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 94 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	0.87	0.78
2	University of Oxford	GB	5	0.45	1.00
3	University of Genoa	IT	1	1.00	0.30
4	University of Illinois Urbana-Champaign	US	5	0.41	0.88
5	University of California, Berkeley	US	0	0.79	0.27
6	University of Cambridge	GB	1	0.45	0.59
7	Birkbeck, University of London	GB	0	0.31	0.64
8	Université de Montréal	CA	1	0.53	0.29
9	Shandong University	CN	3	0.38	0.40
10	Imperial College London	GB	0	0.07	0.64
11	University of Bristol	GB	1	0.18	0.49
12	University of California, Los Angeles	US	1	0.38	0.26
13	Queen's University	CA	1	0.33	0.28
14	University of Michigan	US	2	0.16	0.39
15	Centre National de la Recherche Scientifique	FR	2	-	0.54
16	Université Paris-Saclay	FR	1	-	0.52
17	Université Paris Cité	FR	1	-	0.52
18	Heinrich Heine University Düsseldorf	DE	1	0.29	0.23
19	University of Turku	FI	2	-	0.47
20	University of Göttingen	DE	1	0.26	0.19
21	Philipps-Universität Marburg	DE	0	0.32	0.12
22	Tel Aviv University	IL	2	-	0.44
23	San Jose State University	US	1	-	0.43
24	Stanford University	US	1	-	0.43
25	University of Alaska, Fairbanks	US	0	0.43	0.00
26	ETH Zurich	CH	2	-	0.40
27	Rutgers University	US	1	0.15	0.24
28	University of Waterloo	CA	2	-	0.40
29	University of Parma	IT	1	-	0.39
30	Technion - Israel Institute of Technology	IL	1	-	0.38
31	University of Toronto	CA	1	-	0.37
32	Cardiff University	GB	1	-	0.36
33	University of Freiburg	DE	1	-	0.35
34	Université de Bordeaux	FR	0	0.34	0.01
35	Alfréd Rényi Institute of Mathematics	HU	2	-	0.34
36	University of Padua	IT	1	-	0.34
37	Universität Berlin	DE	0	0.30	0.03
38	Purdue University West Lafayette	US	1	-	0.33
39	Chinese Academy of Sciences	CN	1	-	0.30
40	China University of Mining and Technology (Beijing)	CN	1	-	0.29
41	Concordia University	CA	1	-	0.29
42	University of Mississippi	US	2	-	0.28
43	Dartmouth College	US	1	-	0.28
44	University of Rochester	US	0	0.13	0.14
45	Université Henri Poincaré Nancy 1	FR	0	0.14	0.13
46	Stellenbosch University	ZA	1	-	0.25
47	Universität Ulm	DE	1	-	0.25
48	University of Bucharest	RO	0	0.24	0.00
49	University of Minnesota - Twin Cities	US	0	0.22	0.01
50	University of Helsinki	FI	1	-	0.23
51	University of South Carolina	US	0	0.21	0.03
52	University of Georgia	US	1	-	0.22
53	Universität Freiburg im Breisgau		0	0.22	-
54	Politecnico di Torino	IT	1	-	0.21
55	Victoria University of Wellington	NZ	1	-	0.21
56	Nanjing University	CN	0	0.12	0.08
57	University of Missouri - Columbia		0	0.20	-
58	Brigham Young University	US	1	-	0.18
59	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	1	-	0.18
60	University of Kentucky	US	1	-	0.18
61	Max Planck Institute for Mathematics	DE	1	-	0.17
62	Steklov Mathematical Institute	RU	1	-	0.17
63	Towson University	US	1	-	0.15
64	Adam Mickiewicz University in Poznań	PL	1	-	0.15
65	Shanghai Jiao Tong University	CN	1	-	0.12
66	Central Michigan University	US	1	-	0.12
67	Leiden University	NL	0	0.04	0.08
68	University of Missouri	US	1	-	0.12
69	Xi'an Jiaotong University	CN	1	-	0.12
70	Hellenic Military Academy	GR	1	-	0.11
71	Boğaziçi University	TR	1	-	0.11
72	Koç University	TR	1	-	0.10
73	Shanghai University	CN	1	-	0.10
74	University of Washington		0	0.10	-
75	Nanjing University of Finance and Economics	CN	1	-	0.08
76	University of Wisconsin-Madison	US	0	0.04	0.03
77	Nihon University	JP	1	-	0.07
78	Pontificia Universidad Católica del Perú	PE	1	-	0.07
79	University of Tennessee at Chattanooga	US	1	-	0.07
80	University of Salerno	IT	1	-	0.06
81	University of British Columbia	CA	1	-	0.06
82	Australian National University	AU	1	-	0.03
83	North China University of Water Resources and Electric Power	CN	1	-	0.02
84	University of New South Wales	AU	1	-	0.02
85	University of Minnesota	US	1	-	0.01
86	University of Glasgow	GB	1	-	0.01
87	Kings College London	GB	1	-	-
88	Northern Michigan University	US	1	-	-
89	University of Queensland	AU	1	-	-