Institutions

Where the twin 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; 71 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	Stanford University	US	2	1.00	0.48
2	University of Oxford	GB	4	0.24	1.00
3	Princeton University	US	2	0.58	0.65
4	Royal Holloway University of London	GB	1	0.46	0.77
5	University of Cambridge	GB	2	0.55	0.61
6	Queen's University	CA	3	0.26	0.65
7	University of Illinois Urbana-Champaign	US	4	0.21	0.65
8	University of London	GB	0	0.20	0.64
9	Rutgers University	US	1	0.17	0.62
10	Birkbeck, University of London	GB	0	0.14	0.64
11	University of Turku	FI	2	0.33	0.45
12	University of Genoa	IT	1	0.45	0.26
13	University of Bordeaux	FR	1	0.54	0.12
14	Institute for Advanced Study	US	1	-	0.65
15	University of California, Berkeley	US	0	0.34	0.31
16	Eötvös Loránd University	HU	0	0.26	0.32
17	ETH Zurich	CH	2	0.10	0.48
18	University of Michigan	US	1	0.26	0.29
19	University of California, Los Angeles	US	1	0.16	0.40
20	University of Paris-Saclay	FR	1	0.15	0.40
21	University of Bristol	GB	0	0.09	0.43
22	Pennsylvania State University	US	1	0.23	0.29
23	Dartmouth College	US	1	0.19	0.31
24	Sorbonne University	FR	0	0.11	0.38
25	San Jose State University	US	1	-	0.48
26	Tel Aviv University	IL	2	0.17	0.30
27	University of Milan	IT	0	0.21	0.21
28	University of Freiburg	DE	0	0.12	0.27
29	Université Paris-Est Créteil Val-de-Marne	FR	1	-	0.39
30	Northwestern University	US	1	-	0.38
31	Massachusetts Institute of Technology	US	1	0.24	0.14
32	University of Illinois Chicago	US	1	-	0.36
33	Université de Montréal	CA	1	0.08	0.28
34	University of Toronto	CA	1	-	0.36
35	Harvard University	US	0	0.22	0.14
36	University of California, Santa Barbara	US	1	-	0.36
37	Cardiff University	GB	1	-	0.34
38	Australian National University	AU	1	0.12	0.21
39	University of Parma	IT	1	-	0.33
40	Alfréd Rényi Institute of Mathematics	HU	3	-	0.32
41	University of Padua	IT	1	-	0.32
42	Institut Élie Cartan de Lorraine	FR	1	-	0.30
43	University of Rochester	US	0	0.06	0.23
44	Pomona College	US	1	-	0.29
45	Technion - Israel Institute of Technology	IL	1	-	0.28
46	Peking University	CN	0	0.13	0.14
47	Emory University	US	0	0.17	0.09
48	Yale University	US	0	0.07	0.18
49	Boğaziçi University	TR	1	-	0.24
50	University of Ulm	DE	2	-	0.24
51	Central Michigan University	US	1	-	0.24
52	University of Warsaw	PL	0	0.24	0.00
53	University of Göttingen	DE	1	0.10	0.13
54	University of Helsinki	FI	1	-	0.24
55	University of Waterloo	CA	1	-	0.23
56	University of Colorado Boulder	US	1	-	0.22
57	École Polytechnique Fédérale de Lausanne	CH	1	-	0.22
58	University of Lyon	FR	1	-	0.21
59	University of Missouri	US	1	-	0.21
60	UNSW Canberra	AU	1	-	0.21
61	University of Georgia	US	1	-	0.21
62	Politecnico di Torino	IT	1	-	0.20
63	Brown University	US	2	-	0.19
64	Lomonosov Moscow State University	RU	0	0.03	0.16
65	Nihon University	JP	1	-	0.19
66	Nanjing University	CN	0	0.09	0.10
67	University of Salerno	IT	1	-	0.18
68	Aix-Marseille University	FR	1	-	0.18
69	Towson University	US	1	-	0.18
70	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	1	-	0.18
71	Freie Universität Berlin	DE	0	0.16	0.01
72	University of Wisconsin-Madison	US	1	-	0.16
73	Universidade de São Paulo	BR	0	0.16	0.00
74	Steklov Mathematical Institute	RU	1	-	0.16
75	University of Kentucky	US	1	-	0.16
76	Brigham Young University	US	1	-	0.16
77	Chinese Academy of Sciences	CN	1	-	0.14
78	Université de Paris		0	0.13	-
79	University of Naples Federico II	IT	1	-	0.12
80	Hellenic Military Academy	GR	1	-	0.11
81	Max Planck Institute for Mathematics	DE	1	-	0.10
82	University of New South Wales	AU	0	0.08	0.02
83	University of Washington		0	0.10	-
84	Nanjing University of Finance and Economics	CN	1	-	0.10
85	University of Minnesota - Twin Cities	US	0	0.09	0.00
86	University of Virginia	US	1	-	0.08
87	University of Tennessee at Chattanooga	US	1	-	0.07
88	Utrecht University	NL	0	0.03	0.04
89	University of South Carolina	US	0	0.04	0.03
90	Shandong University	CN	1	0.06	0.01
91	Shanghai Jiao Tong University	CN	1	-	0.07
92	University of Waikato	NZ	1	-	0.07
93	Sofia University	BG	1	-	0.04
94	Aarhus University	DK	1	-	-
95	Case Western Reserve University	US	1	-	-
96	KU Leuven	BE	1	-	-
97	Lehman College, CUNY	US	1	-	-
98	National Institute of Science Education and Research Bhubaneswar	IN	1	-	-
99	The High School Affiliated to Renmin University of China	CN	1	-	-
100	Universidade Tecnologica Federal do Parana	BR	1	-	-
101	University of Queensland	AU	1	-	-
102	University of Utah	US	1	-	-
103	Université de Limoges	FR	1	-	-