There is a very nice lecture by Richard Feynman on Google Video. It has four parts. The lecture is directed towards not necessarily physics audience, which is why I highly recommend it to physics audience.

Richard describes the essence of quantum theory using mathematical concepts in a bit different way than your first year quantum mechanics book does. As a result, one can step away from usual mathematical constructs and still be able to talk about physical phenomena. This puts particular mathematical formalisms back into its proper place, which is being a mere dispensable tool. Way too often we, theoretical physicists, get carried away by "mathematical beauty",  which may have nothing to do with the reality.

Well, as a reminder. Newton needed a proper formal language for mechanics, so, he figured out this thing called calculus. He needed a tool, and he maid one.
In ancient Egypt people needed formal ways to divide land and to figure out taxes, so, geometry originates from Egypt.
Einstein figured that there must be a time dilation in a gravitational field. Adding an already found relation between space and time in Special Relativity, and his ingenious idea of equivalence between accelerated motion and motion in a gravitational field, a need arose for him to have a new formal mathematical tool. Albert was lucky, cause some sort of mathematical tool, which looks appropriate even from the first glance, had already been developed. It is Riemannian Geometry. And within this framework Albert wrote his equation for gravitation. And they work for Mercury, for light bending in gravitational field, etc.
Except for the dark stuff which is required if, and it is a big if, if one believes that Einstein's equation must work on a cosmological scale. But then, Newtonian mechanics does not work on a single electron either. And geometry of Egyptians is not ok on a curved sphere. Math, it seems, must be taken with a grain of salt.

Back to Richard. Please, please, enjoy his lecture.






Somewhere along the lecture, Richard said that after making lots of simple examples involving one particle it is easy to forget that one is dealing with multiple events, period. Particle is a nice concept that a human can visualise and which can even be approximated by a classical mechanics experiment. But an application of these concepts directly to quantum world does not work. It is events that we have in QFT, the simplest and fundamental of which are "creation" and "annihilation" at a point, with everything else being mere combined events and effective objects. And a stellar success of QFT should be suggestive enough to take this point seriously.