For nearly a century, the Siegel zero problem has stood as a formidable challenge within the number theory community. Recently, artificial intelligence (AI) has made its first significant breakthrough in this area. Building on this initial AI-driven progress, mathematicians and AI worked together in a collaborative relay, refining the original 8-page proof down to a concise 5-page document over the course of 12 days.

Previously, mathematician Yitang Zhang had taken on this challenge twice, in 2007 and again in 2022. However, his 2022 paper, which spanned 111 pages, only succeeded in solving a weakened version of the problem. This time, Oxford mathematician Ben Green teamed up with AI to craft the 5-page proof. Notably, on the first page of the paper, Green explicitly stated that no claim to human originality was being made.

The proof employs a classic method of proof by contradiction. It begins by assuming the existence of a Siegel zero and then proceeds to derive a contradiction from this assumption. This ultimately confirms the non-existence of the Siegel zero, thereby removing a significant barrier in the field of classical analytic number theory.

Throughout this process, multiple mathematicians participated in a relay-like effort, continuously optimizing the proof. They clarified parameters, simplified derivations, and ensured the logical coherence of the argument. Meanwhile, AI was deeply involved in each stage of the derivation and writing process. This collaboration marks a new phase in mathematical research, where AI and humans work together seamlessly to push the boundaries of knowledge.