1089 and All That by David Acheson

Acheson, David. 1089 and All That: A Journey into Mathematics. New York: Oxford University Press, 2002.

1089 and All That starts with a little mathematical magic trick. Take any three-digit number in which the first and last numbers differ by at least two (like 553). Reverse it and subtract the numbers (553-355=198). Take this new number and add it to its reverse (198+891=1089). The answer will be 1098 for any three-digit number you pick.

This little trick attracted David Acheson to math as a boy. In his book, he tries to convey some of the wonder, fascination and surprise of mathematics.

A deep understanding of math isn’t necessary to follow the book. Someone who made through high school algebra can follow most of the math fairly easily. Acheson delves into deep waters (geometry, calculus and differential equations), but he doesn’t pile on the equations or expect readers to solve them. He gives the reader enough explanation to follow the basic logic and grasp the proof. The payoff is the unexpected results.

A wide amount of math is covered in this fairly short book, from those areas already mentioned to chaos theory. Much of it is applied math, dealing with mechanical systems, planetary motion and weather prediction.


Acheson is a practicing mathematician and one of the most interesting parts of the book deals with one of his own developments. He lays the foundation throughout the book and casually leads to a chapter in which he turns things upside-down with his take on the Indian rope trick. This has a big gee-whiz factor and itself makes the book worth reading.

Acheson wraps up by returning to something like the magic trick he uses to open the book. In different chapters he introduces some prominent numbers in math: π, e and i. Though they don’t relate to a trick, but they have a mysterious connection that seems even more fascinating.