Institutions

Where Landau's problems on prime numbers research concentrates, three ways

Table Details

Columns

# the headline rank: the average of the Training and Environment scores shown in the next two columns. Average the two numbers on any row and the rows sort by exactly that average, so the # position is always explainable from what you see.
Training score from 0.00 to 1.00: where today's Top 100 earned their PhDs (verified Mathematics Genealogy records; 80 of 100 researchers covered), rank-weighted and scaled so the strongest training ground is 1.00. A dash means no recorded Top 100 alumni and counts as 0 in the average.
Environment score from 0.00 to 1.00: the research gravity around the institution today; every Top 100 researcher contributes by rank and by distance (exponential decay, 100 km scale), scaled so the strongest environment is 1.00. A dash means no verified coordinates yet and counts as 0.
Top 100 how many of the current Top 100 work there. Hover a row for names.
Institution names link to the institution's homepage (or its mathematics department where we have verified that page); links come from the institution's OpenAlex record.

Click any header to sort; the score columns sort strongest-first. Candidates are the union of the Top 100's current institutions and their PhD schools, so pure training grounds appear even when nobody on the list works there today.

#	Institution (hover rows for details)		Top 100	Training	Environment
1	University of Cambridge	GB	2	0.85	0.71
2	Royal Holloway University of London	GB	1	0.74	0.82
3	University of Oxford	GB	4	0.56	1.00
4	Stanford University	US	2	1.00	0.51
5	Princeton University	US	2	0.82	0.51
6	Eötvös Loránd University	HU	2	0.64	0.65
7	University of Illinois Urbana-Champaign	US	5	0.28	0.89
8	Shandong University	CN	2	0.79	0.31
9	University of London	GB	0	0.35	0.69
10	University of Turku	FI	2	0.57	0.45
11	Imperial College London	GB	0	0.33	0.69
12	Birkbeck, University of London	GB	0	0.27	0.69
13	University of Genoa	IT	1	0.63	0.29
14	University of California, Berkeley	US	0	0.56	0.32
15	University of Paris-Saclay	FR	1	0.30	0.58
16	University of Bordeaux	FR	2	0.60	0.23
17	Rutgers University	US	1	0.28	0.52
18	Queen's University	CA	2	0.32	0.47
19	Sorbonne University	FR	0	0.19	0.58
20	Peking University	CN	0	0.18	0.56
21	Purdue University West Lafayette	US	1	0.21	0.53
22	University of Bristol	GB	0	0.30	0.43
23	Pennsylvania State University	US	1	0.37	0.35
24	Hungarian Academy of Sciences	HU	0	0.07	0.65
25	Chinese Academy of Sciences	CN	1	0.11	0.57
26	Alfréd Rényi Institute of Mathematics	HU	3	-	0.65
27	Dartmouth College	US	1	0.31	0.32
28	University of California, Los Angeles	US	1	0.22	0.39
29	University of Göttingen	DE	1	0.33	0.26
30	China University of Mining and Technology (Beijing)	CN	2	-	0.59
31	Université Paris-Est Créteil Val-de-Marne	FR	1	-	0.59
32	Beijing Information Science and Technology University	CN	1	-	0.59
33	Université Paris Cité	FR	2	-	0.58
34	Institute for Advanced Study	US	1	-	0.51
35	San Jose State University	US	1	-	0.50
36	ETH Zurich	CH	2	0.10	0.38
37	University of Michigan	US	1	0.19	0.28
38	Moscow State Pedagogical University	RU	0	0.30	0.15
39	Tel Aviv University	IL	2	0.28	0.16
40	Harvard University	US	0	0.35	0.07
41	Massachusetts Institute of Technology	US	0	0.32	0.07
42	University of Toronto	CA	1	-	0.38
43	Nanjing University	CN	0	0.21	0.17
44	University of Milan	IT	0	0.17	0.21
45	University of Warsaw	PL	0	0.37	0.00
46	Freie Universität Berlin	DE	0	0.34	0.02
47	University of Parma	IT	1	-	0.36
48	Université Henri Poincaré Nancy 1	FR	0	0.08	0.26
49	Emory University	US	0	0.24	0.10
50	Cardiff University	GB	1	-	0.33
51	University of Padua	IT	1	-	0.33
52	Towson University	US	1	-	0.33
53	Lomonosov Moscow State University	RU	0	0.16	0.16
54	Université de Montréal	CA	1	0.02	0.30
55	University of South Carolina	US	0	0.29	0.03
56	University of Freiburg	DE	0	0.08	0.22
57	Universität Konstanz	DE	0	0.03	0.25
58	Australian National University	AU	0	0.17	0.11
59	Pomona College	US	1	-	0.28
60	University of Waterloo	CA	2	-	0.27
61	University of California, Santa Barbara	US	1	-	0.27
62	Institut Élie Cartan de Lorraine	FR	1	-	0.27
63	University of Helsinki	FI	1	-	0.26
64	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	1	-	0.26
65	University of New South Wales	AU	2	-	0.26
66	Northwestern University	US	1	-	0.25
67	University of Tsukuba		0	0.12	0.12
68	University of Georgia	US	1	-	0.24
69	University of Missouri	US	1	-	0.22
70	Technion - Israel Institute of Technology	IL	1	-	0.21
71	University of Rome Tor Vergata	IT	1	-	0.21
72	Nihon University	JP	1	-	0.21
73	Central Michigan University	US	1	-	0.21
74	Brigham Young University	US	1	-	0.21
75	Shanghai Jiao Tong University	CN	1	-	0.20
76	University of Bucharest	RO	0	0.19	0.01
77	University of Colorado Boulder	US	1	-	0.20
78	University of Kentucky	US	1	-	0.20
79	Yale University	US	0	0.06	0.13
80	Tongji University	CN	1	-	0.18
81	Utrecht University	NL	0	0.12	0.05
82	Nanjing University of Finance and Economics	CN	1	-	0.18
83	University of Ulm	DE	1	-	0.17
84	Shanghai University	CN	1	-	0.17
85	Boğaziçi University	TR	1	-	0.17
86	Steklov Mathematical Institute	RU	1	-	0.16
87	Politecnico di Torino	IT	1	-	0.14
88	École Polytechnique Fédérale de Lausanne	CH	1	-	0.13
89	Sofia University	BG	1	-	0.12
90	UNSW Canberra	AU	1	-	0.11
91	University of Mississippi	US	1	-	0.10
92	University of Minnesota - Twin Cities	US	0	0.10	0.00
93	Henan Academy of Sciences	CN	1	-	0.09
94	Iwate University	JP	1	-	0.09
95	Heinrich Heine University Düsseldorf	DE	1	-	0.09
96	Hellenic Military Academy	GR	1	-	0.08
97	University of Science and Technology of China	CN	1	-	0.07
98	University of Salerno	IT	2	-	0.07
99	Victoria University of Wellington	NZ	1	-	0.05
100	Aix-Marseille University	FR	1	-	0.04
101	The High School Affiliated to Renmin University of China	CN	1	-	-
102	University of Queensland	AU	1	-	-