AI Agent Hyra Confirms Optimal Growth Index of 2 for Sum and Difference Sets

Tencent's Hyra agent proves the 50-year-old conjecture that the optimal growth exponent for sum and difference sets is exactly 2, demonstrating AI's capability in pure mathematical reasoning.

Woofun AI reports that Tencent's in-house AI research agent, Hyra, has explicitly proven a mathematical problem that has persisted for over five decades. Collaborating with the Hy3 model, Hyra confirmed that the optimal growth rate exponent for the size of the sum set |A+A| and the difference set |A-A| for a finite integer set A is precisely 2. This finding resolves a gap left by a 1969 theorem, which established an upper bound of 2 but saw no improvement in constructed exponents beyond 1.1 for half a century. The result underscores the potential of AI agents in complex pure mathematical reasoning, though peer review remains pending.