以时间轴串联世界数学的发展历程，呈现重大数学问题的提出背景、求解过程与未解之谜的最新进展，交互式展示数学各分支学科及其关系，并收录世界顶级数学奖项的历年获奖人与获奖原因。资料力求准确、可溯源。https://math-history.example.com/https://math-history.example.com/milestones/zhoubi-suanjing/https://math-history.example.com/milestones/zhoubi-suanjing/中国最古的天文数学典籍，以盖天说立论，并用勾股方圆图给出勾股定理的早期证明。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/apollonius-conics/https://math-history.example.com/milestones/apollonius-conics/阿波罗尼奥斯系统创立圆锥曲线理论，命名抛物线、椭圆与双曲线。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/archimedes/https://math-history.example.com/milestones/archimedes/阿基米德以穷竭法夹逼圆周率、求抛物线面积，并奠定流体静力学基础。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/euclid-elements/https://math-history.example.com/milestones/euclid-elements/公理化的典范，以少数公理与公设推演出整个平面几何体系，奠定西方数学两千余年的演绎传统。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/eudoxus-method/https://math-history.example.com/milestones/eudoxus-method/欧多克索斯以比例论化解无理数危机，并以穷竭法预告了积分思想。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/zeno-paradoxes/https://math-history.example.com/milestones/zeno-paradoxes/芝诺以"阿喀琉斯""飞矢"等悖论逼问运动与无限，预示了极限思想的诞生。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/pythagorean-theorem/https://math-history.example.com/milestones/pythagorean-theorem/毕达哥拉斯学派以"万物皆数"统合数与形，确立了直角三角形三边关系定理。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/thales/https://math-history.example.com/milestones/thales/古希腊七贤之一的泰勒斯以逻辑推理证明几何命题，被认为是将埃及实用测量提升为演绎几何的第一人。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/egyptian-math/https://math-history.example.com/milestones/egyptian-math/阿姆士抄写的《莱因德纸草》以单位分数表与实用几何，展现古埃及的数学成就。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/rhind-papyrus/https://math-history.example.com/milestones/rhind-papyrus/约公元前 1650 年的莱因德纸草书是古埃及数学最完整的文献，含 2/n 分数表与大量应用题。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/babylonian-math/https://math-history.example.com/milestones/babylonian-math/两河流域的楔形文字泥板展示了成熟的六十进制位值制与二次方程解法，比希腊早千年。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/moscow-papyrus/https://math-history.example.com/milestones/moscow-papyrus/古埃及莫斯科纸草给出截头金字塔体积公式，是早期几何的实用高峰。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/jiuzhang-suanshu/https://math-history.example.com/milestones/jiuzhang-suanshu/汉代《九章算术》以筹算统括方田、方程、勾股，确立中国古典数学范式。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/ptolemy-almagest/https://math-history.example.com/milestones/ptolemy-almagest/托勒密造弦表、立托勒密定理，构建影响千年的地心体系数学框架。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/diophantus-arithmetica/https://math-history.example.com/milestones/diophantus-arithmetica/丢番图《算术》开创"失音代数"，研究整数范围内的不定方程，故称丢番图方程。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/mayan-mathematics/https://math-history.example.com/milestones/mayan-mathematics/中美洲玛雅文明发展出含"零"的二十进制位值制，用于历法与天文，是美洲原住民数学的高峰。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/hai-dao-suanjing/https://math-history.example.com/milestones/hai-dao-suanjing/刘徽所撰测望术专书，以重差术用相似三角形测量不可达的高深远，开测绘之先。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/liu-hui/https://math-history.example.com/milestones/liu-hui/刘徽以割圆术求π=3.1416，并为《九章算术》补入极限与推理。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/wu-cao-suan-jing/https://math-history.example.com/milestones/wu-cao-suan-jing/魏晋算学官书之一，以田亩、兵阵、仓窖、赋税、贸易五类官吏所需的算术为题，是"算经十书"中偏重实用的一种。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/bakhshali-manuscript/https://math-history.example.com/milestones/bakhshali-manuscript/早期印度梵文数学写本，含已知最早的"零"符号与平方根逼近法。