The Monster

Watch the video about group theory and a monster.

https://www.youtube.com/watch?v=mH0oCDa74tE

Answer the following questions.

1. Why is the size of a group in and of itself not interesting?
2. Why are groups “useful”?
3. Why is the number 3 mentioned in the video? How does it help us understand what groups are?
4. What is a multiplication table for groups?
5. Why is it desirable to have an abstract definition of a group?
6. According to the video, what is “one of the most monumental achievements in the history of math”?
7. What are the “happy family” and “pariahs”?
8. Why did the presenter choose this number?