There are in fact quite a few mathematical definitions for simple. In addition to what Noether writes,

- a smooth curve curve is said to be simple iff it does not intersect itself at any point (well, possibly the endpoint if it is also closed).
- a representation is simple, or irreducible, iff it has no proper non-trivial invariant subspaces.
- a path connected topological space is said to be simply connected iff its fundamental group is trivial.
- a tensor is simple if it can be expressed as a product of vectors, eg
**A**=**aa**^{T}, Q^{ab}_{c}^{d}=p^{a}q^{b}r_{c}p^{d}