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/hypatia/https://math-history.example.com/milestones/hypatia/亚历山大城的女数学家希帕提娅注释欧几里得与丢番图，是古代最后一位重要的数学教师与思想象征。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/sunzi-suanshu/https://math-history.example.com/milestones/sunzi-suanshu/南北朝算经名篇，含鸡兔同笼与"物不知数"，后者是中国剩余定理的雏形。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/zhang-qiujian/https://math-history.example.com/milestones/zhang-qiujian/南北朝算经，以"百鸡问题"闻名，是早期不定方程多解问题的代表。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/zhui-shu/https://math-history.example.com/milestones/zhui-shu/南朝祖冲之、祖暅之父子所著，以"缀术"求圆周率与球体积，唐代列为最高级算学教材，惜原书失传。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/zu-chongzhi/https://math-history.example.com/milestones/zu-chongzhi/祖冲之将π算至小数点后七位，并与子祖暅提出等积原理（祖暅原理）。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/aryabhata/https://math-history.example.com/milestones/aryabhata/阿耶波多《历算书》编制正弦表、取π=3.1416，开创印度古典数学。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/indian-decimal-zero/https://math-history.example.com/milestones/indian-decimal-zero/印度发明含"零"的十进制位值制，经阿拉伯世界传向欧洲，奠定现代记数。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/wu-jing-suan-shu/https://math-history.example.com/milestones/wu-jing-suan-shu/北周甄鸾所撰，专门注释儒家五经及《周礼》中的数字、历法、度量内容，是经学与算学结合的产物。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/ji-gu-suanjing/https://math-history.example.com/milestones/ji-gu-suanjing/王孝通所著，以"开带从立方"数值求解三次方程，把代数用于工程土方计算。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/brahmagupta/https://math-history.example.com/milestones/brahmagupta/婆罗摩笈多系统给出零与负数法则，并导出二次方程求根公式。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/suan-jing-shi-shu/https://math-history.example.com/milestones/suan-jing-shi-shu/唐代国子监钦定的十部算经教材，标志中国数学教育制度化，并东传日韩。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/xia-hou-yang-suan-jing/https://math-history.example.com/milestones/xia-hou-yang-suan-jing/唐代实用算术书，强调"乘除便捷"与十进制小数思想，并保存了早期"重因""身外加"等速算法口诀。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/al-khwarizmi/https://math-history.example.com/milestones/al-khwarizmi/花拉子米著《代数学》，"algebra"与"algorithm"二词皆源于其名与书名。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/thabit-ibn-qurra/https://math-history.example.com/milestones/thabit-ibn-qurra/阿拉伯翻译家兼数学家塔比特给出生成"亲和数"的公式，并大量译介希腊与印度数学文献。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/alhazen/https://math-history.example.com/milestones/alhazen/阿拉伯学者海桑以实验与数学方法研究光学，提出"海桑问题"，并被视为科学方法论的先驱。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/al-biruni/https://math-history.example.com/milestones/al-biruni/比鲁尼以三角学与天文测量测定地球半径，比较东西方历法，是伊斯兰时代最博学的学者之一。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/omar-khayyam/https://math-history.example.com/milestones/omar-khayyam/海亚姆分类三次方程，借圆锥曲线交点给出几何解，认为其无算术解。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/bhaskara-lilavati/https://math-history.example.com/milestones/bhaskara-lilavati/12世纪印度数学巅峰，含循环法解佩尔方程与微积分思想雏形。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/fibonacci-liber-abaci/https://math-history.example.com/milestones/fibonacci-liber-abaci/斐波那契借《算盘书》把印度—阿拉伯数字引入欧洲，其兔子问题催生斐波那契数列。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/qin-jiushao/https://math-history.example.com/milestones/qin-jiushao/秦九韶创"大衍求一术"与"正负开方术"，确立一般剩余定理与高次方程数值解法。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/li-ye-ce-yuan/https://math-history.example.com/milestones/li-ye-ce-yuan/李冶创立"天元术"，设未知数布列一元高次方程，标志中国方程代数成熟。