To Have Machines Make Math Proofs, Turn Them into a Puzzle
12 days ago
- #Automated Reasoning
- #Mathematics
- #Artificial Intelligence
- Marijn Heule uses SAT (satisfiability) to solve complex mathematical problems in geometry and combinatorics.
- SAT is a form of symbolic AI that relies on binary logic (true/false) to build airtight proofs.
- Heule believes combining SAT with large language models (LLMs) can solve problems beyond human capability.
- SAT solvers work by searching for combinations of true/false values that satisfy given constraints, akin to solving puzzles.
- LLMs can generate plausible mathematical lemmas, while SAT solvers verify their correctness or provide counterexamples.
- Automated proofs can be extremely long and incomprehensible to humans, but Heule argues trust in correctness is more important than understanding.
- Heule envisions a collaborative future where mathematicians, LLMs, and automated reasoning work together to solve open problems.
- Human intuition and creativity remain essential in mathematics, with automation serving as a tool rather than a replacement.