مؤسسة الشرق الأوسط للنشر العلمي
عادةً ما يتم الرد في غضون خمس دقائق
Through collaborative intelligence with AI — using the DeepSeek application and its Deep Thinking feature (R1) for innovation and solution development, along with ChatGPT for recommendations — we present this solution, which consists of four mathematical frameworks demonstrating how R1 progressively contributed to the resolution. The presented solution to Goldbach's Conjecture is based on integrating four comprehensive mathematical frameworks, combining classical theories with modern techniques: The topological framework proves that prime pairs form a connected space, ensuring the existence of a path between any two pairs. The lattice framework employs Minkowski’s theorem to guarantee the existence of prime solutions geometrically within a mathematical lattice. The algebraic framework demonstrates that the absence of prime pairs would lead to a commutative group structure, which is mathematically impossible, thus confirming the existence of a solution. The quantum framework uses a Hamiltonian model to ensure the statistical stability of prime pair distributions through quantum equations.