From the memoirs of L.I. Vernsky, grandson of Igor Tamm, published in Воспоминания о И.Е.Тамме (3е изд., ИЗДАТ, Москва, 1995), pp. 108-109, translation by Google and me. (An alternative, more dramatic but in my view less reliable version of the story was told by G. Gamow in his book My World Line, Viking Press, 1970.)
In the summer of 1920 Igor Tamm decided to leave Crimea, then occupied by Wrangels’s troops, for Elisavetgrad, which was already liberated by units of the the Red 14th and 1st Cavalry Armies. He deliberately left his documents behind, as they were not suitable for leaving the territory occupied by the Whites, nor for crossing to the Reds. He crossed the front line without any problem; in any case, there wasn’t a solid front line. He and an accidental companion decided to spend a night in an empty building on an abandoned homestead. The two were soon detained by a Red Army detachment. Neither of them had any documents with them. To the people who arrested them, it appeared obvious that they were White scouts, deserved to be shot.
Luckily for Tamm, the commander of the detachment was a drop-out student. He grinned grimly while listening to Tamm’s explanation that he had graduated from the Physics and Mathematics Department of the Moscow University.
“So, you’re a mathematician? You’re lying, aren’t you? No problem, we will give you a test now. Here! Derive for me the formula for the expansion of a function in Taylor series. Including the remainder term! If you can do it, you will be freed. If not – you and your friend will face the firing squad.”
Tamm was given a pencil, a piece of paper and a candle. The soldiers brought an armful of fresh hay and locked Tamm and his companion in.
[Igor Tamm said] “My companion calmed down and quickly started to snore… And I was not up to sleep: outside the door was a sentry, and the deadline was the next morning.”
Tamm was nervous: not only his own life was on the table, but also the life of his innocent comrade.
“I was worried, and thus I did not manage to solve the problem. I did get the general idea but I made a mistake somewhere and got myself confused. The morning came and I still couldn’t find the damned mistake!”
In the morning, though no derivation was presented, the commander became convinced that the man knew mathematics. Tamm asked the commander to help him find his mistake.
“You know,” said the commander, “I can’t expand functions anymore… I’ve forgotten everything. I left my university more than two years ago. I was just being strict with you yesterday.”