Humble Pi: When Math Goes Wrong in the Real World

by Matt Parker

Kushim and Nisa are particularly special to me not because they are the first humans whose names have survived but because they made the first ever mathematical mistake, or at least the earliest that has survived (at least, it’s the earliest one I’ve managed to find; let me know if you locate an earlier error). Like a modern trader in Tokyo incorrectly entering numbers into a computer, Kushim entered some cuneiform numbers into a clay tablet incorrectly. From the tablets we can find out a bit about the math that was being used so long ago. For a start, some of the barley records cover an administration period of thirty-seven months, which is three twelve-month years plus one bonus month. This is evidence that the Sumerians could have already been using a twelve-month lunar calendar with a leap month once every three years. In addition, they did not have a fixed number-base system for numbers but rather a counting system using symbols that were five, six, ten, or three times bigger than the next lower in the scale. Once you get through the alien number system, the mistakes are so familiar, they could have been made today. On one tablet, Kushim simply forgets to include three symbols when adding up a total amount of barley. On another one, the symbol for one is used instead of the symbol for ten. I think I’ve made both those mistakes when doing my own bookkeeping. As a species, we are pretty good at math, but we haven’t gotten any better over the last few millennia. I’m sure...