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February 5, 202612 min read

The Flow-State Experiment: Measuring Papercuts in AI Coding Tools

A systematic comparison of Claude Code, Codex CLI, and Gemini CLI measuring the small friction points that disrupt developer flow. Our experiments reveal fundamental differences in how these tools handle mid-task corrections and context.

#ai-coding#claude-code#codex-cli

January 27, 202610 min read

Can You Teach an AI How to Think? Testing Elaborate Reasoning Protocols on Claude Code

We gave Claude Code a 365-line protocol teaching it to think like an ICPC World Finalist. After 300 experiments, the elaborate methodology provided zero improvement over a simple "solve this problem" prompt—but the reasons why reveal something important about agentic AI.

#vibe-coding#Claude-Code#agentic-AI

#nextjs#performance#optimization

Next.js Bundle Analyzer: Optimize Your Build Size

Learn how to use @next/bundle-analyzer to visualize and optimize your Next.js bundle size. Includes real optimization examples and case studies.

March 1, 202614 min read

March 12, 202624 min read

The LLM Collaboration Guide: How to Avoid 20 Critical Bugs in Production

Learn how to turn LLMs from a liability into your most powerful engineering tool. Discover the three-phase workflow, constraint matrix framework, and production readiness checklist that prevents critical bugs in production.

#LLM#AI-Assisted Code#Production

February 5, 202610 min read

The Idiomatic Code Audit: Do AI Tools Write Modern Code?

Testing whether Claude Code, Codex CLI, and Gemini CLI produce modern, idiomatic, and secure code by default. Our experiments reveal a critical gap in library version awareness.

#ai-coding#claude-code#codex-cli

CrewAI Tools: Building Custom Agents & Tool Integration (Guide)

Complete guide to building tools for CrewAI agents. Learn @tool decorator, tool creation, built-in tools, and multi-agent workflows.

March 1, 202616 min read

#crewai#ai-agents#llm

March 14, 202615 min read

Why LLM-Generated Code Accumulated 172 TypeScript Errors: A Technical Deep Dive

During a large-scale refactoring, we discovered 172 hidden TypeScript errors from LLM-generated code. This wasn't random—it revealed systematic patterns in how AI handles legacy removal, type inference, and build configurations. Learn the root causes and how to prevent them.

#vibe coding#TypeScript#LLM code generation

January 14, 202612 min read

The Hidden Cost of "Ship It Fast": When Velocity Becomes Technical Debt

A post-mortem on vibe coding—the practice of prioritizing momentum over maintainability. Learn why shipping fast without foundations is the most expensive shortcut you'll ever take, and how to recover.

#vibe-coding#technical-debt#software-engineering

January 15, 20269 min read

XML vs Natural Language Prompts: An Experimental Comparison

We tested XML-structured versus natural language prompts across 144 experiments spanning code generation, mathematics, reasoning, and complex multi-step tasks. The results reveal significant efficiency gains—but with important caveats.

#vibe-coding#prompt-engineering#XML-prompts

January 6, 202611 min read

Why LLMs Fail at Complex Tasks: The Math Behind Compounding Error in AI Code Generation

Learn why LLMs fail on long reasoning chains due to compounding error. Includes mathematical proofs, real-world AI coding failures, and actionable engineering strategies to mitigate AI hallucinations in software development.

#LLM limitations#compounding error#AI hallucinations

#LLM#AI-Assisted Code#Debugging

The Silent Failure Cascade: Why LLM-Powered Code Breaks in Production

LLM-generated code often fails silently in production due to implicit assumptions. Learn why this happens, how to detect it, and proven strategies to write defensive code that survives the real world.

March 7, 202612 min read

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∫Calculus

The Fundamental Theorem of Calculus

Explore the beautiful connection between differentiation and integration through the Fundamental Theorem of Calculus.

December 27, 202512 min read

#calculus#integration#differentiation

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🔣Number Theory

The Beauty of Prime Numbers

Explore the fascinating world of prime numbers, from ancient discoveries to modern applications in cryptography.

January 3, 202612 min read

#number-theory#primes#mathematics

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∫Calculus

Unleashing the Power of Complex Numbers in Calculus

Discover how Euler's formula and complex exponentials can transform difficult trigonometric integrals into simple algebra.

January 3, 202610 min read

#calculus#complex-numbers#integration

January 9, 20268 min read

Screenshot-to-Code vs. Specs-Driven Development: The 2026 Design Handoff Evolution

A real-world experiment reveals the profound gap between AI visual approximation and production-ready code. Learn why context pipelines are the future of design-to-code workflows.

#vibe coding#AI development#design systems

#SQL#Database#Performance

SQL Query Optimization: Indexes, Execution Plans & Performance (Complete Guide)

Master SQL optimization, use indexes correctly, read execution plans, speed up queries 4000x on 1M rows.

March 7, 20269 min read

January 21, 202615 min read

Few-Shot Prompting for STEM: Claude vs Gemini Across 128 Experiments

We ran 128 experiments comparing Claude Sonnet 4 and Gemini 2.0 Flash on STEM problems with zero-shot through 5-shot prompting. The results challenge common assumptions: accuracy stayed flat while format consistency and token efficiency improved dramatically.

#few-shot prompting#STEM education#prompt engineering

January 6, 202612 min read

Attention Mechanisms in LLMs: The Complete Guide to How Transformers Really Work

Learn how attention mechanisms power large language models (LLMs) like GPT-4 and Claude. This in-depth guide explains Query-Key-Value math, multi-head attention, and long-context processing with real code examples.

#attention mechanisms#transformers#LLM