The Curta was a mechanical calculator small enough to hold in one hand, nicknamed the pepper grinder and the math grenade. Its inventor, Curt Herzstark, grew up in his family’s calculating machine business in 1930s Vienna and set out to shrink a desktop machine to pocket size. His answer was to replace the usual row of ten stepped drums with a single central drum ringed by input sliders, and to handle subtraction by adding a nine’s complement. He secured a key patent in 1938, the year Nazi Germany annexed Austria.

This episode follows what happened next. The family factory was forced to make gauges for the German military, and in 1943 Herzstark, the son of a Catholic mother and a Jewish father, was arrested and sent to Buchenwald. There a camp official offered him a desk and drafting tools: finish the calculator as a victory gift for Hitler and he might live. He redrew the whole machine from memory. After liberation in April 1945 he built prototypes, fled the Soviet zone, and fought his own investors to bring the Curta to market.

• Lifting the crank a fraction of an inch engaged a second set of complement teeth, so the drum subtracted while still turning in the same direction.
• By November 1945 machinists near Weimar had built three working prototypes from the drawings Herzstark made in the camp.
• Backers in Liechtenstein diluted his stock to nearly nothing, but they had left the patents in his name to avoid liability, which forced them to pay him.
• About 140,000 Curtas were made between 1948 and 1972, and rally navigators and pilots kept using them because vibration could not break them.
• Only about 3 percent came back for warranty repair, though many arrived in pieces after curious owners took them apart and could not rebuild them.