An overall university ranking cannot answer a more specific question: in a given discipline, who is the world's best? To this end, institutions such as QS, ShanghaiRanking, and US News each publish "subject rankings," but their rankings are essentially repackagings of existing reputations, with opaque calibers and weights.

大学的整体排名无法回答一个更具体的问题：某一学科领域里，谁才是全球顶尖？为此，QS、软科、US News 等机构各自发布"学科排名"，但其名次本质上仍是对既有声誉的再包装，且口径与权重不透明。

This index does not directly reproduce the subject rankings of QS and similar institutions; instead, it returns to the underlying data of subject evaluation—discipline papers, discipline highly cited works, discipline top scholars, discipline original achievements (Nobel Prizes, Fields Medals, Turing Awards, and other top awards and milestone theories), and discipline talent cultivation and technology transfer—and independently designs weights and computes rankings according to CPPPS's own four-dimension framework of "Scale + Quality + Innovation + Contribution." This is CPPPS's consistent stance: never copy rankings, only compute data, with an open and reproducible algorithm.

本指数不直接转载 QS 等机构的学科排名名次，而是回到学科评价的底层数据——学科论文、学科高被引、学科顶尖学者、学科原创成果（诺奖、菲尔兹奖、图灵奖等顶尖奖项与里程碑理论）、学科人才培养与成果转化——按照 CPPPS「规模 + 质量 + 创新 + 贡献」四维自有评价框架，独立设计权重、独立计算排名。这是 CPPPS 的一贯立场：不抄名次、只算数据、算法公开、可复现。

This edition covers 8 major discipline areas—mathematics, physics, chemistry, computer science, engineering, clinical medicine, economics, and life sciences—evaluating roughly the top 14 universities worldwide in each discipline. Four-dimension mapping: Scale corresponds to total discipline paper output; Quality corresponds to the composite of discipline highly cited works and discipline top scholars; Innovation corresponds to discipline original achievements (top awards and milestone theories); Contribution corresponds to discipline talent cultivation and technology transfer—that is, the degree to which the discipline delivers talent, technology, and industrial value to society at large (a CPPPS-distinctive dimension generally absent from international subject rankings).

本版覆盖 8 大主要学科领域：数学、物理、化学、计算机、工程、临床医学、经济、生命科学，每学科评价全球前 14 名左右顶尖大学。四维映射：规模对应学科论文产出总量；质量对应学科高被引与学科顶尖学者两项合成；创新对应学科原创成果（顶尖奖项与里程碑理论）；贡献对应学科人才培养与成果转化——即该学科为全社会输出人才、技术、产业价值的程度（CPPPS 特色维度，国际学科排名普遍缺失）。

Results: the top institution in mathematics is Princeton University, in physics MIT, in chemistry MIT, in computer science MIT, in engineering MIT, in clinical medicine Harvard University, in economics Harvard University, and in life sciences Harvard University. Overall, Scale (total papers) is not the sole factor determining ranking; the combined effect of Quality, Innovation, and Contribution allows "small but elite" top institutions to rank at the front as well. This ranking is based on publicly known approximate values, is annotated "subject to official sources," remains permanently free and public, and is provided for research and reference only.

评价结果：数学榜首为普林斯顿大学、物理榜首为麻省理工学院、化学榜首为麻省理工学院、计算机榜首为麻省理工学院、工程榜首为麻省理工学院、临床医学榜首为哈佛大学、经济榜首为哈佛大学、生命科学榜首为哈佛大学。整体看，规模（论文总量）并非决定名次的唯一因素，质量、创新与贡献的共同作用使"小而精"的顶尖机构同样能够名列前茅。本排名数据以公开常识近似值为准，标注「以官方为准」，永久免费公开，仅供研究与参考。