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/tusi/https://math-history.example.com/milestones/tusi/纳西尔丁·图西系统建立平面三角与球面三角，提出"图西耦"解释行星运动，被誉为三角学之父。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/yang-hui/https://math-history.example.com/milestones/yang-hui/杨辉保存并阐释贾宪"开方作法本源图"，即二项式系数三角，兼及垛积与幻方。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/zhu-shijie-suan-xue-qi-meng/https://math-history.example.com/milestones/zhu-shijie-suan-xue-qi-meng/朱世杰所撰系统代数入门教材，承前启后，东传朝鲜日本影响深远。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/zhu-shijie-si-yuan-yu-jian/https://math-history.example.com/milestones/zhu-shijie-si-yuan-yu-jian/朱世杰创立"四元术"解四元高次联立方程组，并以垛积招差贯通高阶差分与级数。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/oresme-graphs/https://math-history.example.com/milestones/oresme-graphs/尼科尔·奥雷斯姆用图表表示变速运动，并证明调和级数发散，预示坐标几何。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/madhava-kerala/https://math-history.example.com/milestones/madhava-kerala/14 世纪印度喀拉拉学派的马德哈瓦独立发现正弦、余弦与圆周率的无穷级数，比欧洲早约两百年。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/al-kashi/https://math-history.example.com/milestones/al-kashi/帖木儿帝国天文学家阿尔·卡西推广十进制小数，并以创纪录的精度计算圆周率与正弦表。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/nilakantha/https://math-history.example.com/milestones/nilakantha/喀拉拉学派的尼拉坎塔完善正弦级数，并提出带离心均轮的地动行星模型，早于第谷同类设想。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/durer-polyhedra/https://math-history.example.com/milestones/durer-polyhedra/文艺复兴巨匠丢勒在《测量指南》中系统传授透视与多面体作图，其"幻方"与"多面体"成为数学艺术典范。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/cardano-tartaglia/https://math-history.example.com/milestones/cardano-tartaglia/卡尔达诺《大术》公布三次方程求根公式，并触及四次方程与复数。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/recorde-equals/https://math-history.example.com/milestones/recorde-equals/罗伯特·雷科德在《砺智石》中首次引入"="等号，推动数学记号革新。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/bombelli-algebra/https://math-history.example.com/milestones/bombelli-algebra/拉斐尔·邦贝利系统给出复数运算法则，使三次方程的虚数解获得合法地位。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/vieta-introduction/https://math-history.example.com/milestones/vieta-introduction/韦达《分析方法入门》创立符号代数，以字母统摄已知与未知，开启解析术。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/ricci-xu-euclid/https://math-history.example.com/milestones/ricci-xu-euclid/1607 年利玛窦与徐光启合译欧几里得《几何原本》前六卷，首次将演绎公理化体系引入中国。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/napier-logarithms/https://math-history.example.com/milestones/napier-logarithms/约翰·纳皮尔发明对数，把乘除化为加减，引发计算史上的革命。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/descartes-geometry/https://math-history.example.com/milestones/descartes-geometry/笛卡尔《几何学》以坐标架起代数与几何之桥，开创解析几何。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/desargues-projective/https://math-history.example.com/milestones/desargues-projective/吉拉尔·笛沙格开创射影几何，引入无穷远点与透视对应，埋下19世纪几何复兴伏笔。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/fermat-pierre/https://math-history.example.com/milestones/fermat-pierre/费马以"无穷递降法"开创现代数论，提出费马小定理与著名的大定理。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/pascal-probability/https://math-history.example.com/milestones/pascal-probability/帕斯卡与费马的通信以"赌金分配"问题奠定概率论，并著《算术三角》。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/wallis-infinite-product/https://math-history.example.com/milestones/wallis-infinite-product/约翰·沃利斯以"无穷算术"给出沃利斯乘积，连接π与偶数奇数之比，是微积分的前奏。