Gonzales Digital Image Processing and the Laplacian Operator In Gonzalez' book Digital Image Processing, third edition, he writes on page 182 that 


  It can be shown that the simplest isotropic derivative operator is the laplacian operator 


where the Laplacian is given by 
$\nabla^2f = {\frac {\partial^2 f }{\partial x^2}} + {\frac {\partial^2 f }{\partial y^2}}$, and the particular paper he links in reference is not available for free.

It is :
Rosenfeld A, Kak A.C. Digital Picture Processing, vols. 1 and 2, 2nd ed., Academic Press, New York.

I was looking for insights to why:

a)The Laplacian is isotropic

b) What he means by "simplest". I am assuming this means in terms of computational complexity of things like how many differentiation operations, additions ops, multiplication ops, etc.

Any help appreciated.
Isotropic operator is an operator that has no bias to any particular direction in the image. 
If you see the below Laplacian mask, Edge detection is taking place in every direction.


If you see the below image, three filter kernels are applied. The first kernel detects edges in x direction, the second in y direction and the third is Laplacian kernel detecting edges in all directions, hence it is isotropic.