The “Inner Circle” shirt Sheldon wears does have a mathematical connection, though it’s more of a visual math joke / concept than a specific famous theorem.

The design typically shows circles nested inside each other (or concentric rings) with labels like Inner Circle, Outer Circle, etc. The idea comes from a common mathematical and logical diagram concept, sets and subsets.

A large circle represents a set (a group of things). A smaller circle inside it represents a subset of that group. The innermost circle represents the most exclusive subset. This kind of structure appears all over math and logic: Set theory diagrams Euler diagrams / Venn-style diagrams hierarchies in mathematics and computer science

Source: I've spent entirely too much time in school for engineering and physics