At that time (1935) modern algebra had already come to life (through the work of Emmy Noether and the important treatise of B L van der Waerden), but while it was being applied to some aspects of the foundations of algebraic geometry by van der Waerden... the deeper aspects of birational algebraic geometry... were largely, or even entirely, virgin territory as far as algebraic exploration was concerned.
Sa panahon na (1935) makabagong algebra nagkaroon na dumating sa buhay (sa pamamagitan ng gawain ng Emmy Noether at ang mahalaga treatise ng BL van der Waerden), Ngunit habang ito ay inilalapat sa ilang aspeto ng mga komunidad ng mga algebraic geometry sa pamamagitan ng van der Waerden... ang mga mas malalalim na aspeto ng birational algebraic geometry... ay higit sa lahat, o kahit na buo, birhen teritoryo makaabot algebraic pagsaliksik ay nag-aalala.