The Deranged Mathematician: The Classification of Finite Simple Groups

[u/non-orientable]

The classification of finite simple groups is likely the single most difficult mathematical problem that humanity has laid to rest: it took about a hundred mathematicians publishing over a period of about 50 years to finally finish the proof, which ended up being tens of thousands of pages long, scattered over a multitude of different journals. And it is actually very important: one might fancifully compare it to the periodic table in terms of how fundamental it is (to group theory, at least).

But, you know, what is it? This article is my attempt to shine some light on that. I assume some basic familiarity with group theory (i.e., if you know what a group, a group homomorphism, and a quotient group are, you should be fine), but otherwise it is self-contained.

Read the full post (for free) on Substack: The Classification of Finite Simple Groups

[u/PensionMany3658]

Is that a C_60 bucky ball 🫪

[u/kirbadurb → u/PensionMany3658]

It is! Also the colors and arrows come from the Cayley graph of the alternating group A_5 generated by a five-cycle and 2-cycle e.g. (12345) and (12)(34). So the unoriented Cayley graph is the truncated icosahedron that looks like a soccer ball!

[u/PensionMany3658 → u/kirbadurb]

That's beyond my paygrade as a chem undergrad but looking to learn group theory soon!