Six Variations on the Variational Method

As a graduate student in physics at the University of Michigan many years ago I had the good fortune to take a course in function theory from Norman Steenrod that pretty much changed the course of my life. My experience in that course plus several private conversations convinced me to switch out of physics and into mathematics. I recall one of our sessions particularly, where, in trying to describe what mathematical research was like, Steenrod said that really there were only about a dozen or so ideas in the whole subject, which people just use over and over again, and once you have mastered these you are, so to speak, in business. I wish now I’d had the presence of mind to ask him for his list of the top twelve. In any case, I expect that on anyone’s list, one of the ideas would be the so-called variational method.