My Favorite Math Problem
6 days ago
- #chessboard-problem
- #AI-in-math
- #mathematics
- The problem involves covering a mutilated chessboard (with two opposing diagonal corners removed) using 2x1 blocks.
- The question is a yes or no question about the possibility of such a covering, not about how to do it.
- The problem is simple to state but difficult to solve, illustrating the nature of combinatorial problems.
- It serves as an introduction to higher mathematics concepts like existence proofs and abstract definitions.
- Modern mathematics is highly abstract, with proofs and definitions requiring human intelligence, but computers are starting to contribute.
- Proofs can be seen as types, which are common in programming languages, enabling computers to understand mathematical theory.
- Projects like Microsoft's aim to formalize mathematical knowledge into a computer-readable form.
- AI and LLMs are beginning to generate type-theoretic formulations of mathematical statements, potentially changing mathematical research.