Майлс Рид/Кийт Конрад о теориях и примерах
When general theory proves the existence of some construction, then doing it [explicitly] is a useful exercise that helps one to keep a grip on reality, [but] this should not however be allowed to obscure the fact that the theory is really designed to handle the complicated cases, when explicit computations will often not tell us anything.
http://mathoverflow.net/questions/62083/examples-of-using-class-field-theory
http://mathoverflow.net/questions/62083/examples-of-using-class-field-theory