Institutions

Where Landau's problems on prime numbers 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; 43 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	0.90	0.78
2	University of Cambridge	GB	1	0.76	0.63
3	University of Oxford	GB	4	0.31	1.00
4	University of Illinois Urbana-Champaign	US	4	0.42	0.68
5	Imperial College London	GB	0	0.43	0.65
6	University of California, Berkeley	US	0	0.69	0.34
7	University of Genoa	IT	0	0.91	0.11
8	Université de Bordeaux	FR	0	1.00	0.01
9	University of Göttingen	DE	3	0.55	0.45
10	Birkbeck, University of London	GB	0	0.23	0.65
11	University of Bristol	GB	0	0.44	0.42
12	Shandong University	CN	2	0.38	0.31
13	Sorbonne Université	FR	0	0.25	0.43
14	Eötvös Loránd University	HU	1	0.11	0.52
15	Philipps-Universität Marburg	DE	0	0.35	0.22
16	Stanford University	US	2	-	0.53
17	Alfréd Rényi Institute of Mathematics	HU	1	-	0.53
18	San Jose State University	US	1	-	0.52
19	Beijing Information Science and Technology University	CN	1	-	0.51
20	China University of Mining and Technology (Beijing)	CN	1	-	0.51
21	Purdue University West Lafayette	US	1	-	0.50
22	Université de Montréal	CA	2	0.01	0.48
23	Comenius University Bratislava	SK	1	-	0.48
24	Centre National de la Recherche Scientifique	FR	2	-	0.45
25	Universität Berlin	DE	0	0.40	0.05
26	Université Paris Cité	FR	1	-	0.42
27	Heidelberg University	DE	0	0.28	0.14
28	Queen's University	CA	0	0.35	0.07
29	Utrecht University	NL	0	0.32	0.09
30	Institute of Science and Technology Austria	AT	2	-	0.41
31	Université Paris-Saclay	FR	0	0.01	0.38
32	Butler University	US	1	-	0.39
33	University of Alaska, Fairbanks	US	0	0.36	0.00
34	University of Waterloo	CA	2	0.16	0.20
35	Tongji University	CN	1	-	0.35
36	University of Michigan	US	2	-	0.34
37	Technische Universität Darmstadt	DE	0	0.19	0.15
38	University of Parma	IT	1	-	0.33
39	Institut Élie Cartan de Lorraine	FR	1	-	0.33
40	Rutgers University	US	2	-	0.33
41	Shanghai Jiao Tong University	CN	1	-	0.33
42	University of Padua	IT	1	-	0.33
43	University of New South Wales	AU	0	0.30	0.01
44	University of Wales	GB	1	-	0.32
45	Princeton University	US	1	-	0.31
46	University of Cologne	DE	2	-	0.30
47	Dartmouth College	US	1	-	0.30
48	Shandong Normal University	CN	1	-	0.30
49	University of Turku	FI	1	-	0.29
50	University of California, Los Angeles	US	1	-	0.29
51	University of Freiburg	DE	1	-	0.28
52	Tianjin University	CN	1	-	0.28
53	RAND Corporation	US	1	-	0.27
54	University of Wisconsin-Madison	US	0	0.24	0.03
55	University of Toronto	CA	1	-	0.25
56	Graz University of Technology	AT	1	-	0.25
57	University of Wrocław	PL	1	-	0.25
58	University of Georgia	US	1	-	0.25
59	Tufts University	US	1	-	0.24
60	Massachusetts Institute of Technology	US	1	-	0.23
61	Université Laval	CA	2	-	0.23
62	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	1	-	0.22
63	University of Colorado Boulder	US	1	-	0.22
64	Henan Academy of Sciences	CN	1	-	0.22
65	Finnish Academy of Science and Letters	FI	1	-	0.22
66	University of Missouri	US	1	-	0.22
67	Université Grenoble Alpes	FR	0	0.13	0.08
68	Stellenbosch University	ZA	1	-	0.20
69	Brown University	US	1	-	0.19
70	University of Hong Kong	HK	2	-	0.19
71	University of Mississippi	US	1	-	0.18
72	University of South Carolina	US	0	0.15	0.03
73	Universität Zürich	CH	0	0.03	0.14
74	University of Canberra	AU	1	-	0.17
75	Universidade de Brasília	BR	1	-	0.16
76	Baltazar Zaprešić University of Applied Sciences	HR	1	-	0.16
77	Andhra University	IN	1	-	0.14
78	University of Kentucky	US	1	-	0.14
79	University of Lyon	FR	1	-	0.14
80	Château Gombert	FR	1	-	0.13
81	Lomonosov Moscow State University	RU	1	0.10	0.03
82	Towson University	US	1	-	0.13
83	Brigham Young University	US	1	-	0.13
84	Aix-Marseille Université	FR	1	-	0.12
85	Nagoya University	JP	1	-	0.12
86	Victoria University of Wellington	NZ	1	-	0.12
87	South China University of Technology	CN	1	-	0.12
88	Tata Institute of Fundamental Research	IN	1	-	0.09
89	Indian Institute of Technology Bhubaneswar	IN	1	-	0.09
90	University of Bucharest	RO	0	0.08	0.00
91	University of Calgary	CA	1	-	0.08
92	University of Manitoba	CA	1	-	0.07
93	Southwest University	CN	1	-	0.07
94	Nanjing Normal University	CN	1	-	0.06
95	Sofia University "St. Kliment Ohridski"	BG	2	-	0.05
96	Sogang University	KR	1	-	0.04
97	Tel Aviv University	IL	0	0.02	0.01
98	University of Virginia	US	1	-	0.03
99	Technion - Israel Institute of Technology	IL	1	-	0.01
100	Federal University of Uberlândia	BR	1	-	-