An Old Story
There is something to be said for good stories. This is an old story, told to me years ago by my high-school physics teacher, Farhad Riahi. I don't remember it well enough to do it the justice that it deserves. However, it also shouldn't be lost to time, and I don't know anyone else who would tell it. So here it is.
Farhad Riahi was in no small part responsible for my own love of science. He taught everything from introductory mechanics to special relativity in his small, the first-floor classroom on the corner of Commonwealth Ave and Dartmouth St. It was a small room with while walls and wooden floors. The heat didn't work so we'd take exams wear hats and jackets in the winter. He was a master of weaving stories of the people, places, and history of sciences as part of his lectures. This is the story of his qualifying examples.
Mr. Riahi was born in Iran, and got his PhD in physics under the Nobel Laureate Wolfgang Pauli at ETH Zurich. Qualifying exams are part of pretty much every PhD program, the style and kind varies from program to program but the intent is the same; to determine if the PhD student has the skills and qualifications to complete a PhD and should be granted candidancy, allowing further study. These exams are generally early on in the pursuit of the degree and are generally meant to demonstrate both breadth and depth of the student's knowledge and understanding of their field of study. At ETH Zurich in Farhad's time ther students would study relentlessly leading up to the exam where they would be asked questions orally in front of a panel of professors to assess their understanding of physics. Anything in the field of physics at the time was fair game. These exams were stressful to say the least.
When it came time for Farhad to take his exams, he was waiting outside the room in the library as the professors grilled the previous student. By this point there was no point in more studying. To keep his mind off his impending questioning, he started looking at books on the shelf across from him, picking one at random and leafing through it. It was a book that discussed various interesting problems of integration that arose in physics. Including one particular problem that, at first glance appeared entirely unintegrable. However, the book described how, through a clever change of coordinates then successive changes of variables, it could be quickly solved. Ultimately, it was an impossible problem made easy through clever thought. I wish I remembered the problem, but do not.
After some time Farhad was called into the exam room. One the professors on the panel asked him to start writing an quation on the board. And low and behold, it was the same integration problem from the book! Now, the professors expected students to stuggle with the problem. Farhad new he just couldn't write the answer from the book on the board because then he would simply be asked another question. So appreciating the need for some acting, Farhad put on a show. He looked stumped. He thought out-loud, "what about a change of variables?...no, that wouldn't work....but what if we change coordiantes first? Yes! Then if we change coordinates it works out!".
Farhad ultimately passed his exams, successfully answering the rest of his questions. But he always said he was incredibly greatful for the confidence boost and setting a good first impression by knocking the first question out of the park. This story always reminds me there can be serindipity when we need it most, but helping it along with some good showmanship never hurts.