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/mei-wending/https://math-history.example.com/milestones/mei-wending/清初梅文鼎会通中西历算，著书七十余种，是清代"西学中源"说的代表与国算复兴的关键人物。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/seki-takakazu/https://math-history.example.com/milestones/seki-takakazu/江户时代的关孝和创立日本"和算"，独立发现行列式、消元法与微积分思想，与西方几乎同时。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/newton-leibniz-calculus/https://math-history.example.com/milestones/newton-leibniz-calculus/1684年莱布尼茨发表首篇微积分论文，与牛顿各自创立无穷小算法，奠定现代分析基石。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/bernoulli-family/https://math-history.example.com/milestones/bernoulli-family/雅各布与约翰·伯努利推动微积分应用，开创变分法雏形与概率早期结果。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/leibniz-binary/https://math-history.example.com/milestones/leibniz-binary/莱布尼茨于 1703 年正式发表二进制，并因与《周易》六十四卦的"巧合"而兴奋，视其为普遍符号语言的雏形。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/ming-antu/https://math-history.example.com/milestones/ming-antu/清代蒙古族数学家明安图以"割圆连比例"独立导出三角函数幂级数，早于欧洲同类展开约数十年。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/euler-seven-bridges/https://math-history.example.com/milestones/euler-seven-bridges/欧拉将七桥问题抽象为"一笔画"，证明不可行，由此创立图论并孕育拓扑思想。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/euler-leonhard/https://math-history.example.com/milestones/euler-leonhard/欧拉以海量著述统一分析学，并在数论与图论开创方向，被誉为其时代最富创造力的数学家。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/lagrange/https://math-history.example.com/milestones/lagrange/拉格朗日《分析力学》以变分原理统一力学，创立分析力学并推动变分法成型。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/gauss-fundamental-theorem/https://math-history.example.com/milestones/gauss-fundamental-theorem/高斯1799年给出代数基本定理首个实质证明，并创立最小二乘法。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/laplace/https://math-history.example.com/milestones/laplace/拉普拉斯以《天体力学》用分析统一行星运动，提出拉普拉斯变换与概率论的贝叶斯化，是 18 世纪数学物理的顶峰。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/gauss-disquisitiones/https://math-history.example.com/milestones/gauss-disquisitiones/高斯1801年出版《算术研究》，奠基现代数论并系统建立同余理论。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/cauchy-weierstrass/https://math-history.example.com/milestones/cauchy-weierstrass/柯西与魏尔斯特拉斯以极限与ε-δ语言为微积分奠基严格基础。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/fourier-analysis/https://math-history.example.com/milestones/fourier-analysis/傅里叶论证任意函数可展为三角级数，开创傅里叶分析并推动函数概念革命。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/abel-quintic/https://math-history.example.com/milestones/abel-quintic/阿贝尔1824年严格证明一般五次方程无根式解，开启方程可解性研究。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/non-euclidean-geometry/https://math-history.example.com/milestones/non-euclidean-geometry/19世纪罗巴切夫斯基、波约与黎曼独立突破平行公设，开创非欧几何。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/galois-theory/https://math-history.example.com/milestones/galois-theory/伽罗瓦以群与域刻画方程根式可解性，创立群论并彻底解决五次方程问题。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/hamilton-quaternions/https://math-history.example.com/milestones/hamilton-quaternions/哈密顿1843年发现四元数，突破乘法交换律，开创超复数代数。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/boole-algebra/https://math-history.example.com/milestones/boole-algebra/布尔1854年创立逻辑代数，以代数运算刻画推理，奠基数理逻辑。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/riemannian-geometry/https://math-history.example.com/milestones/riemannian-geometry/黎曼1854年演说创立黎曼几何，以度量与曲率统一弯曲空间。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/cayley-matrices/https://math-history.example.com/milestones/cayley-matrices/阿瑟·凯莱系统建立矩阵代数，使线性变换成为可计算的数学对象。