[banskiachtar]

A saddle is a critical point that's not a local extremum--the Hessian could just be zero, for example, like x^4-y^4 at (0,0).

[mjw]

Ah yep, true. I'd forgotten you can still get the saddle effect from higher-order derivatives, the Hessian eigenvalues aren't enough to characterise it.

I was thinking of examples like (x-y)^2 at zero, although I guess that's still a local minimum, just not a unique local minimum in any neighbourhood.