Most of the central results in this area were proved in the period between 1900 and 1950. The theory takes its name from some of the early ideas, conjectures and results such as those on the Hilbert class field, which took a generation to settle up to 1930. The ideal class , is also seen as a Galois group of a field extension a structure built on top of K and possibly involving irrational numbers going beyond square roots.