Algebraic Number Theory and Rings - Math History II

Explore the historical development of algebraic number theory and rings in this 27-minute math history lecture. Delve into the 19th-century shift towards studying extension fields of rational numbers as new domains for arithmetic. Examine key concepts such as abstract rings, algebraic integers in number fields, and Gaussian integers. Learn about the challenges of unique factorization in algebraic number rings and how Kummer and Dedekind addressed them with the introduction of ideals. Consider the foundational issues in current formulations of this field and the potential need for new algebraic techniques to create a more solid framework. Gain insights into this fascinating area of number theory and its historical evolution.