Institutions

Where the n^2+1 prime conjecture 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; 45 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	2	0.87	0.87
2	University of Cambridge	GB	2	1.00	0.68
3	University of Oxford	GB	2	0.62	1.00
4	Université de Bordeaux	FR	2	0.87	0.54
5	University of Illinois Urbana-Champaign	US	4	0.69	0.72
6	Queen's University	CA	1	0.86	0.43
7	Sorbonne Université	FR	0	0.35	0.87
8	University of London	GB	0	0.41	0.72
9	Université Paris-Saclay	FR	1	0.27	0.86
10	University of Bristol	GB	0	0.53	0.55
11	Philipps-Universität Marburg	DE	0	0.61	0.41
12	University of Michigan	US	2	0.35	0.57
13	Imperial College London	GB	0	0.19	0.72
14	Université Paris Cité	FR	2	0.03	0.87
15	Centre National de la Recherche Scientifique	FR	1	-	0.89
16	Rutgers University	US	2	-	0.80
17	Eötvös Loránd University	HU	2	-	0.78
18	Alfréd Rényi Institute of Mathematics	HU	2	-	0.78
19	Université Henri Poincaré Nancy 1	FR	0	0.13	0.63
20	Princeton University	US	1	-	0.74
21	University of Göttingen	DE	1	0.31	0.37
22	Institut Élie Cartan de Lorraine	FR	1	-	0.64
23	Université de Lorraine	FR	1	-	0.63
24	Institute of Technology	US	0	0.49	0.09
25	UNSW Sydney	AU	2	-	0.58
26	City University of New York	US	1	-	0.53
27	University of South Carolina	US	1	0.33	0.20
28	University of Wales	GB	1	-	0.52
29	University of Alaska, Fairbanks	US	0	0.51	0.00
30	Universität Berlin	DE	0	0.48	0.03
31	University of Waterloo	CA	1	0.14	0.36
32	University of Freiburg	DE	1	-	0.49
33	University of California, Berkeley	US	0	0.39	0.09
34	University of Nottingham	GB	0	0.12	0.36
35	University of Toronto	CA	1	-	0.48
36	University of Calgary	CA	2	-	0.48
37	Universität Konstanz	DE	0	0.16	0.29
38	University of Georgia	US	1	0.08	0.35
39	ETH Zurich	CH	1	-	0.43
40	University of Glasgow	GB	2	-	0.41
41	University of Marburg	DE	1	-	0.41
42	Pomona College	US	1	-	0.39
43	Pennsylvania State University	US	1	-	0.39
44	Université de Montréal	CA	1	-	0.38
45	Dartmouth College	US	1	-	0.38
46	University of California, Los Angeles	US	1	-	0.38
47	Towson University	US	1	-	0.37
48	Purdue University West Lafayette	US	1	-	0.37
49	University of Tsukuba		0	0.17	0.19
50	Nanjing University of Finance and Economics	CN	1	-	0.36
51	Nanjing Normal University	CN	1	-	0.36
52	Nanjing University	CN	1	-	0.36
53	Paderborn University	DE	1	-	0.36
54	Stellenbosch University	ZA	1	-	0.35
55	Max Planck Institute for Mathematics	DE	1	-	0.35
56	University, New Brunswick	CA	0	0.34	0.01
57	Sofia University "St. Kliment Ohridski"	BG	1	-	0.34
58	Technical University of Sofia	BG	1	-	0.33
59	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	1	-	0.33
60	Nihon University	JP	1	-	0.33
61	Heinrich Heine University Düsseldorf	DE	1	-	0.32
62	École Polytechnique Fédérale de Lausanne	CH	1	-	0.31
63	University of Colorado Boulder	US	1	-	0.30
64	University of Turku	FI	1	-	0.30
65	Central Michigan University	US	1	-	0.27
66	University of Debrecen	HU	1	0.09	0.18
67	Yangzhou University	CN	2	-	0.25
68	Leiden University	NL	0	0.13	0.11
69	Steklov Mathematical Institute	RU	1	-	0.24
70	University of Missouri	US	1	-	0.21
71	Voronezh State University	RU	1	-	0.21
72	Vladimir State Pedagogical Institute	RU	1	-	0.20
73	University of Helsinki	FI	1	-	0.20
74	Georgia Institute of Technology	US	1	-	0.18
75	Université Laval	CA	1	-	0.18
76	University of Bucharest	RO	0	0.15	0.02
77	Utrecht University	NL	0	0.05	0.12
78	University of Salerno	IT	1	-	0.16
79	Stanford University	US	1	-	0.16
80	University of Genoa	IT	1	-	0.15
81	Northwestern University	US	1	-	0.15
82	China University of Mining and Technology (Beijing)	CN	1	-	0.15
83	Xi'an Jiaotong University	CN	1	-	0.15
84	Institute of Mathematical Sciences	IN	1	-	0.13
85	Australian National University	AU	1	-	0.12
86	Iwate University	JP	1	-	0.12
87	Jimei University	CN	1	-	0.11
88	University of Wisconsin-Madison	US	0	0.06	0.04
89	University of Jerusalem		0	0.09	-
90	University of British Columbia	CA	1	-	0.09
91	Hebrew University of Jerusalem	IL	1	-	0.06
92	Koç University	TR	1	-	0.04
93	Indian Institute of Science Education and Research Berhampur	IN	1	-	0.03
94	Nanyang Technological University	SG	1	-	0.01
95	Aix-Marseille University	FR	1	-	-
96	Saint Louis University Madrid	ES	1	-	-
97	Simon Bolivar University	ES	1	-	-
98	Universidad Autónoma de Madrid	ES	1	-	-
99	University of Bath	GB	1	-	-
100	University of Northern British Columbia	CA	1	-	-