Amateur Mathematicians Use AI to Solve Long-Standing Erdős Problems

The article highlights the surprising success of amateur mathematicians in using AI tools to solve long-standing Erdős problems. These problems, known for their simple statements but difficult solutions, have served as signposts for progress in various mathematical disciplines. The use of AI models like ChatGPT has enabled researchers to find relevant references, improve existing results, and even generate complete solutions to previously unsolved problems. The combination of ChatGPT for generating proofs and Aristotle for verifying their correctness represents a significant advancement in AI-assisted mathematical research.

While the initial attempts with ChatGPT were prone to hallucinations, recent improvements have made it a valuable tool for mathematical exploration. The success of Kevin Barreto and Liam Price in solving Erdős problem number 205 demonstrates the potential of AI to democratize mathematical research, allowing amateurs to contribute to the field. However, it's important to note that five of the six solved problems had pre-existing solutions, suggesting that AI is currently better at rediscovering known results than generating entirely new ones.

Despite this limitation, the use of AI in mathematics holds significant promise. AI can assist researchers in exploring complex mathematical landscapes, generating hypotheses, and verifying proofs. However, it's crucial to maintain a balance between AI assistance and human intuition to avoid over-reliance on AI and ensure the continued development of human mathematical creativity.