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These posts explore the philosophy and practice of generic programming as taught by Alex Stepanov, architect of the C++ Standard Template Library.

The central insight: algorithms arise from algebraic structure. The same algorithm that works on integers works on matrices, polynomials, and modular integers---not by accident, but because they share algebraic properties. When you recognize "this is a monoid" or "this is a Euclidean domain," you immediately know which algorithms apply.

Each post demonstrates one beautiful idea with minimal, pedagogical C++ code (~100-300 lines). The implementations prioritize clarity over cleverness---code that reads like a textbook that happens to compile.

Core Topics

• Monoids and exponentiation: The Russian peasant algorithm reveals the universal structure of repeated operations
• Rings and fields: Modular arithmetic teaches which algorithms apply where
• Euclidean domains: The same GCD algorithm works for integers and polynomials
• Generic concepts: C++20 concepts express algebraic requirements as compile-time contracts

Further Reading

• Stepanov & Rose, From Mathematics to Generic Programming
• Stepanov & McJones, Elements of Programming