"Class field theory can be divided into two parts, local and global. In each part it is the study of all the abelian extensions of a certain base field. The underlying philosophy is to describe all abelian extensions in terms of objects residing within, or close to, the base field."
Onorato Timothy O'Meara was an American mathematician known for his work in number theory, linear groups and quadratic forms. He was provost emeritus and professor emeritus of mathematics at the University of Notre Dame.
"The spinor genus is due to Eichler. His early results (1952) established the theory over the rational field and also, in certain special cases, over a number field. Kneser (1956) extended this to number fields in general. At about the same time Watson obtained Eichlers results by elementary methods over the rational field."
"It was not until my second year as a doctoral student that I began to understand that mathematics was an ever-expanding universe. My thesis advisor at Princeton was Emil Artin, one of the great algebraists of the century. Unfortunately, or perhaps fortunately, he offered me no advice in the selection of a thesis topic. I think it was a fluke that I got started at all. But once I did, a whole new world opened up, to which I would devote a vast amount of time and energy for over thirty years."