What don't you buy about them being the fourth fundamental circuit type?

Its mathematically provable, proven in the 60's actually. Here watch this for a decent introduction. https://www.youtube.com/watch?v=bKGhvKyjgLY

Well I can see resistors, capacitors and inductors as fundamental but when you beyond that I'm not convinced that a resistor with hysteresis is particularly more fundamental than an inductor with hysteresis (as in core memory) or a capacitor with hysteresis (not sure they've invented that yet) or a diode for that matter. The "we've discovered the forth fundamental component" stuff seems a little like hype to me. Not to knock its potential value for building computers.

I tend to agree with a comment elsewhere: if memristance is a fourth "fundamental" element of any importance, it would have had to be well-understood (and compensated for) as a parasitic property of other components. It's not, unless you count purely thermal effects.