一、评价依据

This algorithm follows the CPPPS proprietary evaluation-algorithm specification: it does not excerpt rankings from public lists but computes them from underlying public data, designing its own weights and ranking independently. The underlying data derive from public knowledge in each discipline (each school's discipline paper volume, highly cited scale, the number of top scholars and Nobel/Fields/Turing laureates, and its reputation in talent cultivation and industrial transformation), but it discards the subjective survey weights of "academic reputation + employer reputation" used by QS and similar institutions and remaps them onto the CPPPS four-dimension framework:

本算法遵循 CPPPS 自有评价算法规范：不摘抄公开榜单名次，用底层公开数据自算，设计自有权重、独立排名。底层数据来源于学科领域的公开常识（各校学科论文体量、高被引规模、顶尖学者与诺奖/菲尔兹/图灵奖得主数量、人才培养与产业转化声誉），但放弃 QS 等机构"学术声誉+雇主声誉"的主观问卷权重，重新映射到 CPPPS 四维框架：

规模：学科论文产出总量，衡量该学科的基础研究体量与持续性。
质量：学科高被引论文与学科顶尖学者两项合成，衡量"质"——被引多、大师多，才是真正的强学科。
创新：学科原创成果，以顶尖奖项（数学-菲尔兹/沃尔夫奖，物理/化学/临床医学/经济-诺贝尔奖，计算机-图灵奖）与里程碑原创理论为标志，衡量学科的开创性。
贡献：学科人才培养与成果转化，衡量该学科向社会输出的人才、技术与产业价值——CPPPS 特色维度，源自「利他价值观」：学科的价值最终在于造福社会。

二、数学模型

Each underlying indicator is first range-normalized to [0,1] within the same discipline, and then weight-aggregated by the four dimensions:

各底层指标先在同一学科内做极差标准化到 [0,1]，再按四维权重加权求和：

规模 S = 学科论文数′ 质量 Q = ( 学科高被引′ + 学科顶尖学者′ ) / 2 创新 I = 学科原创成果′（顶尖奖项 + 里程碑理论）贡献 C = 学科人才培养/成果转化′ 学科指数 = 100 × ( 0.20·S + 0.35·Q + 0.25·I + 0.20·C )

Weight settings: Quality is highest (35%, as "quality" is the decisive factor in a discipline's strength), Innovation is second (25%, since top awards and original theories mark a discipline's height), and Scale (20%) and Contribution (20%) are balanced—among which the Contribution dimension is CPPPS's most distinctive feature relative to international subject rankings, highlighting a discipline's social value.

权重设定：质量最高（35%，"质"是学科强弱的决定性因素），创新次之（25%，顶尖奖项与原创理论是学科高度的标志），规模（20%）与贡献（20%）并重——其中贡献维度是 CPPPS 相较国际学科排名最鲜明的特色，突出学科的社会价值。

三、指标与权重依据

维度	底层指标	权重	处理	依据
规模	学科论文数	20%	线性归一	研究产出总量与持续性
质量	学科高被引	17.5%	线性归一	影响力：被引越多，质越强
质量	学科顶尖学者	17.5%	线性归一	大师密度：院士/讲席/高引学者
创新	学科原创成果	25%	线性归一	诺奖/菲尔兹/图灵 + 里程碑理论
贡献	人才培养/成果转化	20%	线性归一	输出人才与产业价值（CPPPS 特色）

The weights sum to 100%. Compared with the QS subject-ranking caliber of "academic reputation (about 40%) + employer reputation (about 10%) + citations per paper + H-index and other bibliometric indicators," CPPPS differs in that: ① it completely removes subjective surveys (reputation votes) and switches entirely to verifiable objective achievements; ② it separates "original achievements (top awards)" into an independent "Innovation" dimension with a 25% weight, highlighting pioneering work; ③ it adds a "Contribution" dimension (talent cultivation and technology transfer) with a 20% weight—a social-value perspective generally absent from international subject rankings.

