Product Thinking on Chen Kai Blog

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.

Product Thinking (4): Self-Healing Systems — Teaching Machines to Fix Themselves

Tue, 02 Jun 2026 09:00:00 +0000

The Bug That Fixed Itself#

One morning in late May 2026, I woke up to a DingTalk notification from my research agent system:

“self_heal Rule 37 triggered: restarted research-pipeline after 3 consecutive OOM kills. Root cause: scanner thread retained full PDF buffers across iterations. Applied patch: explicit del after extraction. Validation: 45 minutes post-patch, RSS stable at 1.2 GB (was 2.4 GB pre-patch).”

Product Thinking (3): UX & Design Systems — Tokens, Dark Mode, and Bilingual

Mon, 01 Jun 2026 09:00:00 +0000

The Problem With “Just Make It Look Good”#

Every engineer who has ever touched CSS knows the feeling: you open a stylesheet written six months ago and find forty-seven shades of grey, twelve font sizes that follow no discernible scale, and a dark mode implementation consisting of filter: invert(1) on the body element. The code works. The site renders. But every new feature requires archaeology — digging through layers of ad-hoc decisions to figure out what the “right” shade of muted text is supposed to be.

Product Thinking (2): Security Engineering — Defense Without Paranoia

Sun, 31 May 2026 09:00:00 +0000

The Kind of Security That Disappears#

I used to think security was something you bolted on: a checklist before release, a penetration test once a quarter, a code review with “security” in the title. I was wrong. The systems I have built over the past two years taught me a different lesson — the best security is the kind you forget about because it is already woven into the system itself.

Product Thinking (1): Architecture Design — From Monolith to Autonomous Agents

Sat, 30 May 2026 09:00:00 +0000

The Shape of a System#

Every architecture is a frozen argument. It records what you believed about the problem at the time you committed the code. Looking back across four systems I built over eighteen months — a marketing content platform (~70k lines TypeScript), a zero-dependency skill routing engine, an autonomous research agent (~315k lines Python), and a multi-model coding orchestrator — I can trace how my architectural instincts shifted. Not always forward. Sometimes sideways. But there is a clear progression: from “keep it in one process” to “let the agents govern themselves.”