Further human + AI + proof assistant work on Knuth's "Claude Cycles" problem

This Action Pack explores combining human expertise, AI, and formal proof assistants to tackle complex mathematical problems like Knuth's "Claude Cycles." It demonstrates how AI can act as a co-pilot for discovery, with proof assistants ensuring rigorous verification in advanced research workflows.

intermediate1 hour5 steps

The play

Understand the Human-AI-Proof Assistant Triad
Grasp the collaborative model for solving complex problems: human insight for direction, AI for exploration/generation, and formal proof assistants for rigorous verification and absolute correctness.
Set Up a Formal Proof Assistant Environment
Install and configure a modern formal proof assistant (e.g., Lean 4, Coq, Isabelle/HOL). Familiarize yourself with its basic syntax, theorem definitions, and proof modes.
Experiment with AI for Conjecture Generation
Use a large language model (LLM) to generate mathematical conjectures, logical statements, or code snippets for a small, well-defined problem. Focus on tasks where AI can suggest novel ideas or explore solution spaces.
Verify AI Output Using a Proof Assistant
Take an AI-generated statement or partial solution. Attempt to formally prove or disprove it within your chosen proof assistant. This step is crucial for validating AI's suggestions and ensuring correctness.
Iterate and Refine the Hybrid Workflow
Document your process, noting where AI provided valuable assistance and where human intuition and formal verification were indispensable. Continuously refine how you integrate these tools for tackling increasingly complex challenges.

Starter code

-- Lean 4 example: Define a natural number and prove a simple property
import Mathlib.Data.Nat.Basic

def my_number : Nat := 5

theorem my_number_is_positive : my_number > 0 := by
  dsimp [my_number]
  decide

Source

Articletwitter.com