I was reading one of the books of Feynman's Lectures on Physics, a chapter about the principle of least action. Unlike most of the chapters, which are based on Feynman's lectures at Caltech but edited into book form, this one is an almost-verbatim transcription of the lecture from that day.

It begins with Feynman describing how he was first introduced to the subject one day after physics class in high school. His teacher, a Mr. Bader, thought he looked bored, so he pulled him aside and told him about the variational principle for mechanics, which is really a cool thing if you get into it. Feynman goes on to describe the motion of particles along their possible paths, and how a perturbation of a particle's path away from the "true" path increases the Lagrangian of the system, and how to derive physical statements from this fact, and so on.

It's a good lecture, focused mainly on mechanics and electromagnetism. Towards the end, Feynman describes how it can be applied to calculate the behavior of quantum particles as well.

He writes:

"... So in the limiting case in which Planck's constant goes to zero, the correct quantum-mechanical laws can be summarized by simply saying 'Forget about all these probability amplitudes. The particle does go on a special path, namely, that one for which S does not vary in the first approximation.' That's the relation between the principle of least action and quantum mechanics. The fact that quantum mechanics can be formulated in this way was discovered in 1942 by a student of that same teacher, Bader, I spoke of at the beginning of this lecture."

That student, of course, was Feynman himself, and the integral-over-paths description of quantum mechanical behavior is the heart of the body of work that Feynman would go on to receive the Nobel Prize for, two years later. He was already a giant in this field. And yet, despite the opportunity in front of a few hundred starry-eyed Caltech freshmen, with no idea that his words would go on to be reprinted for millions of eyes, he describes this great thing he'd done with so much modesty and grace that you might not even know he had anything to do with it.

That's class!

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