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; 49 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	Royal Holloway University of London	GB	1	1.00	0.83
2	University of Oxford	GB	4	0.76	1.00
3	University of Cambridge	GB	2	0.84	0.74
4	University of Illinois Urbana-Champaign	US	5	0.40	1.00
5	University of Genoa	IT	1	0.91	0.34
6	Imperial College London	GB	0	0.45	0.71
7	University of California, Berkeley	US	0	0.74	0.35
8	University of London	GB	0	0.36	0.71
9	Birkbeck, University of London	GB	0	0.34	0.71
10	Queen's University	CA	2	0.50	0.48
11	Université Paris-Saclay	FR	1	0.40	0.54
12	University of Bristol	GB	1	0.43	0.43
13	Université de Bordeaux	FR	2	0.63	0.19
14	University of Michigan	US	2	0.27	0.51
15	Sorbonne Université	FR	0	0.20	0.53
16	Beijing Information Science and Technology University	CN	1	-	0.71
17	China University of Mining and Technology (Beijing)	CN	2	-	0.71
18	Chinese Academy of Sciences	CN	1	-	0.69
19	University of Göttingen	DE	1	0.42	0.27
20	University of California, Los Angeles	US	1	0.29	0.38
21	Alfréd Rényi Institute of Mathematics	HU	2	-	0.66
22	Eötvös Loránd University	HU	2	-	0.65
23	Purdue University West Lafayette	US	1	-	0.58
24	Stanford University	US	2	-	0.55
25	Shandong University	CN	2	0.21	0.34
26	San Jose State University	US	1	-	0.55
27	Université Paris-Est Créteil Val-de-Marne	FR	1	-	0.54
28	Université Paris Cité	FR	2	-	0.54
29	University of Turku	FI	2	-	0.51
30	University of Alaska, Fairbanks	US	0	0.51	0.00
31	Universität Berlin	DE	0	0.47	0.02
32	Institute of Technology	US	0	0.41	0.07
33	Philipps-Universität Marburg	DE	0	0.36	0.12
34	ETH Zurich	CH	2	-	0.46
35	University of Parma	IT	1	-	0.41
36	University of Toronto	CA	1	-	0.40
37	University of Freiburg	DE	1	-	0.40
38	University of South Carolina	US	0	0.35	0.03
39	Australian National University	AU	0	0.26	0.12
40	Rutgers University	US	2	-	0.37
41	Universität Konstanz	DE	0	0.05	0.32
42	University of Padua	IT	1	-	0.36
43	Université de Montréal	CA	1	0.06	0.30
44	University of Wales	GB	1	-	0.33
45	University of Tsukuba		0	0.19	0.13
46	Princeton University	US	1	-	0.32
47	Dartmouth College	US	1	-	0.32
48	University of Waterloo	CA	2	-	0.31
49	Shanghai Jiao Tong University	CN	1	-	0.31
50	Tongji University	CN	1	-	0.30
51	Stellenbosch University	ZA	1	-	0.30
52	Pennsylvania State University	US	1	-	0.29
53	Shanghai University	CN	1	-	0.29
54	University of Helsinki	FI	1	-	0.29
55	Pomona College	US	1	-	0.29
56	Towson University	US	1	-	0.28
57	University, New Brunswick	CA	0	0.28	0.00
58	University of Bucharest	RO	0	0.27	0.01
59	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	1	-	0.28
60	Université Henri Poincaré Nancy 1	FR	0	0.10	0.18
61	University of Georgia	US	1	-	0.27
62	UNSW Sydney	AU	1	-	0.26
63	Tianjin University	CN	1	-	0.26
64	University of Missouri	US	1	-	0.25
65	Nihon University	JP	1	-	0.23
66	Universität Ulm	DE	1	-	0.23
67	University of Kentucky	US	1	-	0.22
68	University of Glasgow	GB	1	-	0.21
69	Utrecht University	NL	0	0.16	0.05
70	Brigham Young University	US	1	-	0.20
71	Technion - Israel Institute of Technology	IL	1	-	0.19
72	Nanjing University of Finance and Economics	CN	1	-	0.19
73	Central Michigan University	US	1	-	0.19
74	Institut Élie Cartan de Lorraine	FR	1	-	0.18
75	Politecnico di Torino	IT	1	-	0.17
76	University of Minnesota - Twin Cities	US	0	0.16	0.00
77	Sofia University "St. Kliment Ohridski"	BG	1	-	0.16
78	Henan Academy of Sciences	CN	1	-	0.14
79	University of Colorado Boulder	US	1	-	0.14
80	Universität Freiburg im Breisgau		0	0.14	-
81	UNSW Canberra	AU	1	-	0.13
82	Iwate University	JP	1	-	0.12
83	Hellenic Military Academy	GR	1	-	0.11
84	Boğaziçi University	TR	1	-	0.11
85	University of Mississippi	US	1	-	0.10
86	Tel Aviv University	IL	0	0.01	0.09
87	University of Salerno	IT	2	-	0.10
88	Aix-Marseille Université	FR	1	-	0.10
89	Heinrich Heine University Düsseldorf	DE	1	-	0.09
90	Steklov Mathematical Institute	RU	1	-	0.09
91	University of British Columbia	CA	1	-	0.08
92	University of Calgary	CA	1	-	0.06
93	Victoria University of Wellington	NZ	1	-	0.02
94	Kings College London	GB	1	-	-
95	University of Queensland	AU	1	-	-