I recently had a flurry of correspondence with translators of The Maths Behind (available wherever etc., but also soon in Swedish and Korean): embarrassingly, they had caught several mistakes in the book. These things happen; we try to put them right and move on.

However, it got me wondering: can I use the translators’ corrections to get a sense of how many errors there are in the whole book?

Of course I can, or else I wouldn’t be writing about it!

Let’s suppose there are $n$ errors in the book, and that the translators each have a fixed probability of finding each error. We’ll call Mr. Svensson of Sweden’s - probability $p_s$, and Ms. Kim of Korea’s probability $p_k$.

Mr Svensson found 8 errors, and Ms Kim found 15; only two were common to both.

We then have (assuming independence):

  • $n p_s = 8$
  • $n p_k = 15$
  • $n p_s p_k = 2$

Eliminating $n p_s$ from the first and third equations gives $p_k = \frac{1}{4}$; similarly, $p_s = \frac{2}{15}$ and $n$, horrifyingly, is 60. (I’ve found at least a couple of others, but suppose there must be another 40-odd lying around).

Of course, there’s scope for improving the model - perhaps modelling the number of errors found by each as some kind of distribution to find reasonable ranges for $n$, perhaps giving the whole thing to Sam Hartburn to read and find all of them.

If you have better ideas (or if you’ve spotted a misprint!), I’d love to hear about it in the comments below.