ABSTRACT
Connections with physics go back to Dixon-Ginsparg-Harvey in 1988, in a paper titled “Beauty and the beast: Superconformal symmetry in a Monster module”. Simple groups have an importance for group theory approximating what primes have for number theory. One of the greatest accomplishments of twentieth century math is surely the classification of the finite simple groups. Number theory is infatuated with modular stuff because it is exceedingly rich, with lots of connections to other areas of math and math phys; it is a battleground on which many innocent-looking but hard-to-crack problems can be slain; and last generation’s number theorists also worked on modular stuff. A confusion sometimes arises between the terms ‘generators’ and ‘basis’. Both generators and basis vectors build up the whole algebra; the difference lies in which operations people are permitted to use.