合计权重 100%。与 QS 学科排名"学术声誉（约40%）+雇主声誉（约10%）+篇均引用+H指数等文献指标"的口径相比，CPPPS 的差异在于：①彻底剔除主观问卷（声誉票），全部改用可核查的客观成果；②将"原创成果（顶尖奖项）"独立成"创新"维度并赋予 25% 权重，凸显开创性；③增设"贡献"维度（人才培养与成果转化）并赋予 20% 权重，这是国际学科排名普遍缺失的社会价值视角。

四、数据来源与局限性

The five underlying indicators (discipline paper count, discipline highly cited works, discipline top scholars, discipline original achievements, and talent cultivation/technology transfer) are all publicly known approximate values, referencing each school's public discipline scale, the number of Nobel/Fields/Turing laureates, the list of highly cited scholars, and its industrial-transformation reputation, annotated "subject to official sources." Limitations: ① paper calibers (publication habits differ greatly across disciplines) are not fully unified; ② the definitions of "top scholars" and "original achievements" involve some subjectivity; ③ the sample is about 14 institutions per discipline and does not cover all universities; ④ different disciplines are not directly comparable (this index only ranks within disciplines and does not produce cross-discipline overall scores). The ranking is for research and reference only.

底层五项指标（学科论文数、学科高被引、学科顶尖学者、学科原创成果、人才培养/成果转化）均为公开常识近似值，参考各校公开的学科规模、诺奖/菲尔兹/图灵奖得主数量、高被引学者名单与产业转化声誉，标注「以官方为准」。局限性：①论文口径（不同学科发文习惯差异大）未完全统一；②"顶尖学者"与"原创成果"的界定存在一定主观性；③每学科样本约 14 所，未覆盖全部高校；④不同学科之间不直接可比（本指数只做学科内排名，不做跨学科总分排序）。排名仅供研究与参考。

五、参考文献

QS World University Rankings by Subject：各学科排名方法（学术声誉、雇主声誉、篇均引用、H 指数）。
上海软科（ARWU/GRAS）：世界一流学科排名。
科睿唯安（Clarivate）：高被引学者（Highly Cited Researchers）名单。
诺贝尔奖官方网站：物理学、化学、生理学或医学、经济学奖项历年得主。
国际数学联盟（IMU）：菲尔兹奖；沃尔夫基金会：沃尔夫奖。
美国计算机协会（ACM）：图灵奖。
各校公开的学科建设、科研产出与人才培养数据（以官方为准）。
CPPPS 自有评价算法规范（规模+质量+创新+贡献四维框架）。

排名	大学	学科指数	规模	质量	创新	贡献	梯队
1	普林斯顿大学Princeton University	92.86	64.3	100.0	100.0	100.0	A++
2	麻省理工学院Massachusetts Institute of Technology	81.66	78.6	90.8	66.7	87.5	A++
3	哈佛大学Harvard University	78.77	89.3	81.2	60.0	87.5	A++
4	剑桥大学University of Cambridge	77.39	92.9	65.7	73.3	87.5	A+
5	斯坦福大学Stanford University	71.25	71.4	78.2	53.3	81.2	A+
6	加州大学伯克利University of California, Berkeley	68.63	100.0	62.7	46.7	75.0	A+
7	牛津大学University of Oxford	65.32	85.7	53.1	53.3	81.2	A+
8	巴黎高等师范École Normale Supérieure	48.4	0.0	50.2	83.3	50.0	A+
9	苏黎世联邦理工ETH Zurich	45.14	53.6	37.6	40.0	56.2	A
10	清华大学Tsinghua University	34.78	89.3	22.2	6.7	37.5	A
11	巴黎-萨克雷大学Université Paris-Saclay	29.32	71.4	9.6	26.7	25.0	A
12	北京大学Peking University	25.51	85.7	9.6	0.0	25.0	A
13	东京大学University of Tokyo	18.69	64.3	0.0	13.3	12.5	A
14	纽约大学New York University	15.51	35.7	9.6	20.0	0.0	A

