Group theory | Math History | NJ Wildberger

Here we give an introduction to the historical development of group theory, hopefully accessible even to those who have not studied group theory before, showing how in the 19th century the subject evolved from its origins in number theory and algebra to embracing a good part of geometry.

Actually the historical approach is a very fine way of learning about the subject for the first time.

We discuss how group theory enters perhaps first with Euler's work on Fermat's little theorem and his generalization of it, involving arithmetic mod n. We mention Gauss' composition of quadratic forms, and then look at permutations, which played an important role in Lagrange's approach to the problem of solving polynomial equations, and was then taken up by Abel and Galois.

The example of the symmetric group is at the heart of the subject, and so we examine S_3. In the 19th century groups of transformations became to be intimately tied to symmetries of geometries, with the work of Klein and Lie. A nice example that ties together the algebraic and geometric sides of the subject is the symmetry groups of the Platonic solids.

Video Contents:
00:00 Group theory Introduction
01:13 Origins in Algebra - theory of equations
03:55 Euler 1758: Theorem
07:25 The numbers less than n relatively prime to n
09:50 Group properties
16:34 Theory of polynomial equations
23:38 Permutations - Levi Ben Gershon (1321)
32:38 Multiplication table of S_3
41:44 Lagrange theorem's
44:34 Polyhedral groups

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[RenormalizedAdvait]

I wish I had access to this content back in the days of my academic career, I would have devoted my life to pure mathematics. The group theory was a dreaded topic back in my college days, even the professors seems to have mugged up all the theorems and vomited dry, meaningless stuff to students only to help them pass their paper. Terrible. Thank you professor for this timeless content.

[georgesadler]

Professor Wildberger, thank you for the video.

[youngjin]

love your work on the history of mathematics. So I can make a big picture! bless you.

[TheObsidianSnake]

Great lecture! I feel like this video would benefit a lot of people taking mathematics at uni!

[CrocodileMundi]

wooo!! Thanks for posting another math history video, I love this series of yours :)

[Tommy_]

Good lecture.
PS. To the cameraman: "To focus or not to focus that is the question."

[best-phone]

Thank you a lot :) In my country theres any guide in my language which could help me. You and the teacher are great :) Thanks!

[rajender]

Great lecture and is very helpful...Thanks for doing it :)