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/riemann-hypothesis-stated/https://math-history.example.com/milestones/riemann-hypothesis-stated/黎曼1859年论文提出ζ函数零点猜想，连通素数分布，成世纪难题。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/lie-groups/https://math-history.example.com/milestones/lie-groups/索菲斯·李创立李群与李代数，用连续变换群统一微分方程的对称性研究。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/dedekind-reals/https://math-history.example.com/milestones/dedekind-reals/戴德金用"分割"严格构造实数，奠定连续性与完备性的分析基石。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/klein-erlangen/https://math-history.example.com/milestones/klein-erlangen/克莱因1872年以变换群统一各类几何，提出埃尔朗根纲领。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/cantor-set-theory/https://math-history.example.com/milestones/cantor-set-theory/康托尔1874年起创立集合论，证明无穷有不同层级，革新数学基础。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/kovalevskaya/https://math-history.example.com/milestones/kovalevskaya/首位获数学博士学位的女性，奠定偏微分方程解的存在唯一性定理。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/hilbert-basis/https://math-history.example.com/milestones/hilbert-basis/希尔伯特1888年以非构造性证明确立基定理，革新不变量理论与代数。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/hilbert-23/https://math-history.example.com/milestones/hilbert-23/1900年希尔伯特在巴黎提出23个数学问题，为20世纪数学设定研究议程。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/poincare-conjecture-stated/https://math-history.example.com/milestones/poincare-conjecture-stated/1904年庞加莱提出三维单连通闭流形同胚于三维球面，拓扑学核心难题。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/ramanujan/https://math-history.example.com/milestones/ramanujan/自学成才的印度数学家拉马努金留下近四千个公式与恒等式，深刻影响现代数论、分析与模形式。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/noether-emmy/https://math-history.example.com/milestones/noether-emmy/诺特创立现代交换环与理想论，并证明对称性与守恒律对应的诺特定理。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/godel-incompleteness/https://math-history.example.com/milestones/godel-incompleteness/1931年哥德尔证明：含算术的一致形式系统存在不可判定命题，且不能自证相容。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/kolmogorov-probability/https://math-history.example.com/milestones/kolmogorov-probability/1933年柯尔莫哥洛夫以测度论为基础建立概率公理，奠定现代概率论根基。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/bourbaki/https://math-history.example.com/milestones/bourbaki/1935年起布尔巴基以结构主义重写数学基础，深刻影响现代数学语言与教学。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/turing-computability/https://math-history.example.com/milestones/turing-computability/1936年图灵提出图灵机模型与停机问题不可判定，奠定计算机科学理论基础。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/category-theory-founded/https://math-history.example.com/milestones/category-theory-founded/1945年艾伦伯格与麦克兰恩创立范畴论，成为现代数学统一语言。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/hodge-conjecture-stated/https://math-history.example.com/milestones/hodge-conjecture-stated/1950年前后霍奇提出猜想，关联代数簇的拓扑上同调类与代数子簇。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/nash-equilibrium/https://math-history.example.com/milestones/nash-equilibrium/1950年纳什定义并证明有限博弈至少存在一个均衡点，奠定非合作博弈论。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/yang-mills-theory/https://math-history.example.com/milestones/yang-mills-theory/1954年杨振宁与米尔斯提出非阿贝尔规范理论，成为粒子物理标准模型核心。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/chaos-theory/https://math-history.example.com/milestones/chaos-theory/1963年洛伦兹发现确定性系统对初值的敏感依赖，开启混沌理论。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/birch-swinnerton-dyer/https://math-history.example.com/milestones/birch-swinnerton-dyer/1960年代伯奇与斯温纳顿-戴尔据数值实验提出BSD猜想，关联椭圆曲线秩与L函数。