排名	大学	学科指数	规模	质量	创新	贡献	梯队
1	麻省理工学院Massachusetts Institute of Technology	98.75	100.0	100.0	95.0	100.0	A++
2	哈佛大学Harvard University	85.5	90.0	83.3	80.0	91.7	A++
3	斯坦福大学Stanford University	79.33	80.0	83.3	70.0	83.3	A++
4	加州理工学院California Institute of Technology	71.38	10.0	79.2	100.0	83.3	A+
5	剑桥大学University of Cambridge	69.92	60.0	66.7	85.0	66.7	A+
6	普林斯顿大学Princeton University	69.75	30.0	75.0	90.0	75.0	A+
7	加州大学伯克利University of California, Berkeley	65.67	70.0	66.7	60.0	66.7	A+
8	牛津大学University of Oxford	54.17	50.0	50.0	60.0	58.3	A+
9	苏黎世联邦理工ETH Zurich	46.54	40.0	45.8	50.0	50.0	A
10	清华大学Tsinghua University	28.21	90.0	12.5	10.0	16.7	A
11	东京大学University of Tokyo	26.71	70.0	12.5	20.0	16.7	A
12	芝加哥大学University of Chicago	24.79	0.0	29.2	45.0	16.7	A
13	康奈尔大学Cornell University	12.46	30.0	4.2	20.0	0.0	A
14	北京大学Peking University	12.0	60.0	0.0	0.0	0.0	A

排名	大学	学科指数	规模	质量	创新	贡献	梯队
1	麻省理工学院Massachusetts Institute of Technology	96.59	88.9	100.0	95.2	100.0	A++
2	加州大学伯克利University of California, Berkeley	86.31	77.8	92.6	85.7	84.6	A++
3	哈佛大学Harvard University	83.03	66.7	85.2	85.7	92.3	A++
4	斯坦福大学Stanford University	72.75	55.6	77.7	76.2	76.9	A+
5	剑桥大学University of Cambridge	71.0	55.6	70.3	85.7	69.2	A+
6	加州理工学院California Institute of Technology	66.35	0.0	74.2	100.0	76.9	A+
7	苏黎世联邦理工ETH Zurich	59.88	44.4	62.9	66.7	61.5	A+
8	牛津大学University of Oxford	52.68	33.3	55.5	57.1	61.5	A+
9	清华大学Tsinghua University	43.84	88.9	29.7	38.1	30.8	A
10	中国科学院大学University of Chinese Academy of Sciences	40.6	100.0	29.7	28.6	15.4	A
11	东京大学University of Tokyo	34.95	44.4	29.7	38.1	30.8	A
12	北京大学Peking University	30.0	66.7	18.4	28.6	15.4	A
13	新加坡国立大学National University of Singapore	23.98	66.7	14.8	9.5	15.4	A
14	南洋理工大学Nanyang Technological University	11.11	55.6	0.0	0.0	0.0	A

排名	大学	学科指数	规模	质量	创新	贡献	梯队
1	麻省理工学院Massachusetts Institute of Technology	98.0	90.0	100.0	100.0	100.0	A++
2	斯坦福大学Stanford University	92.23	80.0	96.4	95.7	92.9	A++
3	卡内基梅隆大学Carnegie Mellon University	84.17	65.0	92.3	87.0	85.7	A++
4	加州大学伯克利University of California, Berkeley	76.86	60.0	84.5	78.3	78.6	A+
5	哈佛大学Harvard University	50.82	20.0	53.6	60.9	64.3	A+
6	苏黎世联邦理工ETH Zurich	46.54	30.0	50.0	52.2	50.0	A+
7	清华大学Tsinghua University	45.93	100.0	31.0	26.1	42.9	A+
8	牛津大学University of Oxford	33.52	10.0	34.5	43.5	42.9	A+
9	剑桥大学University of Cambridge	31.39	20.0	26.8	43.5	35.7	A
10	北京大学Peking University	28.48	65.0	15.5	17.4	28.6	A
11	伊利诺伊大学香槟University of Illinois Urbana-Champaign	16.28	50.0	3.6	8.7	14.3	A
12	佐治亚理工学院Georgia Institute of Technology	14.28	40.0	3.6	8.7	14.3	A
13	新加坡国立大学National University of Singapore	6.0	30.0	0.0	0.0	0.0	A
14	滑铁卢大学University of Waterloo	2.17	0.0	0.0	8.7	0.0	A

