Artifical intelligence and inherent mathematical difficulty
Summary
The paper “Artificial Intelligence and Inherent Mathematical Difficulty” by Walter Dean and Alberto Naibo examines whether AI could eventually automate the discovery and proof of new mathematical results. The authors argue that although automated theorem provers, SAT solvers, and large language models have made impressive progress, fundamental results from computability and complexity theory indicate that mathematical proof discovery contains inherent difficulties that cannot simply be eliminated by faster computers or better AI.
Many successful AI approaches essentially perform sophisticated forms of brute-force search, which work particularly well for problems with relatively low logical complexity but become increasingly ineffective as the complexity of mathematical statements grows.
The paper therefore challenges optimistic claims that AI will routinely solve major open problems such as the Riemann Hypothesis or Goldbach's Conjecture, while acknowledging that AI may substantially transform mathematical practice by assisting with exploration, formalization, verification, and discovery.
ARTICLE / ARCHIVE
Summary
The paper “Artificial Intelligence and Inherent Mathematical Difficulty” by Walter Dean and Alberto Naibo examines whether AI could eventually automate the discovery and proof of new mathematical results. The authors argue that although automated theorem provers, SAT solvers, and large language models have made impressive progress, fundamental results from computability and complexity theory indicate that mathematical proof discovery contains inherent difficulties that cannot simply be eliminated by faster computers or better AI.
Many successful AI approaches essentially perform sophisticated forms of brute-force search, which work particularly well for problems with relatively low logical complexity but become increasingly ineffective as the complexity of mathematical statements grows.
The paper therefore challenges optimistic claims that AI will routinely solve major open problems such as the Riemann Hypothesis or Goldbach's Conjecture, while acknowledging that AI may substantially transform mathematical practice by assisting with exploration, formalization, verification, and discovery.
ARTICLE / ARCHIVE
┌────────────────────────────────┐
│ KONSTANTINOS MICHAILIDIS │
└────────────────────────────────┘
│ KONSTANTINOS MICHAILIDIS │
└────────────────────────────────┘