[Claude and Codex Successively Discover Counterexamples, AI Begins Tackling Mathematical Challenges] According to monitoring by 动察 Beating, Anthropic mathematician Levent Alpöge used Claude Fable to discover a three-dimensional counterexample to the Jacobian conjecture. This problem has remained unresolved since 1939 and is listed among the important mathematical challenges of the 21st century. The polynomial mapping provided by Fable has a Jacobian determinant consistently equal to −2, yet it maps three distinct inputs to the same output. As a result, it cannot be invertible, disproving the three-dimensional and higher-dimensional versions, while the two-dimensional version remains unsolved. Subsequently, OpenAI researcher Aaron Lou had the internal Codex model independently attempt the problem. Without internet access, the model also identified an essentially identical counterexample and even wrote out the derivation process. In the future, mathematicians may assign numerous open problems to different models simultaneously. AI can repeatedly experiment, searching for counterexamples, loopholes, and new approaches, then verify them using symbolic computation or formal proof tools. Many directions that previously lacked the time for exhaustive exploration could now be rapidly examined, potentially accelerating scientific discovery. However, this does not mean problems will automatically become simpler. Models are equally capable of generating large volumes of seemingly rigorous but erroneous proofs, shifting the academic challenge from "unable to find answers" to "unable to verify answers in time." The greater risk lies in genuine breakthroughs. RSA security relies on the difficulty of factoring large integers, while Diffie-Hellman and elliptic curve cryptography depend on the difficulty of solving discrete logarithms. If AI discovers sufficiently fast new algorithms, parts of the public-key systems used in website encryption, digital signatures, banking transactions, and blockchain could become invalid, forcing a global emergency overhaul of cryptographic standards. [Original Article Link]