Algebras as a means of understanding mathematics. A joint AMS-MAA lecture presented in Columbus, OH, USA, August 1990. Videotape (NTSC; 60 min VHS). (English) Zbl 0925.00031

AMS-MAA Joint Lecture Series. Providence, RI: American Mathematical Society (AMS). Video (1991).
Publisher’s description: What is the real nature of algebra? How does algebra help us to gain insight into other areas of mathematics? The author probes these and other questions in this insightful videotaped lecture. With almost sixty years of distinguished mathematical research to his credit, Mac Lane has a commanding perspective on algebra and how it connects to other branches of mathematics. Algebra is, on the one hand, a field of research which today is split into many different subfields. On the other hand, algebra is an instrument for the deeper understanding of the meaning of various mathematical results. As an example, Mac Lane discusses the concept of automorphism, which, in the hands of Noether and Artin, furthered the understanding of Galois theory. In another instance, he illustrates how homology groups clarify connectivity in topology. In a lecture that ranges from categories to braids, from tensor products to spectral sequences, Mac Lane shows how algebra forms a common thread uniting them all. The lecture would be accessible to those at the level of an advanced undergraduate.


00A35 Methodology of mathematics
00A05 Mathematics in general