排名	大学	学科指数	规模	质量	创新	贡献	梯队
1	麻省理工学院Massachusetts Institute of Technology	98.18	90.9	100.0	100.0	100.0	A++
2	斯坦福大学Stanford University	83.36	63.6	91.6	85.7	85.7	A++
3	加州大学伯克利University of California, Berkeley	70.43	54.5	74.8	76.2	71.4	A++
4	清华大学Tsinghua University	60.96	100.0	50.3	47.6	57.1	A+
5	加州理工学院California Institute of Technology	53.57	0.0	62.6	81.0	57.1	A+
6	苏黎世联邦理工ETH Zurich	53.15	36.4	54.2	61.9	57.1	A+
7	剑桥大学University of Cambridge	48.15	27.3	45.8	66.7	50.0	A+
8	帝国理工学院Imperial College London	32.67	36.4	29.0	38.1	28.6	A+
9	南洋理工大学Nanyang Technological University	30.9	72.7	16.8	19.0	28.6	A
10	佐治亚理工学院Georgia Institute of Technology	22.81	54.5	12.2	19.0	14.3	A
11	新加坡国立大学National University of Singapore	17.27	45.5	8.4	9.5	14.3	A
12	密歇根大学University of Michigan	15.68	45.5	3.8	9.5	14.3	A
13	上海交通大学Shanghai Jiao Tong University	15.58	63.6	0.0	0.0	14.3	A
14	加州大学洛杉矶University of California, Los Angeles	6.8	27.3	3.8	0.0	0.0	A

世界学科指数World Discipline Index

综述Overview

分层梯队Tiers

各学科顶尖大学排名Top Universities by Discipline

算法详细论述Methodology

一、评价依据

二、数学模型

三、指标与权重依据

四、数据来源与局限性

五、参考文献

说明Notes

排名	大学	学科指数	规模	质量	创新	贡献	梯队
1	哈佛大学Harvard University	95.66	100.0	93.1	92.3	100.0	A++
2	麻省理工学院Massachusetts Institute of Technology	92.57	70.0	100.0	100.0	92.9	A++
3	芝加哥大学University of Chicago	80.31	40.0	86.2	100.0	85.7	A++
4	斯坦福大学Stanford University	72.7	50.0	79.3	76.9	78.6	A+
5	普林斯顿大学Princeton University	65.19	10.0	79.3	84.6	71.4	A+
6	伦敦政治经济学院London School of Economics and Political Science	61.39	80.0	58.6	53.8	57.1	A+
7	加州大学伯克利University of California, Berkeley	56.74	40.0	58.6	61.5	64.3	A+
8	牛津大学University of Oxford	47.21	50.0	44.8	46.2	50.0	A+
9	剑桥大学University of Cambridge	45.28	50.0	37.9	53.8	42.9	A
10	耶鲁大学Yale University	43.13	20.0	44.8	53.8	50.0	A
11	哥伦比亚大学Columbia University	33.59	30.0	31.0	38.5	35.7	A
12	宾夕法尼亚大学University of Pennsylvania	31.25	40.0	24.0	30.8	35.7	A
13	西北大学Northwest University	25.0	0.0	27.6	38.5	28.6	A
14	清华大学Tsinghua University	10.0	50.0	0.0	0.0	0.0	A