Core Viewpoint - The article discusses the collaborative breakthroughs in solving the "Sums and differences of sets problem" achieved by AI and human mathematicians, highlighting the advancements made by DeepMind's AlphaEvolve and subsequent improvements by mathematicians like Robert Gerbicz and Fan Zheng [2][4][30]. Group 1: AlphaEvolve's Contributions - DeepMind's AlphaEvolve improved the matrix multiplication algorithm and broke the record for the "Sums and differences of sets problem," which had been stagnant for 18 years [2][4]. - AlphaEvolve utilized a semi-automated search process, generating numerous candidate solutions through the Gemini model and refining them via an automated evaluation system [14][16]. - The best-performing algorithm constructed a set of 54,265 integers, raising the lower bound of θ to 1.1584, surpassing the previous record of 1.14465 set 18 years ago [18]. Group 2: Human Mathematicians' Improvements - Hungarian mathematician Robert Gerbicz developed a new method that constructs a large set with specific constraints, achieving θ=1.173050, which surpassed AlphaEvolve's result [20][25]. - Gerbicz's approach involved using combinatorial principles to avoid redundant calculations, leading to a set with over 10^43546 elements [24]. - Fan Zheng further improved the result to θ=1.173077 by introducing a theoretical analysis framework, demonstrating that asymptotic analysis can provide systematic methods for further improvements [27][29]. Group 3: Collaborative Dynamics - The results from AlphaEvolve and subsequent human contributions illustrate a complementary relationship between AI and human mathematicians, rather than a competitive one [30][31]. - AlphaEvolve's strength lies in its ability to explore a wide range of problems, allowing human experts to focus on specific areas for deeper investigation and progress [31][32].