My view of standard mathematical operations (+ - * /) is that they are spatially unidimensional in the sense that every mathematical calculation can be expressed in a single line (using proper parenthesis). Or more precisely, an operator always takes two elements, one at its "left" and one at its "right".
For example,
$$\dfrac{\dfrac{3}{5}+19}{x+1} - 9$$
is equivalent to
$$(3/5+19)/(x+1)-9$$
where each operator has a component at each side, all in a uni-dimensional space (i.e. a line).
Is there a mathematical field where operators are "non-unidimensional"?
For example, a 2D operator could take one element at each side, and also one element above:
$$ 5 \overset{7}{\lozenge} 8 = 21 $$
Which could be combined so that:
$$ 5 \overset{ 1 \overset{8}{\lozenge} 5 }{\lozenge} 8 = 96 $$
This operator cannot be reduced to a 1 dimension (unless you re-specify it as a function on 1D operators).
A 3D operator could take elements at each side, above, and in front (cannot shown here).