Institutions

Where Legendre's 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 93 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	1	0.90	0.76
2	University of Oxford	GB	5	0.46	1.00
3	University of Genoa	IT	1	1.00	0.28
4	University of Illinois Urbana-Champaign	US	5	0.40	0.78
5	University of Cambridge	GB	1	0.46	0.58
6	University of California, Berkeley	US	0	0.78	0.24
7	Birkbeck, University of London	GB	0	0.33	0.62
8	Université Paris-Saclay	FR	1	0.37	0.40
9	Imperial College London	GB	0	0.09	0.62
10	University of Bristol	GB	1	0.21	0.50
11	Shandong University	CN	3	0.37	0.34
12	Université de Montréal	CA	1	0.41	0.26
13	University of California, Los Angeles	US	1	0.39	0.24
14	University of Warwick	GB	1	-	0.61
15	Queen's University	CA	1	0.32	0.26
16	University of Göttingen	DE	1	0.29	0.17
17	University of Turku	FI	2	-	0.45
18	University of Michigan	US	2	0.10	0.35
19	University of Alaska, Fairbanks	US	0	0.42	0.00
20	Université Paris-Est Créteil Val-de-Marne	FR	1	-	0.41
21	Tel Aviv University	IL	2	-	0.40
22	Université Paris Cité	FR	1	-	0.40
23	Philipps-Universität Marburg	DE	0	0.31	0.10
24	San Jose State University	US	1	-	0.39
25	Stanford University	US	1	-	0.38
26	Universität Berlin	DE	0	0.35	0.03
27	Rutgers University	US	1	0.15	0.22
28	Université de Bordeaux	FR	0	0.36	0.00
29	Cardiff University	GB	1	-	0.36
30	ETH Zurich	CH	2	-	0.35
31	University of Parma	IT	1	-	0.35
32	Technion - Israel Institute of Technology	IL	1	-	0.35
33	University of Toronto	CA	1	-	0.33
34	University of Waterloo	CA	2	-	0.32
35	Alfréd Rényi Institute of Mathematics	HU	2	-	0.30
36	University of Freiburg	DE	1	-	0.30
37	Purdue University West Lafayette	US	1	-	0.30
38	University of Padua	IT	1	-	0.30
39	University of Rochester	US	0	0.15	0.13
40	University of Mississippi	US	2	-	0.26
41	University of South Carolina	US	0	0.24	0.02
42	Heinrich Heine University Düsseldorf	DE	1	0.13	0.13
43	Concordia University	CA	1	-	0.25
44	Dartmouth College	US	1	-	0.25
45	University of Bucharest	RO	0	0.23	0.00
46	Chinese Academy of Sciences	CN	1	-	0.23
47	University of Minnesota - Twin Cities	US	0	0.22	0.01
48	China University of Mining and Technology (Beijing)	CN	1	-	0.23
49	Universität Freiburg im Breisgau		0	0.22	-
50	Stellenbosch University	ZA	1	-	0.22
51	Universität Ulm	DE	1	-	0.21
52	University of Helsinki	FI	1	-	0.21
53	University of Georgia	US	1	-	0.20
54	Politecnico di Torino	IT	1	-	0.19
55	Université Henri Poincaré Nancy 1	FR	0	0.08	0.11
56	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	1	-	0.18
57	Victoria University of Wellington	NZ	1	-	0.18
58	Nanjing University	CN	0	0.11	0.06
59	Brigham Young University	US	1	-	0.17
60	University of Kentucky	US	1	-	0.17
61	University of Missouri	US	1	-	0.15
62	Towson University	US	1	-	0.15
63	Adam Mickiewicz University in Poznań	PL	1	-	0.14
64	Steklov Mathematical Institute	RU	1	-	0.13
65	Shanghai Jiao Tong University	CN	1	-	0.12
66	Max Planck Institute for Mathematics	DE	1	-	0.11
67	Leiden University	NL	0	0.05	0.06
68	Central Michigan University	US	1	-	0.11
69	Boğaziçi University	TR	1	-	0.11
70	Hellenic Military Academy	GR	1	-	0.11
71	Koç University	TR	1	-	0.10
72	Shanghai University	CN	1	-	0.10
73	University of Washington		0	0.09	-
74	Pontificia Universidad Católica del Perú	PE	1	-	0.08
75	University of Wisconsin-Madison	US	0	0.05	0.03
76	University of Missouri - Columbia		0	0.08	-
77	Nanjing University of Finance and Economics	CN	1	-	0.07
78	University of Salerno	IT	1	-	0.06
79	Nihon University	JP	1	-	0.06
80	University of Tennessee at Chattanooga	US	1	-	0.06
81	Xi'an Jiaotong University	CN	1	-	0.04
82	UNSW Canberra	AU	1	-	0.03
83	University of British Columbia	CA	1	-	0.02
84	North China University of Water Resources and Electric Power	CN	1	-	0.02
85	University of New South Wales	AU	1	-	0.02
86	University of Glasgow	GB	1	-	0.01
87	University of Minnesota	US	1	-	0.01
88	Kings College London	GB	1	-	-
89	Northern Michigan University	US	1	-	-
90	University of Queensland	AU	1	-	-