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; 69 of 96 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	Eötvös Loránd University	HU	2	1.00	1.00
2	Royal Holloway University of London	GB	2	0.83	0.76
3	University of Cambridge	GB	2	0.95	0.62
4	Princeton University	US	1	0.81	0.70
5	University of Oxford	GB	2	0.60	0.86
6	University of Paris-Saclay	FR	1	0.66	0.76
7	Rutgers University	US	2	0.65	0.74
8	University of Illinois Urbana-Champaign	US	4	0.66	0.70
9	University of Bordeaux	FR	2	0.83	0.50
10	Stanford University	US	1	0.99	0.15
11	Sorbonne University	FR	0	0.34	0.79
12	Hungarian Academy of Sciences	HU	0	0.13	0.99
13	University of London	GB	0	0.39	0.64
14	Alfréd Rényi Institute of Mathematics	HU	3	-	1.00
15	University of Turku	FI	1	0.58	0.28
16	University of Bristol	GB	0	0.50	0.34
17	Pennsylvania State University	US	1	0.47	0.36
18	Université Paris Cité	FR	2	0.02	0.80
19	Imperial College London	GB	0	0.18	0.64
20	Université Paris-Est Créteil Val-de-Marne	FR	1	-	0.80
21	Dartmouth College	US	1	0.42	0.34
22	Queen's University	CA	1	0.33	0.39
23	Columbia University	US	0	0.24	0.46
24	Université Henri Poincaré Nancy 1	FR	0	0.12	0.55
25	University of Göttingen	DE	1	0.31	0.35
26	Philipps-Universität Marburg	DE	0	0.27	0.38
27	Nanjing University	CN	1	0.28	0.36
28	Moscow State Pedagogical University	RU	0	0.45	0.18
29	University of Michigan	US	1	0.36	0.26
30	Institut Élie Cartan de Lorraine	FR	1	-	0.55
31	Massachusetts Institute of Technology	US	0	0.47	0.08
32	University of Lorraine	FR	1	-	0.55
33	University of New South Wales	AU	2	-	0.53
34	Harvard University	US	0	0.43	0.08
35	University of South Carolina	US	1	0.31	0.19
36	City University of New York	US	1	-	0.50
37	Lomonosov Moscow State University	RU	0	0.30	0.19
38	University of Warsaw	PL	0	0.48	0.00
39	Freie Universität Berlin	DE	0	0.45	0.03
40	University of California, Berkeley	US	0	0.36	0.09
41	University of Waterloo	CA	1	0.13	0.32
42	University of Toronto	CA	1	-	0.43
43	University of Nottingham	GB	0	0.11	0.30
44	University of Georgia	US	1	0.07	0.32
45	University of Marburg	DE	1	-	0.38
46	Nanjing University of Finance and Economics	CN	1	-	0.37
47	Nanjing Normal University	CN	1	-	0.36
48	Pomona College	US	1	-	0.36
49	University of California, Los Angeles	US	1	-	0.36
50	Universität Konstanz	DE	0	0.15	0.20
51	Towson University	US	1	-	0.34
52	Xi'an Jiaotong University	CN	1	0.20	0.14
53	Purdue University West Lafayette	US	1	-	0.34
54	University of Tsukuba		0	0.16	0.17
55	Paderborn University	DE	1	-	0.33
56	Max Planck Institute for Mathematics	DE	2	-	0.33
57	University of Rome Tor Vergata	IT	1	-	0.31
58	ETH Zurich	CH	1	-	0.31
59	Sofia University	BG	1	-	0.31
60	Technical University of Sofia	BG	1	-	0.31
61	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	1	-	0.30
62	Heinrich Heine University Düsseldorf	DE	1	-	0.30
63	Nihon University	JP	1	-	0.30
64	University of Concepción	CL	0	0.29	0.00
65	Université de Montréal	CA	1	-	0.29
66	University of Debrecen	HU	1	0.08	0.20
67	University of Colorado Boulder	US	1	-	0.28
68	École Polytechnique Fédérale de Lausanne	CH	1	-	0.26
69	Emory University	US	0	0.08	0.17
70	Yangzhou University	CN	2	-	0.25
71	University of Science and Technology of China	CN	2	-	0.25
72	Leiden University	NL	0	0.12	0.10
73	Shandong University	CN	0	0.21	0.01
74	University of Bucharest	RO	0	0.19	0.02
75	Central Michigan University	US	1	-	0.20
76	Pontifical Catholic University of Chile	CL	1	-	0.20
77	University of Missouri	US	1	-	0.20
78	Steklov Mathematical Institute	RU	1	-	0.20
79	Voronezh State University	RU	1	-	0.19
80	University of Helsinki	FI	1	-	0.19
81	University of Salerno	IT	1	-	0.18
82	University of Calgary	CA	1	-	0.17
83	Georgia Institute of Technology	US	1	-	0.17
84	Université Laval	CA	1	-	0.16
85	Utrecht University	NL	0	0.05	0.11
86	Hebrew University of Jerusalem	IL	1	0.09	0.06
87	University of Genoa	IT	1	-	0.14
88	China University of Mining and Technology (Beijing)	CN	1	-	0.14
89	Northwestern University	US	1	-	0.13
90	Institute of Mathematical Sciences	IN	1	-	0.12
91	UNSW Canberra	AU	1	-	0.12
92	Iwate University	JP	1	-	0.11
93	University of British Columbia	CA	1	-	0.10
94	University of Wisconsin-Madison	US	1	0.05	0.04
95	Koç University	TR	1	-	0.04
96	Aix-Marseille University	FR	1	-	0.03
97	Indian Institute of Science Education and Research Berhampur	IN	1	-	0.03
98	Saint Louis University Madrid	ES	1	-	-
99	Simon Bolivar University	ES	1	-	-
100	The High School Affiliated to Renmin University of China	CN	1	-	-
101	University of Bath	GB	1	-	-
102	University of Northern British Columbia	CA	1	-	-