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Amateur armed with ChatGPT solves an Erdős problem (scientificamerican.com)

796 points by pr337h4m · 80 days ago · 560 comments on HN

Article summary

A 23-year-old amateur mathematician used ChatGPT Pro to solve a 60-year-old math problem, known as an Erdős problem, by asking the AI to provide a proof. The problem concerns special sets of whole numbers, and the AI's solution used a new method that had not been thought of by humans before. Experts believe this solution may have broader applications in mathematics. The amateur mathematician had no advanced mathematics training and was able to solve the problem with the help of the AI.

Main themes

  • Mathematics and AI
  • Erdős problems
  • ChatGPT capabilities
  • Mathematical proofs
  • Collaboration between humans and AI

What commenters say

  • The free version of ChatGPT is not capable of producing the same level of proof as the Pro version, which has access to more advanced models and larger context windows.
  • The Pro version of ChatGPT is able to produce novel and creative proofs, but these proofs may require expert verification to ensure their correctness.
  • Formalizing mathematical problems in a language like Lean can help verify the correctness of proofs, but this requires a certain level of mathematical maturity to understand and check the formalization.
  • Different AI models, such as DeepSeek and ChatGPT, can produce independent and unique proofs of the same mathematical problem, which can provide alternative perspectives and insights.
  • The process of AI models solving mathematical problems can be fascinating to watch, as it reveals the iterative and sometimes messy process of mathematical discovery.
  • The ability of AI models to solve mathematical problems does not necessarily mean that they understand the underlying mathematics, but rather that they are able to recognize patterns and apply learned approaches.
  • The use of AI in mathematics can be seen as a collaboration between humans and machines, where the AI provides new insights and approaches, and humans verify and build upon these results.
  • The difference in capabilities between the free and Pro versions of ChatGPT raises questions about the accessibility and affordability of advanced AI tools for mathematical research and discovery.