Number Theory

Exact Mean Rho-Length Formula for Power Map Dynamics via d-Adic Valuation

What Happens When You Let an AI Loose on 1,000 Erdős Problems

I pointed Claude Code at the Erdős problem database with vague instructions to 'find interesting things.' It built 92 Python modules, ran 131 subagents, and computed exact Ramsey numbers nobody had computed before. I mostly watched.

Exact Rational Arithmetic

Rational numbers give exact arithmetic where floating-point fails. The implementation connects GCD, the Stern-Brocot tree, and the algebraic structure of fields.

Is It Prime?

The Miller-Rabin primality test demonstrates how probabilistic algorithms achieve arbitrary certainty, trading absolute truth for practical efficiency.

Modular Arithmetic as Rings

Integers modulo N form a ring, an algebraic structure that determines which algorithms apply. Understanding this structure unlocks algorithms from cryptography to competitive programming.

One Algorithm, Infinite Powers

The Russian peasant algorithm computes products, powers, Fibonacci numbers, and more, once you see the underlying algebraic structure.