news.volyx.in

Claude Fable produced a counterexample to the Jacobian Conjecture (xcancel.com)

803 points by loubbrad · 39 days ago · 515 comments on HN

Article summary

Claude Fable has produced a counterexample to the Jacobian Conjecture, a famous problem in mathematics that has gone unsolved for 85 years. The counterexample is a polynomial function from a 3-dimensional space to itself with a non-zero constant Jacobian determinant. The function maps different inputs to the same output, disproving the conjecture. This breakthrough was announced in a tweet and has been verified by others using symbolic algebra.

Main themes

  • Jacobian Conjecture
  • Mathematical Counterexamples
  • AI-assisted Discovery
  • Academic Research
  • LLM Capabilities
  • Critique of AI Intelligence

What commenters say

  • The counterexample to the Jacobian Conjecture is a significant breakthrough in mathematics, demonstrating the power of AI-assisted discovery.
  • The discovery of the counterexample is not surprising, given the simplicity of the polynomial function and the fact that it was found through brute-force search.
  • Some argue that LLMs are not truly intelligent, but rather stochastic parrots that can perform complex tasks without understanding the underlying context.
  • Others believe that LLMs have the potential to make significant contributions to various fields, including mathematics and medicine, and that their capabilities should not be dismissed.
  • The announcement of the counterexample in a tweet highlights the changing nature of academic research and the role of social media in disseminating scientific discoveries.
  • The fact that the counterexample was found by an AI system raises questions about the role of human intuition and creativity in mathematical discovery.
  • Some critics argue that LLMs are not capable of true intelligence or consciousness, and that their abilities are limited to pattern recognition and manipulation.
  • The discovery of the counterexample has sparked a debate about the potential applications and limitations of LLMs in various fields, including mathematics, medicine, and beyond.