Tencent's Hyra AI Solves Half-Century-Old Math Problem

Tencent's research AI agent Hyra, based on the Hy3 model, has made a breakthrough in additive combinatorics, providing a complete answer to an open problem that had remained unsolved for over half a century. The problem involves how much a finite set of integers expands under addition and subtraction, with the classic inequality giving an upper bound of 2, but mathematicians were unsure if 2 was optimal. Hyra proved that 2 is indeed the supremum by constructing explicit sets that can approach any value below 2. During the research, Hyra improved the best result from about 1.14 to 1.21, then proposed the core idea using base-12 digit structures and symmetric additive bases on cyclic groups to complete the proof. The paper, explicit constructions, and Lean formal proof are all publicly available, showcasing AI's potential in mathematical reasoning.