The difference between an amateur and a professional is that as an amateur one is at liberty to study only those things one likes, but as a professional, you must also study what one does not like. Consequently there are parts of a mathematical education that will seem laborious to a student just as all those hours of winter running in the cold and rain will be unattractive, but essential to the aspiring Olympic athlete. If students asked why they needed to learn some of the more intricate and unexciting parts of calculus, I used to tell them this story, one that the Russian physicist George Gamow tells us in his quirky autobiography, My world line. It is about the remarkable experience of one of Gamow’s friends, a young physicist from Vladivostok called Igor Tamm, who went on to share the Nobel prize for physics in 1958 for his part in discovering and understanding what is now known as the “Cerenkov Effect”.
In the Russian revolutionary period, Tamm was a young professor teaching physics at the University of Odessa in the Ukraine. Food was in short supply in the city and so he made a trip to a nearby village, which was under the apparent control of the communists, in an attempt to trade some silver spoons for something more edible like chickens. Suddenly the village was captured by an anti communist bandit leader and his militia, armed with rifles and explosives. The bandits were suspicious of Tamm, who was dressed in city clothes, and took him to their leader, who demanded to know who he was and what he did. Tamm tried to explain that he was merely a university professor looking for food.
“what kind of professor ?” the bandit leader asked.
“I teach mathematics” Tamm replied.
“Mathematics ?” said the bandit. “All right! Then give me an estimate of the error one makes by cutting off Maclaurin’s series at the 9th term. Do this and you will go free. If you fail, and you will be shot!”
Tamm was not a little astonished. At gunpoint, somewhat nervously, he managed to work out the answer to the problem : a tricky piece of mathematics that students are taught in their first course of calculus in a university degree course of mathematics. He showed it to the bandit leader, who perused it and declared “Correct ! Go home !”.
Tamm never discovered who that strange bandit leader was. He probably ended up in charge of university quality assurance somewhere.