In 2022, Fields Medal laureate Hugo Duminil-Copin foresaw that the enduring challenge in probability theory—the continuity phase transition conjecture in percolation theory, which had confounded academia for more than fifty years—would ultimately be resolved by artificial intelligence. Nearly at the same time, engineers at Anthropic uploaded to GitHub a complete proof code generated by their advanced internal large model, Claude. This code was rigorously verified by Lean, marking the announcement that AI had cracked the 70-year-old unsolved conjecture concerning continuous phase transitions in percolation theory for spaces ranging from three to ten dimensions. This conjecture centers on whether an infinitely large connected network can exist at the critical point. Prior to this, human mathematicians had only successfully proven cases in two dimensions and dimensions above eleven. Dimensions three through ten had become research bottlenecks due to the absence of suitable analytical tools.

In 2024, two mathematicians attempted to simplify the proof of the conjecture by focusing on verifying a specific algebraic inequality, but they were unable to achieve a breakthrough. Building on earlier human research, AI successfully completed the derivation through an ingenious approach that had not been considered by humans. This development elicited a range of responses within the mathematical community. Some hailed it as a remarkable breakthrough, while others felt disheartened that AI had accomplished the feat first. Some scholars are still awaiting AI to generate a proof process that is comprehensible to human mathematicians. This event has also prompted reflections on the future trajectory of mathematical research. Proving theorems does not constitute the entirety of mathematics. Historically, the process of tackling challenging problems has often led to the development of new mathematical tools and ideas. Looking ahead, mathematicians may be freed from the tedium of intricate derivations, allowing them to focus on more creative and exploratory endeavors.