&quot;I was good at mental arithmetic and saved myself a lot of money back in the Soviet Union.&quot;<p>This reveals a weakness in western education. People in the former Soviet Union learned a lot of mathematics in the traditional way (a mixture of clever mental calculating skills and a good grounding in theory) simply because they had no alternative and there were many problems to be solved requiring higher math skills.<p>Americans, on the other hand, (as well as being famously lazy about math) now rely almost completely on calculators and computers and are gradually abandoning both mental calculation and deep theory in mathematics. An EMP will someday zap all our electronics and we&#x27;ll get our comeuppance, and we&#x27;ll have to try to remember exactly why the integral of x^2 is x^3&#x2F;3 + constant.<p>As I sailed solo around the world 25 years ago I spent a lot of my free time practicing mental math. One day in Israel I read my receipt at a restaurant and realized the waitress had inflated the cost by performing a creative kind of addition. I corrected her figures, lectured her, and paid the difference as a tip. It occurs to me that she could get away with creative addition with 99% of people, even well-educated people, because nearly no one checks the addition on a receipt.<p>Hans Bethe and Richard P. Feynman were both formidable mental calculators, at a time when that skill was valuable. There are stories about how (when they were both at Los Alamos) they would have contests to see which could produce the quickest result using somewhat different methods. This was at a time when a matrix calculation required a roomful of &quot;calculators&quot; sitting at mechanical adding machines all day long, sometimes for weeks, estimating the yield of a nuclear explosion.