The advanced Gemini Deep Think has collaborated with experts to tackle 18 complex research challenges across various domains, including algorithm optimization and economics. Key advancements include resolving classic computer science issues like “Max-Cut” and “Steiner Tree” by integrating continuous mathematics tools, as detailed in sections 4.1 and 4.2. Notably, Gemini validated a decade-old conjecture in online submodular optimization through a novel combinatorial counterexample (Section 3.1). In AI optimization, the system automated noise filtration, proving the effectiveness of its adaptive penalty method (Section 8.3). Furthermore, it redefined economic theories related to continuous auction dynamics using advanced topology (Section 8.4) and innovatively calculated gravitational radiation from cosmic strings (Section 6.1). This showcases AI’s role as a scientific collaborator, enhancing researchers’ workflows. The findings underscore a transformative era in scientific inquiry, propelled by collaborative human-AI efforts. For comprehensive insights, refer to the full paper.
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