Experience using AI software to prove Euler sum results [pdf] (www.davidhbailey.com)

Recent assessments of large language models (LLMs) for proving mathematical results have revealed both significant progress and persistent limitations. David H. Bailey from Lawrence Berkeley National Laboratory evaluated the capabilities of various LLMs, including ChatGPT and DeepSeek, in tackling Euler sum problems—a complex area of mathematical research involving infinite series and harmonic functions. Although LLMs like DeepSeek showed promising performance in generating coherent proofs, they often made critical algebraic errors, lacked detailed reasoning, and failed to provide appropriate citations or valid results. For instance, while ChatGPT attempted to use established mathematical identities, it produced incorrect derivations that undermined its accuracy. This evaluation is significant for the AI/ML community as it highlights the potential applications of LLMs in advanced mathematical research while also emphasizing their current shortcomings. As AI tools continue to evolve, understanding their limitations will be crucial for mathematicians looking to incorporate these technologies into their workflows. The findings reiterate the necessity for human oversight in the use of AI for research, suggesting a future where hybrid approaches—combining human intuition with AI efficiency—may lead to breakthroughs in mathematical discovery. This monitoring of LLM capabilities is essential as advancements may soon enable more effective use of AI in solving complex problems.