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/langlands-program/https://math-history.example.com/milestones/langlands-program/1967年朗兰兹提出连接数论与表示论的宏大对应，成为现代数论指导性框架。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/p-vs-np-stated/https://math-history.example.com/milestones/p-vs-np-stated/1971年库克形式化NP完全性并提出P对NP问题，成为理论计算机科学核心难题。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/black-scholes/https://math-history.example.com/milestones/black-scholes/1973年布莱克、舒尔斯与默顿建立期权定价公式，开创金融工程。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/mandelbrot-fractal/https://math-history.example.com/milestones/mandelbrot-fractal/1975年曼德博创立分形几何，以分数维刻画自相似的自然复杂形状。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/four-color-theorem-proof/https://math-history.example.com/milestones/four-color-theorem-proof/1976年阿佩尔与哈肯借助计算机完成四色定理证明，首例重大计算机辅助证明。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/classification-finite-groups/https://math-history.example.com/milestones/classification-finite-groups/有限单群分类定理（"巨定理"）由百余位数学家逾万页论文完成，约2004年补全。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/fermat-proof-wiles/https://math-history.example.com/milestones/fermat-proof-wiles/1994年怀尔斯结合模形式与椭圆曲线证明费马大定理，终结358年猜想。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/kepler-proof-hales/https://math-history.example.com/milestones/kepler-proof-hales/1998年黑尔斯借助计算机证明球最密堆积密度，2014年形式化验证完成。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/millennium-problems/https://math-history.example.com/milestones/millennium-problems/2000年克莱数学研究所公布七大难题，每题悬赏百万美元，仅庞加莱已解。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/navier-stokes-stated/https://math-history.example.com/milestones/navier-stokes-stated/纳维–斯托克斯方程描述流体运动，其三维修道存在性与光滑性仍属开放难题。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/poincare-proof-perelman/https://math-history.example.com/milestones/poincare-proof-perelman/2002–2003年佩雷尔曼用里奇流证明庞加莱与几何化猜想，拒领大奖。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/abc-conjecture-mochizuki/https://math-history.example.com/milestones/abc-conjecture-mochizuki/2012年望月新一以宇宙际Teichmüller理论声称证明ABC猜想，学界分歧至今。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/zhang-yitang/https://math-history.example.com/milestones/zhang-yitang/2013年张益唐证明存在无穷多对差小于7000万的素数，开启素数间隔研究热潮。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/milestones/mirzakhani/https://math-history.example.com/milestones/mirzakhani/米尔扎哈尼在黎曼曲面与模空间的几何动力学上取得突破，2014年成首位女性菲尔兹奖得主。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/birch-swinnerton-dyer/https://math-history.example.com/problems/birch-swinnerton-dyer/椭圆曲线有理点群的秩等于其哈斯–韦伊 L 函数在 s=1 处零点阶数。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/abc-conjecture/https://math-history.example.com/problems/abc-conjecture/对互素正整数 a+b=c，其根 rad(abc) 通常不小于 c；它统御众多丢番图方程。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/classification-of-finite-simple-groups/https://math-history.example.com/problems/classification-of-finite-simple-groups/每个有限单群必属循环、交错、李型或 26 个散在型之一；证明 ~1981 完成。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/collatz-conjecture/https://math-history.example.com/problems/collatz-conjecture/对任意正整数反复"偶则除2、奇则3n+1"，是否总归约到 1。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/existence-of-odd-perfect-numbers/https://math-history.example.com/problems/existence-of-odd-perfect-numbers/是否存在不等于自身及其因子之和的奇完全数，即满足 σ(n)=2n 的奇数 n。