Institutions

Where the Riemann hypothesis 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	University of Bristol	GB	1	1.00	0.50
2	University of Michigan	US	2	0.85	0.39
3	University of Illinois Urbana-Champaign	US	3	0.26	0.83
4	Rikkyo University	JP	1	-	1.00
5	Tokyo Institute of Technology	JP	1	-	1.00
6	Tokyo University of Science	JP	1	-	1.00
7	American Institute of Mathematics	US	3	-	0.96
8	University of California, Los Angeles	US	0	0.15	0.78
9	University of Oxford	GB	1	0.28	0.56
10	University of York	GB	2	0.15	0.69
11	University of Rochester	US	1	0.32	0.46
12	RAND Corporation	US	1	-	0.75
13	University of British Columbia	CA	1	0.46	0.25
14	University of Graz	AT	0	0.16	0.54
15	University of California, Irvine	US	1	-	0.69
16	University of Mississippi	US	2	0.21	0.46
17	Vilnius University	LT	2	-	0.66
18	UNSW Sydney	AU	2	-	0.65
19	University of New South Wales	AU	1	-	0.65
20	University of California, Riverside	US	1	-	0.64
21	University of Manchester	GB	1	-	0.63
22	University of California, Berkeley	US	0	0.26	0.37
23	Kyushu University	JP	1	-	0.60
24	Stanford University	US	1	-	0.58
25	San Jose State University	US	1	-	0.58
26	University of Genoa	IT	1	0.21	0.35
27	Graz University of Technology	AT	2	-	0.54
28	University of Cambridge	GB	0	0.17	0.27
29	Northwestern University	US	1	-	0.43
30	Abdus Salam International Centre for Theoretical Physics	IT	1	-	0.42
31	The Abdus Salam International Centre for Theoretical Physics (ICTP)	IT	1	-	0.42
32	University, New Brunswick	CA	0	0.42	0.00
33	University of Minnesota - Twin Cities	US	0	0.17	0.25
34	UNSW Canberra	AU	1	-	0.40
35	University of Padua	IT	1	-	0.39
36	University of Lethbridge	CA	2	-	0.38
37	Université Paris-Est Créteil Val-de-Marne	FR	0	0.11	0.27
38	Goethe University Frankfurt	DE	0	0.22	0.15
39	Williams College	US	1	-	0.37
40	Adam Mickiewicz University in Poznań	PL	2	-	0.35
41	CERFIM	CH	2	-	0.35
42	Nagoya University	JP	2	-	0.35
43	University of Missouri	US	1	-	0.34
44	Institute of Technology	US	0	0.27	0.07
45	University of Milan	IT	0	0.09	0.25
46	Ruhr West University of Applied Sciences	DE	1	-	0.33
47	Université de Lorraine	FR	1	-	0.33
48	Université de Montréal	CA	1	0.27	0.05
49	Carleton College	US	1	-	0.32
50	Šiauliai University	LT	1	-	0.32
51	Rutgers University	US	2	-	0.32
52	Cornell University	US	1	-	0.32
53	Queen's University	CA	1	0.01	0.30
54	Universidad de Sevilla	ES	1	0.14	0.18
55	Pontificia Universidad Católica del Perú	PE	1	-	0.31
56	Centre National de la Recherche Scientifique	FR	2	-	0.31
57	University of Waterloo	CA	1	-	0.30
58	Institute for Advanced Study	US	1	-	0.30
59	University of Bucharest	RO	0	0.29	0.00
60	Kansas State University	US	1	-	0.28
61	Yonsei University	KR	1	-	0.28
62	Université Paris-Saclay	FR	1	-	0.27
63	University of Melbourne	AU	1	-	0.25
64	University of Minnesota	US	1	-	0.25
65	The Ohio State University	US	1	-	0.25
66	Incheon National University	KR	1	-	0.24
67	Universität Zürich	CH	0	0.08	0.16
68	École Polytechnique Fédérale de Lausanne	CH	1	-	0.24
69	Brigham Young University	US	1	-	0.24
70	Comenius University Bratislava	SK	1	-	0.24
71	University of Bahrain	BH	1	-	0.23
72	Max Planck Institute for Mathematics	DE	1	-	0.23
73	University of Bonn	DE	1	-	0.23
74	Utah Valley University	US	1	-	0.23
75	Universität Salzburg	AT	0	0.07	0.16
76	Johannes Kepler University of Linz	AT	1	-	0.22
77	Columbia University	US	1	-	0.22
78	University of Sousse	TN	1	-	0.22
79	Norwegian University of Science and Technology	NO	3	-	0.21
80	University of Würzburg	DE	1	-	0.21
81	University of Hawaiʻi at Mānoa	US	1	-	0.20
82	Universität Würzburg		0	0.20	-
83	Université de Bordeaux	FR	0	0.19	0.00
84	Tel Aviv University	IL	1	-	0.19
85	University of Texas at Austin	US	0	0.18	0.00
86	Université de Lille	FR	0	0.07	0.10
87	University of Sarajevo	BA	1	-	0.16
88	Boğaziçi University	TR	1	-	0.16
89	Universität Stuttgart	DE	0	0.03	0.13
90	Tianjin University	CN	1	-	0.14
91	Universität Hannover		0	0.13	-
92	Université Pantheon-Sorbonne : Paris I		0	0.12	-
93	Indian Institute of Technology Indore	IN	1	-	0.12
94	Universität Ulm	DE	1	-	0.12
95	Indian Institute of Technology Gandhinagar	IN	1	-	0.11
96	Leiden University	NL	0	0.01	0.08
97	Hellenic Military Academy	GR	1	-	0.08
98	Institute of Mathematical Sciences	US	0	0.05	0.00
99	Universiteit Nijmegen		0	0.05	-
100	Northwest University	CN	1	-	0.04
101	Moscow State Pedagogical Institute	RU	0	0.04	0.00
102	University of Barcelona	ES	1	-	0.04
103	National Sun Yat-sen University	TW	1	-	0.03
104	Åbo Akademi University	FI	1	-	0.03
105	University of New South Wales Canberra	AU	1	-	-