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; 71 of 89 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	0.80	0.76
2	University of Oxford	GB	5	0.41	1.00
3	Stanford University	US	1	1.00	0.40
4	Shandong University	CN	3	0.91	0.35
5	Tel Aviv University	IL	2	0.80	0.42
6	University of Genoa	IT	1	0.91	0.29
7	University of Illinois Urbana-Champaign	US	5	0.36	0.81
8	University of Turku	FI	2	0.55	0.47
9	University of Cambridge	GB	1	0.42	0.59
10	University of California, Berkeley	US	0	0.71	0.25
11	Princeton University	US	0	0.76	0.19
12	Birkbeck, University of London	GB	0	0.30	0.63
13	Eötvös Loránd University	HU	0	0.52	0.31
14	University of Paris-Saclay	FR	1	0.33	0.41
15	Imperial College London	GB	0	0.08	0.63
16	University of Bristol	GB	1	0.19	0.50
17	University of Warwick	GB	1	-	0.62
18	University of California, Los Angeles	US	1	0.35	0.25
19	Dartmouth College	US	1	0.33	0.26
20	Université de Montréal	CA	1	0.32	0.26
21	Queen's University	CA	1	0.29	0.26
22	Peking University	CN	0	0.26	0.24
23	ETH Zurich	CH	2	0.18	0.29
24	University of Göttingen	DE	1	0.26	0.18
25	Pennsylvania State University	US	0	0.39	0.05
26	Harvard University	US	0	0.37	0.05
27	Université Paris-Est Créteil Val-de-Marne	FR	1	-	0.42
28	Université Paris Cité	FR	1	-	0.41
29	San Jose State University	US	1	-	0.40
30	Emory University	US	0	0.30	0.09
31	Adam Mickiewicz University in Poznań	PL	1	0.24	0.14
32	Cardiff University	GB	1	-	0.37
33	Rutgers University	US	1	0.13	0.23
34	Technion - Israel Institute of Technology	IL	1	-	0.36
35	University of Parma	IT	1	-	0.36
36	University of Warsaw	PL	0	0.34	0.01
37	University of Freiburg	DE	0	0.20	0.15
38	McGill University	CA	0	0.09	0.26
39	University of Toronto	CA	1	-	0.34
40	University of Bordeaux	FR	0	0.32	0.00
41	University of Waterloo	CA	2	-	0.32
42	Alfréd Rényi Institute of Mathematics	HU	2	-	0.31
43	Freie Universität Berlin	DE	0	0.28	0.03
44	Australian National University	AU	0	0.28	0.03
45	Yale University	US	0	0.24	0.07
46	University of Padua	IT	1	-	0.31
47	Purdue University West Lafayette	US	1	-	0.30
48	University of Mississippi	US	2	-	0.27
49	University of Rochester	US	0	0.14	0.13
50	Concordia University	CA	1	-	0.26
51	Chinese Academy of Sciences	CN	1	-	0.25
52	China University of Mining and Technology (Beijing)	CN	1	-	0.25
53	Heinrich Heine University Düsseldorf	DE	1	0.12	0.12
54	University of South Carolina	US	0	0.21	0.02
55	University of Michigan	US	1	0.09	0.14
56	University of Helsinki	FI	1	-	0.22
57	University of Bucharest	RO	0	0.22	0.00
58	University of Georgia	US	1	-	0.21
59	Clemson University	US	0	0.12	0.08
60	University of Minnesota - Twin Cities	US	0	0.20	0.00
61	Politecnico di Torino	IT	1	-	0.19
62	University of Ulm	DE	1	-	0.19
63	Victoria University of Wellington	NZ	1	-	0.19
64	Brigham Young University	US	1	-	0.18
65	Nanjing University	CN	0	0.10	0.07
66	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	1	-	0.17
67	University of Kentucky	US	1	-	0.17
68	University of Missouri	US	1	-	0.16
69	Towson University	US	1	-	0.15
70	Université Henri Poincaré Nancy 1	FR	0	0.07	0.07
71	Steklov Mathematical Institute	RU	1	-	0.14
72	Shanghai Jiao Tong University	CN	1	-	0.11
73	Max Planck Institute for Mathematics	DE	1	-	0.11
74	Boğaziçi University	TR	1	-	0.11
75	Hellenic Military Academy	GR	1	-	0.11
76	Leiden University	NL	0	0.05	0.06
77	Koç University	TR	1	-	0.10
78	Shanghai University	CN	1	-	0.09
79	Pontificia Universidad Católica del Perú	PE	1	-	0.09
80	University of Washington		0	0.08	-
81	Central Michigan University	US	1	-	0.07
82	Nanjing University of Finance and Economics	CN	1	-	0.07
83	University of Missouri - Columbia		0	0.07	-
84	University of Wisconsin-Madison	US	0	0.04	0.03
85	Nihon University	JP	1	-	0.06
86	University of Salerno	IT	1	-	0.06
87	University of Tennessee at Chattanooga	US	1	-	0.06
88	Xi'an Jiaotong University	CN	1	-	0.04
89	UNSW Canberra	AU	1	-	0.03
90	University of Rome Tor Vergata	IT	1	-	0.02
91	University of British Columbia	CA	1	-	0.02
92	North China University of Water Resources and Electric Power	CN	1	-	0.02
93	Dalhousie University	CA	1	-	-
94	Kings College London	GB	1	-	-
95	The High School Affiliated to Renmin University of China	CN	1	-	-
96	University of Queensland	AU	1	-	-