Institutions

Where Legendre's 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; 47 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	Royal Holloway University of London	GB	1	0.89	0.70
2	University of Genoa	IT	1	1.00	0.38
3	University of Cambridge	GB	1	0.78	0.58
4	University of Illinois Urbana-Champaign	US	5	0.35	1.00
5	Université de Bordeaux	FR	0	0.97	0.01
6	Université de Montréal	CA	2	0.38	0.60
7	Eötvös Loránd University	HU	1	0.47	0.51
8	Birkbeck, University of London	GB	0	0.29	0.59
9	Queen's University	CA	1	0.49	0.34
10	University of Oxford	GB	3	0.05	0.78
11	University of Toronto	CA	1	0.38	0.43
12	University of California, Berkeley	US	0	0.52	0.28
13	Université Paris-Saclay	FR	0	0.28	0.40
14	University of California, Los Angeles	US	1	0.36	0.30
15	Moscow State Pedagogical Institute	RU	0	0.45	0.19
16	University of Michigan	US	3	-	0.62
17	Université du Québec à Montréal	CA	1	-	0.59
18	Heinrich Heine University Düsseldorf	DE	1	0.27	0.26
19	Université Paris Cité	FR	1	0.07	0.44
20	Alfréd Rényi Institute of Mathematics	HU	1	-	0.51
21	University of Parma	IT	1	-	0.51
22	Université Henri Poincaré Nancy 1	FR	0	0.11	0.39
23	Northwestern University	US	1	-	0.49
24	Sorbonne Université	FR	0	0.04	0.45
25	University of Göttingen	DE	1	0.26	0.22
26	University of Illinois Chicago	US	1	-	0.48
27	Universität Darmstadt	DE	0	0.32	0.14
28	University of Turku	FI	2	-	0.47
29	Centre National de la Recherche Scientifique	FR	4	-	0.46
30	Philipps-Universität Marburg	DE	0	0.31	0.15
31	University of Padua	IT	1	-	0.46
32	Stanford University	US	1	-	0.45
33	Shandong University	CN	2	0.28	0.17
34	University of Alaska, Fairbanks	US	0	0.44	0.00
35	China University of Mining and Technology (Beijing)	CN	2	-	0.44
36	Beijing Information Science and Technology University	CN	1	-	0.44
37	San Jose State University	US	1	-	0.43
38	State Key Laboratory of Cryptology	CN	1	-	0.43
39	University of Waterloo	CA	2	-	0.43
40	Institut Élie Cartan de Lorraine	FR	1	-	0.40
41	ETH Zurich	CH	1	0.13	0.27
42	Emory University	US	0	0.29	0.10
43	Château Gombert	FR	1	-	0.39
44	Aix-Marseille Université	FR	1	-	0.39
45	University of Freiburg	DE	1	-	0.38
46	Université Laval	CA	2	-	0.38
47	Dartmouth College	US	1	-	0.38
48	Rutgers University	US	1	-	0.38
49	University of Bristol	GB	2	-	0.38
50	Tongji University	CN	1	-	0.35
51	University of Milan	IT	1	-	0.34
52	Universität Berlin	DE	0	0.32	0.02
53	University of Bergamo	IT	1	-	0.34
54	Graduate Center, CUNY	US	1	-	0.33
55	Vilnius University	LT	1	-	0.32
56	UNSW Sydney	AU	1	-	0.32
57	University of Lyon	FR	1	-	0.31
58	Durham University	GB	1	-	0.31
59	Stellenbosch University	ZA	1	-	0.31
60	Shanghai Jiao Tong University	CN	1	-	0.30
61	Technion - Israel Institute of Technology	IL	1	-	0.30
62	Graz University of Technology	AT	1	-	0.29
63	Lomonosov Moscow State University	RU	0	0.08	0.20
64	Politecnico di Torino	IT	1	-	0.28
65	Universität Ulm	DE	1	-	0.27
66	Andhra University	IN	1	-	0.26
67	University of Colorado Boulder	US	1	-	0.26
68	University of Georgia	US	1	-	0.25
69	University of Salerno	IT	2	-	0.24
70	Tel Aviv University	IL	1	-	0.23
71	University of Minnesota - Twin Cities	US	0	0.22	0.00
72	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	1	-	0.22
73	Abdus Salam International Centre for Theoretical Physics	IT	1	-	0.22
74	Université de Lille	FR	0	0.03	0.18
75	University of South Carolina	US	0	0.18	0.03
76	Steklov Mathematical Institute	RU	1	-	0.21
77	Brigham Young University	US	1	-	0.20
78	University of Waikato	NZ	1	-	0.20
79	Ghent University	BE	1	-	0.19
80	University of Bucharest	RO	0	0.19	0.01
81	Boğaziçi University	TR	1	-	0.18
82	Sogang University	KR	1	-	0.17
83	Towson University	US	1	-	0.17
84	University of Kentucky	US	1	-	0.16
85	University of Mumbai	IN	0	0.10	0.06
86	Victoria University of Wellington	NZ	1	-	0.15
87	University of Zanjan	IR	1	-	0.15
88	Baltazar Zaprešić University of Applied Sciences	HR	1	-	0.13
89	Leiden University	NL	1	-	0.12
90	Hellenic Military Academy	GR	1	-	0.09
91	University, New Brunswick	CA	0	0.07	0.01
92	University of Missouri	US	1	-	0.08
93	Indian Institute of Technology Bombay	IN	1	-	0.07
94	Sofia University "St. Kliment Ohridski"	BG	1	-	0.06
95	Nanjing University of Posts and Telecommunications	CN	1	-	0.04
96	Örebro University	SE	1	-	0.04
97	University of Lethbridge	CA	1	-	0.02
98	Meiji Gakuin University	JP	1	-	-