The Complete Conquest of the Seven Millennium Problems and the Extension of Technological Knowledge V2.0: Opening the Second Door of Mathematical Geometry — From Astrophysics to Aerospace Engineering/千禧年七大題的全攻克與科技知識延伸 V2.0:推開數學幾何的第二道門——從天文物理到航太工程

Description — English Abstract This work presents V2.0 of an interdisciplinary framework connecting the seven Millennium Prize Problems, mathematical geometry, physical phenomena, astrophysics, and aerospace engineering. Building upon the V1.0 framework that extended mathematical geometry toward Earth, life, mechanical engineering, and biomimetic systems, V2.0 opens a second branch toward space, astrophysical environments, and aerospace engineering. The central knowledge chain is: Mathematical Geometry → Structural Mapping → Known Physical Law → Observable → Engineering Hypothesis → Simulation → Experiment. Within this framework, the Poincaré Conjecture, Hodge Conjecture, Riemann Hypothesis, Birch and Swinnerton-Dyer Conjecture, Yang–Mills and the Mass Gap, Navier–Stokes equations, and P versus NP are examined as seven mathematical-geometric entry points involving space, topology, local–global structure, spectra, curves, fields, flows, stability, search spaces, and computational complexity. These structures are further mapped toward astrophysical and aerospace domains including planetary and astrophysical fluids, hypersonic aerodynamics, shock waves and boundary layers, aerodynamic heating, plasma and electromagnetic environments, orbital dynamics, gravity-assist trajectories, lightweight and adaptive aerospace structures, autonomous spacecraft navigation, and space-system resource allocation. The proposed directions are organized into three advanced engineering systems: Hypersonic Aerodynamics and Thermal Systems; Space Plasma, Fields and Adaptive Materials; and Orbital Dynamics and Autonomous Space Systems. V2.0 maintains a strict distinction between different levels of knowledge: Analogy ≠ Structural Mapping ≠ Physical Law ≠ Mathematical Proof. Structural correspondence is therefore not treated as formal mathematical proof or as direct engineering validation. Instead, the framework establishes explicit handoff points through which mathematical geometry may be connected to known physical laws, measurable observables, engineering hypotheses, numerical simulations, falsification, and physical experiments. Together, V1.0 and V2.0 establish a two-branch knowledge framework: Mathematics → Geometry → Physics → Earth / Life → Mechanical & Biomimetic Engineering Mathematics → Geometry → Physics → Space / Cosmos → Astrophysics & Aerospace Engineering The objective is not to abandon mathematics or computation, but to establish a bridge through which mathematical geometry can reconnect with the observable physical universe and continue toward testable and realizable engineering knowledge. Research WebsitePCS ObservatoryORCID — 0009-0006-8999-8293Visual Appendix: From Physical Intuition and Structure toMathematical GeometryThese figures illustrate the way I move back and forth among design, physics, structure, geometry, andmathematics as a process of observation and reconstruction.Mathematical geometry is a tool I learned through design, while physics gives me theintuition to discover phenomena.Physics lets me see structure; structure lets me map geometry; geometry lets me seemathematics. Mathematics helps me reconstruct geometry; geometry lets me mapstructure; structure lets me align with physics. 描述 — 中文 摘要 本文提出千禧年七大難題之數學幾何、物理現象、天文物理與航太工程跨領域知識框架的 V2.0。研究延續 V1.0 由數學幾何通往地球、生命、機械工程與仿生系統的知識交接方法,進一步推開第二道門,將研究範圍延伸至太空、天文物理環境與航太工程。 本研究的核心知識鏈為: 數學幾何 → 結構映射 → 已知物理定律 → 可觀測量 → 工程假說 → 模擬 → 實驗。 在此框架中,Poincaré 猜想、Hodge 猜想、Riemann 假設、Birch and Swinnerton-Dyer 猜想、Yang–Mills 與質量間隙、Navier–Stokes 方程,以及 P versus NP,被重新視為七個不同的數學幾何入口,涵蓋空間、拓撲、局部—整體結構、頻譜、曲線、場、流動、穩定性、搜尋空間與計算複雜度。 這些結構進一步與天文物理及航太領域建立研究映射,包括行星與天體流體、高超音速空氣動力學、激波與邊界層、氣動加熱、電漿與電磁環境、軌道動力學、重力助推軌跡、輕量化與自適應航太結構、自主航太器導航,以及太空系統資源配置。 本文進一步將相關研究方向歸納為三個進階工程體系:高超音速氣動力學與熱系統、太空電漿/場與自適應材料,以及軌道動力學與自主太空系統。 V2.0 嚴格維持不同知識層級之間的界線: 類比 ≠ 結構映射 ≠ 物理定律 ≠ 數學證明。 因此,結構上的對應並不直接被視為形式數學證明,也不等同於已完成的工程驗證。本文建立的是明確的知識交接點,使數學幾何可以進一步連接已知物理定律、可測量的觀測量、工程假說、數值模擬、反證與物理實驗。 V1.0 與 V2.0 共同形成一個雙分支知識框架: 數學 → 幾何 → 物理 → 地球/生命 → 機械與仿生工程 數學 → 幾何 → 物理 → 太空/宇宙 → 天文物理與航太工程 本研究的目的並不是放棄數學或計算,而是在數學幾何與可觀測物理宇宙之間建立交接橋梁,使數學結構能夠繼續向可驗證、可模擬與可實現的工程知識延伸。 研究網站PCS ObservatoryORCID — 0009-0006-8999-8293 數學幾何是我學設計的工具,而物理是讓我發現現象的直觀。 物理讓我看見結構,結構讓我映射幾何,幾何讓我看見數學;數學幫助我重建幾何,幾 何讓我映射結構,結構讓我對齊物理。