Historical Development of Group Theory - From Number Theory to Geometry

Explore the historical development of group theory in this comprehensive 59-minute lecture. Trace the evolution of this mathematical field from its roots in number theory and algebra to its expansion into geometry during the 19th century. Learn about Euler's work on Fermat's little theorem, Gauss' composition of quadratic forms, and the role of permutations in solving polynomial equations. Examine the symmetric group S_3 and discover how groups of transformations became linked to geometric symmetries through the work of Klein and Lie. Investigate the symmetry groups of Platonic solids as a bridge between algebraic and geometric aspects of group theory. Gain insights into key concepts such as Lagrange's theorem and polyhedral groups, making this lecture accessible even to those new to the subject.

Group theory Introduction
Origins in Algebra - theory of equations
Euler 1758: Theorem
The numbers less than n relatively prime to n
Group properties
Theory of polynomial equations
Permutations - Levi Ben Gershon 1321
Multiplication table of S_3
Lagrange theorem's
Polyhedral groups