Secrets of Mental Math
by Arthur Benjamin & Michael Shermer
A practical bag of arithmetic tricks — worth it only if you actually drill them.
- Status
- Read · October 2022
- Bought
- October 19, 2022
- For
- Engineers who want sharper mental arithmetic · People who do estimation or back-of-envelope math often · Anyone who enjoys recreational number tricks
The one-paragraph verdict
Benjamin’s core insight is simple and correct: compute left-to-right instead of the right-to-left way you were taught, so you can speak the answer as you go. The techniques for squaring, multiplying, and estimating are clean and genuinely fast once they’re in muscle memory. The catch — and most reviews land on this — is that the book reads more like a workbook than a book. The chapters get repetitive, and none of it sticks without deliberate drilling, which the breezy “mathemagician” framing slightly undersells. Shermer’s contribution is light; this is Benjamin’s show.
Who should read it
If you do estimation, capacity math, or back-of-envelope sizing often, the squaring and left-to-right multiplication tricks are worth the practice. It also suits anyone who just likes number play. Skip it if you want a deep number-theory read — this is mechanics, not theory — or if you won’t commit to the practice problems, because passive reading buys you almost nothing here.
Where it earned its place
It gave me one durable habit: estimate first, left to right, and trust the leading digits. That reflex is useful far beyond arithmetic — it’s the same instinct as sanity-checking a query plan or a latency number before believing it. I don’t pull off the party-trick squarings, but the estimation muscle stuck.
Skip it if…
You’re after mathematical depth rather than calculation speed, or you know yourself well enough to admit the practice problems will go untouched. Without the reps, it’s a fun afternoon and nothing more.
[Secrets of Mental Math on Goodreads]