Institutions

Where the n^2+1 prime conjecture 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; 36 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 London	GB	0	1.00	0.63
2	University of Cambridge	GB	1	0.70	0.58
3	Université de Bordeaux	FR	1	0.90	0.31
4	University of Illinois Urbana-Champaign	US	3	0.43	0.77
5	Sorbonne Université	FR	0	0.26	0.80
6	Princeton University	US	1	-	1.00
7	Rutgers University	US	2	-	1.00
8	Institute for Advanced Study	US	2	-	0.99
9	Université Paris-Saclay	FR	0	0.18	0.70
10	University of Oxford	GB	2	-	0.83
11	University of Bristol	GB	0	0.33	0.49
12	Centre National de la Recherche Scientifique	FR	2	-	0.82
13	Université Paris Cité	FR	1	-	0.79
14	Royal Holloway University of London	GB	1	-	0.77
15	University of Michigan	US	2	0.14	0.59
16	Philipps-Universität Marburg	DE	0	0.23	0.49
17	Queen's University	CA	0	0.62	0.09
18	Hungarian Academy of Sciences	HU	0	0.03	0.63
19	Institut Élie Cartan de Lorraine	FR	1	-	0.65
20	Université de Lorraine	FR	1	-	0.64
21	Alfréd Rényi Institute of Mathematics	HU	2	-	0.64
22	Eötvös Loránd University	HU	1	-	0.64
23	Shandong University	CN	2	0.21	0.42
24	University of Freiburg	DE	1	0.09	0.52
25	Tongji University	CN	1	-	0.61
26	Columbia University	US	1	-	0.61
27	University of Göttingen	DE	1	0.22	0.39
28	Shanghai University	CN	1	-	0.58
29	Shanghai Jiao Tong University	CN	1	-	0.56
30	Universität Darmstadt	DE	0	0.25	0.29
31	University of Toronto	CA	2	-	0.50
32	University of Wales	GB	1	-	0.49
33	University of Marburg	DE	2	-	0.49
34	University of Calgary	CA	2	-	0.48
35	ETH Zurich	CH	1	-	0.46
36	University of South Carolina	US	1	0.24	0.18
37	Shandong University of Finance and Economics	CN	1	-	0.41
38	Finnish Academy of Science and Letters	FI	1	-	0.40
39	University of Waterloo	CA	1	0.03	0.37
40	Universität Konstanz	DE	0	0.06	0.33
41	Université Laval	CA	2	-	0.39
42	Dartmouth College	US	1	-	0.39
43	Universität Berlin	DE	0	0.34	0.05
44	Université de Montréal	CA	1	-	0.38
45	Gesellschaft Fur Mathematik Und Datenverarbeitung	DE	1	-	0.38
46	Towson University	US	1	-	0.38
47	Universität Stuttgart	DE	0	0.10	0.27
48	Max Planck Institute for Mathematics	DE	1	-	0.37
49	Stellenbosch University	ZA	1	-	0.36
50	Purdue University West Lafayette	US	1	-	0.36
51	University of Alaska, Fairbanks	US	0	0.36	0.00
52	University of Turku	FI	1	-	0.36
53	University of California, Berkeley	US	0	0.27	0.08
54	University of Illinois Chicago	US	1	-	0.35
55	Graz University of Technology	AT	1	-	0.35
56	University of Glasgow	GB	1	-	0.34
57	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	1	-	0.34
58	Paderborn University	DE	1	-	0.34
59	University of Georgia	US	1	-	0.34
60	Beijing Information Science and Technology University	CN	1	-	0.32
61	China University of Mining and Technology (Beijing)	CN	1	-	0.32
62	University of Colorado Boulder	US	1	-	0.31
63	Heinrich Heine University Düsseldorf	DE	1	-	0.31
64	University of Milan	IT	0	0.23	0.08
65	Brigham Young University	US	1	-	0.30
66	Vladimir State Pedagogical Institute	RU	2	-	0.30
67	Château Gombert	FR	1	-	0.30
68	Sofia University "St. Kliment Ohridski"	BG	2	-	0.30
69	Baltazar Zaprešić University of Applied Sciences	HR	1	-	0.29
70	École Polytechnique Fédérale de Lausanne	CH	1	-	0.28
71	Nanjing University of Posts and Telecommunications	CN	1	-	0.28
72	Pomona College	US	1	-	0.27
73	Central Michigan University	US	1	-	0.26
74	University, New Brunswick	CA	0	0.25	0.01
75	UNSW Sydney	AU	1	-	0.26
76	Steklov Mathematical Institute	RU	1	-	0.25
77	Universität Ulm	DE	1	-	0.25
78	University of Ulm	DE	1	-	0.25
79	Nanjing Normal University	CN	1	-	0.25
80	University of Missouri	US	1	-	0.21
81	Voronezh State University	RU	1	-	0.21
82	Boğaziçi University	TR	1	-	0.16
83	Chennai Mathematical Institute	IN	1	-	0.16
84	Institute of Mathematical Sciences	IN	1	-	0.16
85	University of Salerno	IT	1	-	0.15
86	Stanford University	US	1	-	0.13
87	Xi'an Jiaotong University	CN	1	-	0.13
88	University of Florida	US	1	-	0.12
89	Petrozavodsk State University	RU	1	-	0.11
90	University of Rostock	DE	1	-	0.11
91	Indian Institute of Technology Gandhinagar	IN	1	-	0.10
92	Charles University	CZ	1	-	0.08
93	Harish-Chandra Research Institute	IN	1	-	0.05
94	University of Warsaw	PL	1	-	0.05
95	Jimei University	CN	1	-	0.04
96	University of Minnesota - Twin Cities	US	0	0.02	0.00
97	University of Tsukuba	JP	1	-	0.00
98	University of Northern British Columbia	CA	1	-	-