Institutions

Where the Riemann hypothesis research concentrates, three ways

Reading the 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; 41 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	Ctry	Top 100	Training	Environment
1	University of Bristol	GB	1	1.00	0.56
2	University of Michigan	US	2	0.76	0.45
3	University of Illinois Urbana-Champaign	US	3	0.28	0.82
4	American Institute of Mathematics	US	2	-	1.00
5	California Institute of Technology	US	2	-	1.00
6	University of California, Los Angeles	US	0	0.14	0.81
7	Centre National de la Recherche Scientifique	FR	4	-	0.87
8	University of Rochester	US	1	0.33	0.53
9	University of Oxford	GB	2	0.17	0.67
10	Collège de France	FR	1	-	0.82
11	University of York	GB	2	0.05	0.75
12	RAND Corporation	US	1	-	0.78
13	Université Paris-Est Créteil Val-de-Marne	FR	0	0.02	0.74
14	Université Paris-Saclay	FR	1	-	0.74
15	University of Graz	AT	0	0.16	0.58
16	University of British Columbia	CA	1	0.46	0.27
17	Tokyo University of Science	JP	1	-	0.73
18	Rikkyo University	JP	1	-	0.73
19	University of Nottingham	GB	0	0.21	0.49
20	University of California, Irvine	US	1	-	0.70
21	Vilnius University	LT	2	-	0.69
22	University of Manchester	GB	1	-	0.68
23	University of California, Riverside	US	1	-	0.67
24	UNSW Sydney	AU	1	-	0.61
25	University of New South Wales	AU	1	-	0.61
26	Graz University of Technology	AT	2	-	0.59
27	Princeton University	US	0	0.25	0.32
28	Kyushu University	JP	1	-	0.56
29	University of Genoa	IT	1	0.18	0.37
30	University of Mississippi	US	2	0.15	0.36
31	University of Cambridge	GB	0	0.17	0.32
32	Abdus Salam International Centre for Theoretical Physics	IT	1	-	0.47
33	The Abdus Salam International Centre for Theoretical Physics (ICTP)	IT	1	-	0.47
34	Toronto Metropolitan University	CA	1	-	0.44
35	Northwestern University	US	1	-	0.44
36	University of Würzburg	DE	1	0.20	0.23
37	University of Waterloo	CA	1	-	0.43
38	Stanford University	US	1	-	0.42
39	CERFIM	CH	2	-	0.39
40	University of Padua	IT	1	-	0.38
41	Adam Mickiewicz University in Poznań	PL	2	-	0.38
42	Williams College	US	1	-	0.38
43	Nagoya University	JP	2	-	0.38
44	Cornell University	US	1	-	0.37
45	University of Milan	IT	0	0.09	0.27
46	San Jose State University	US	1	-	0.36
47	Queen's University	CA	1	0.01	0.34
48	University of Missouri	US	1	-	0.35
49	Université de Montréal	CA	1	0.29	0.06
50	Rutgers University	US	2	-	0.35
51	Comenius University Bratislava	SK	1	-	0.34
52	Šiauliai University	LT	1	-	0.34
53	Pontificia Universidad Católica del Perú	PE	1	-	0.34
54	University of Lethbridge	CA	2	-	0.33
55	University of California, Berkeley	US	0	0.07	0.26
56	Goethe University Frankfurt	DE	0	0.22	0.11
57	Institute for Advanced Study	US	1	-	0.32
58	Kansas State University	US	1	-	0.30
59	Helmut Schmidt University	DE	1	-	0.29
60	Australian National University	AU	1	-	0.28
61	University of Melbourne	AU	1	-	0.28
62	Brigham Young University	US	1	-	0.27
63	Carleton College	US	1	-	0.27
64	Utah Valley University	US	1	-	0.27
65	Kent State University	US	1	-	0.26
66	Johannes Kepler University of Linz	AT	1	-	0.26
67	Norwegian University of Science and Technology	NO	4	-	0.25
68	University of Bahrain	BH	1	-	0.25
69	Universität Salzburg	AT	0	0.08	0.18
70	University of Bucharest	RO	0	0.25	0.00
71	University of Minnesota - Twin Cities	US	0	0.03	0.22
72	The Ohio State University	US	1	-	0.25
73	Institute of Technology	US	0	0.17	0.07
74	Universität Zürich	CH	0	0.09	0.15
75	University of Minnesota	US	1	-	0.23
76	École Polytechnique Fédérale de Lausanne	CH	1	-	0.22
77	University of Hawaiʻi at Mānoa	US	1	-	0.21
78	Universidad de Sevilla	ES	1	-	0.21
79	University of Texas at Austin	US	0	0.19	0.00
80	Tel Aviv University	IL	1	-	0.19
81	University of Sarajevo	BA	1	-	0.18
82	Boğaziçi University	TR	1	-	0.17
83	Université de Lille	FR	0	0.02	0.14
84	Indian Institute of Technology Indore	IN	1	-	0.15
85	Emory University	US	0	0.15	0.00
86	Universität Ulm	DE	1	-	0.14
87	Indian Institute of Technology Gandhinagar	IN	1	-	0.13
88	Incheon National University	KR	1	-	0.10
89	Hellenic Military Academy	GR	1	-	0.10
90	Max Planck Institute for Mathematics	DE	1	-	0.07
91	National Sun Yat-sen University	TW	1	-	0.07
92	Leiden University	NL	0	0.02	0.05
93	Institute of Mathematical Sciences	US	0	0.06	0.00
94	University of Barcelona	ES	1	-	0.05
95	Xi'an Technological University	CN	1	-	0.04
96	Åbo Akademi University	FI	1	-	0.04
97	Tianjin University	CN	1	-	0.03
98	Russian Academy of Sciences	RU	1	-	0.02