Product Thinking (5): Abstraction Thinking — From Math to Systems

Wed, 03 Jun 2026 09:00:00 +0000

The Instinct You Cannot Unlearn#

There is a moment in every abstract algebra course where the professor writes something like this on the board:

Let $\phi: G \to H$ be a group homomorphism. Then $\ker(\phi) \trianglelefteq G$ , and $G/\ker(\phi) \cong \text{im}(\phi)$ .

The first isomorphism theorem. When I first saw it, I thought it was a curiosity — a proof exercise to survive, then forget. I was wrong. That theorem planted something in my brain that never left: the instinct that every structure has a quotient, that what you throw away defines what you keep, and that two things that look nothing alike can be the same thing in disguise if you find the right map between them.

Abstraction on Chen Kai Blog

Product Thinking (5): Abstraction Thinking — From Math to Systems

The Instinct You Cannot Unlearn#