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/continuum-hypothesis/https://math-history.example.com/problems/continuum-hypothesis/实数集的基数是否恰为紧接可数集之后的第一个不可数基数，即 2^{ℵ0}=ℵ1。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/four-squares-theorem/https://math-history.example.com/problems/four-squares-theorem/每个自然数都可写成四个整数平方之和；拉格朗日 1770 年证明。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/fermat-last-theorem/https://math-history.example.com/problems/fermat-last-theorem/方程 $x^n + y^n = z^n$ 在整数 $n>2$ 时不存在正整数解；从费马写下"惊奇的边注"到怀尔斯证明，历时 358 年。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/fundamental-theorem-of-algebra/https://math-history.example.com/problems/fundamental-theorem-of-algebra/复系数非常数多项式必有复根；高斯 1799 年给出首个证明。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/four-color-theorem/https://math-history.example.com/problems/four-color-theorem/任何平面地图都可用四种颜色着色使相邻区域不同色；1976 年 Appel–Haken 用计算机辅助证明。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/goldbach-conjecture/https://math-history.example.com/problems/goldbach-conjecture/任一大于 2 的偶数都可写成两个素数之和；近三百年未解，陈景润达"1+2"最佳。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/hodge-conjecture/https://math-history.example.com/problems/hodge-conjecture/非奇异复射影代数簇上的某些上同调类（霍奇类）是否总可由代数子簇的几何对象生成。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/independence-of-parallel-postulate/https://math-history.example.com/problems/independence-of-parallel-postulate/欧氏平行公设不能由其余公理推出；罗巴切夫斯基等建立非欧几何证明独立。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/insolubility-of-quintic/https://math-history.example.com/problems/insolubility-of-quintic/一般五次方程不能由系数经四则运算与开方求解；阿贝尔与伽罗瓦确立。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/kepler-conjecture/https://math-history.example.com/problems/kepler-conjecture/相同球体最密堆积密度为 π/√18；1611 年开普勒提出，1998 年黑尔斯证明。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/navier-stokes-existence-smoothness/https://math-history.example.com/problems/navier-stokes-existence-smoothness/三维不可压缩纳维–斯托克斯方程在任意初值下是否始终存在全局光滑解，抑或会出现有限时间奇点。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/p-vs-np/https://math-history.example.com/problems/p-vs-np/所有可在多项式时间内验证的问题是否也能在多项式时间内求解，即 P 是否等于 NP。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/poincare-conjecture/https://math-history.example.com/problems/poincare-conjecture/单连通的三维闭流形必同胚于三维球面；2002–2003 年佩雷尔曼以里奇流证明。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/prime-number-theorem/https://math-history.example.com/problems/prime-number-theorem/小于 x 的素数个数 π(x) 渐近于 x/ln x；1896 年阿达马与德拉瓦莱普桑独立证明。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/quadratic-reciprocity/https://math-history.example.com/problems/quadratic-reciprocity/刻画两奇素数 p、q 的二次剩余可解性的对称定律；高斯 1796 年首次严格证明。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/riemann-hypothesis/https://math-history.example.com/problems/riemann-hypothesis/黎曼 ζ 函数的所有非平凡零点实部均为 1/2；千禧年难题之一，关乎素数分布。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/twin-prime-conjecture/https://math-history.example.com/problems/twin-prime-conjecture/是否存在无穷多对相差为 2 的素数（孪生素数），即 p 与 p+2 均素数。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/weak-goldbach/https://math-history.example.com/problems/weak-goldbach/任一大于 5 的奇数可表为三素数之和；2013 年哈儿佛戈特证明。Tue, 04 Aug 2026 03:19:21 GMThttps://math-history.example.com/problems/yang-mills-mass-gap/https://math-history.example.com/problems/yang-mills-mass-gap/四维量子杨-米尔斯理论是否存在且具严格数学定义，并存在正的质量间隙。Tue, 04 Aug 2026 03:19:21 GMT