noether's advisor, paul gordan, was known as the "king of invariant theory", and his chief contribution to mathematics was his 1870 solution of the finite basis problem for invariants of homogeneous polynomials in two variables. he proved this by giving a constructive method for finding all of the invariants and their generators, but was not able to carry out this constructive approach for invariants in three or more variables. in 1890, david hilbert proved a similar statement for the invariants of homogeneous polynomials in any number of variables. furthermore, his method worked, not only for the special linear group, but also for some of its subgroups such as the special orthogonal group.