- why quantum mechanics was developed in the first place,
- the key empiric puzzle of quantum things that act as particles under certain conditions and as waves under other conditions,
- the way quantum mechanics tries to solve this puzzle (the weakest part of the lecture),
- the fact that the mathematical model is compatible with significantly different philosophical (ontological) interpretations, and
- why the standard proposed solution leads to the “paradox of measurement” (i.e. the results of measurements turn out to be non-deterministic, although both the behavior of the measured stuff and the inner functioning of the measuring devices are supposed to be governed by entirely deterministic processes).
Excerpt from Fashion, Faith and Fantasy in the New Physics of the Universe, Lecture 3: FANTASY @ Princeton University (2003)
The only thing you won’t properly get from it is the explanation about the mathematical part. That’s explained much better by Feynman here.