me a double take but a second reading the next day, I could see what he was getting at which made progress easy. What he also demonstrates is that the technique as applied to numbers you should know, assuming you know your times tables up to 12, and get the same answers. This is actually a reassuring way to know inside your head that it does work. In later chapters, he explains about checksums which enables you to spot potential errors. The word ‘checksum’ might be familiar to you these days from the old dial-up days of downloading where it was used to check that no digital data was lost. Although I never heard the two systems were related, as this predates the computerised version one has to think there is some link.

Again, the vulgarities of deadline has meant I couldn’t get into the habit of trying all his techniques out with the examples provided but I’ve noticed a slight change in how I do arithmetic after a first reading and I spread the reading of this book out over a couple weeks to ensure I absorbed the information.

At the back of the book there is an advanced section dealing with the technique in algebraic terms but I suspect you would have to be getting really comfortable to get to grips with that.

As this book and the one I reviewed last month, ‘Think Like A Maths Genius’ by Arthur Benjamin and Michael Shermer, were released by the same publishing company, I’m not going to hesitate in comparing the two. Each system has its merits but I would be more inclined to go for this book if you have more time to practice and the Benjamin/Shermer book if you want to learn quickly. Don’t mix the two books up and remember, both will work if you practice at the subject. You will either read slowly working your way through all the examples or go back and polish up the method until it becomes second nature.

I do wonder if the people who’ve bought the previous editions have started this book and then left it on the shelf never to be read again, mostly because I’ve never heard people proclaiming themselves to be using the technique. What does become most obvious from both books is the relationships between numbers that can be used to make maths easier. If you want to out-wit people who can only do sums with a calculator than both offer interesting solutions.

GF Willmetts

August 2013

(pub: Souvenir Press. 270 page small enlarged paperback. Price: £ 9.99 (UK). ISBN: 98-0-28562-916-5)

check out website:


Geoff Willmetts has been editor at SFCrowsnest for some 21 plus years now, showing a versatility and knowledge in not only Science Fiction, but also the sciences and arts, all of which has been displayed here through editorials, reviews, articles and stories. With the latter, he has been running a short story series under the title of ‘Psi-Kicks’ If you want to contribute to SFCrowsnest, read the guidelines and show him what you can do. If it isn’t usable, he spends as much time telling you what the problems is as he would with material he accepts. This is largely how he got called an Uncle, as in Dutch Uncle. He’s not actually Dutch but hails from the west country in the UK.

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.