Aristotle from HarmonicMath has solved Erdős Problem 124 in LEAN (xenaproject.wordpress.com)

Aristotle, an AI developed by HarmonicMath, has achieved a significant milestone by autonomously solving Erdős Problem 124 using the Lean proof assistant, marking a breakthrough in the formalization of mathematics with AI. This accomplishment not only resolves a long-standing open problem posed by the prolific mathematician Paul Erdős but also showcases the growing synergy between AI technology and mathematical research. The problem was originally listed among open conjectures in 1997, and Aristotle managed to produce a simple yet elegant solution, prompting excitement through its unexpected efficacy and hinting at the potential for AI to contribute meaningfully to complex mathematical discussions. The completion of Problem 124 and Aristotle's ability to generate proofs reflects an important evolution in how mathematical formalization can be conducted, especially when paired with large language models. As Aristotle's method of interacting with formal systems improves, it demonstrates a new era of combining AI with traditional theorem proving. This progression could lead to more rapid formal verification of mathematical conjectures and data integration across mathematical databases, thereby enriching the field of AI and mathematics with automated, certified results. A further implication is that the ease of use and speed of achieving proof formalization could significantly lower the barriers for mathematicians looking to collaborate with AI tools in their research.