Since the combinatorics related discussion on this thread has waned...
I was wondering what you guys knew about symmetry groups, their relation to
symmetry in general,
supersymmetry, and
M-Theory.
I believe understanding
lie algebra and
gauge theories are an important part of understanding these things.
There is a lot of hefty math in there, and
String Theory appeals to many people who aren't mathematically inclined. So if there is a way to transform the math to some pictures or some other form of intuitive understanding, I think it would go a long way to actually understanding string theory (as opposed to just being aware of it).
Also, I like knowing the "skeletal rigorous framework" for a mathematical ideas. By this I mean, the minimum set of definitions and theorems needed to understand a mathematical idea. But I haven't figured out what it is for M-Theory yet.
Anyone care to collaborate on this thread to create an informal, multi-type friendly, math-flavored exposition?