Institutions

Where the Goldbach 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; 81 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	Shandong University	CN	3	0.94	0.81
2	University of London	GB	0	1.00	0.73
3	Princeton University	US	1	0.91	0.38
4	University of Oxford	GB	3	0.29	1.00
5	Eötvös Loránd University	HU	1	0.49	0.79
6	University of Cambridge	GB	1	0.39	0.74
7	Stanford University	US	1	0.61	0.52
8	University of Bristol	GB	1	0.41	0.58
9	Chinese Academy of Sciences	CN	0	0.32	0.63
10	University of California, Berkeley	US	0	0.55	0.34
11	University of Turku	FI	1	0.57	0.32
12	Peking University	CN	0	0.27	0.62
13	Royal Holloway University of London	GB	1	-	0.86
14	Hungarian Academy of Sciences	HU	0	0.06	0.79
15	Lomonosov Moscow State University	RU	1	0.48	0.33
16	Alfréd Rényi Institute of Mathematics	HU	2	-	0.80
17	McGill University	CA	0	0.14	0.66
18	University of Göttingen	DE	1	0.33	0.43
19	University of Illinois Urbana-Champaign	US	2	0.26	0.49
20	University of Genoa	IT	0	0.59	0.13
21	Sorbonne Université	FR	0	0.18	0.52
22	Université de Lille	FR	1	0.25	0.44
23	China University of Mining and Technology (Beijing)	CN	1	-	0.66
24	Beijing Information Science and Technology University	CN	1	-	0.66
25	Université du Québec à Montréal	CA	1	-	0.66
26	Université de Montréal	CA	2	-	0.66
27	Concordia University	CA	1	-	0.65
28	Moscow State Pedagogical Institute	RU	0	0.31	0.30
29	Université Paris Cité	FR	1	0.09	0.51
30	Comenius University Bratislava	SK	1	-	0.59
31	Purdue University West Lafayette	US	1	0.06	0.51
32	University of New South Wales	AU	0	0.22	0.33
33	Nanjing University	CN	1	0.13	0.41
34	Centre National de la Recherche Scientifique	FR	2	-	0.52
35	University of Toronto	CA	1	0.27	0.25
36	San Jose State University	US	2	-	0.51
37	Utrecht University	NL	0	0.25	0.25
38	University of Michigan	US	2	0.07	0.42
39	University of California, Los Angeles	US	1	-	0.48
40	Steklov Institute of Mathematics	RU	1	0.23	0.25
41	RAND Corporation	US	1	-	0.46
42	University of Cologne	DE	1	-	0.46
43	Heinrich Heine University Düsseldorf	DE	1	-	0.46
44	Sofia University "St. Kliment Ohridski"	BG	2	-	0.44
45	Institute of Science and Technology Austria	AT	1	-	0.43
46	University of Padua	IT	1	-	0.42
47	Nanjing Normal University	CN	1	-	0.41
48	University of Parma	IT	1	-	0.40
49	University of Waterloo	CA	1	0.12	0.27
50	Freie Universität Berlin	DE	0	0.31	0.07
51	University of Freiburg	DE	1	0.20	0.19
52	Durham University	GB	1	-	0.38
53	Heidelberg University	DE	0	0.20	0.16
54	Henan Academy of Sciences	CN	1	-	0.36
55	Columbia University	US	0	0.16	0.20
56	Philipps-Universität Marburg	DE	0	0.10	0.25
57	University of Kentucky	US	1	-	0.35
58	Graz University of Technology	AT	1	-	0.35
59	Pomona College	US	1	-	0.35
60	Towson University	US	1	-	0.34
61	Rutgers University	US	1	0.01	0.33
62	Universität Konstanz	DE	0	0.18	0.15
63	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	1	-	0.33
64	UNSW Sydney	AU	1	-	0.33
65	Technische Universität Darmstadt	DE	0	0.15	0.17
66	Queen's University at Kingston	CA	0	0.24	0.08
67	Rikkyo University	JP	1	-	0.31
68	Saitama University	JP	1	-	0.31
69	Kyushu University	JP	1	-	0.30
70	University of Missouri	US	1	-	0.30
71	Southwest University	CN	1	-	0.29
72	University of Ferrara	IT	1	-	0.29
73	West Virginia University	US	0	0.20	0.07
74	Edinburgh Napier University	GB	1	-	0.27
75	Universität Ulm	DE	1	-	0.27
76	Centrum Wiskunde & Informatica	NL	1	-	0.26
77	University of South Carolina	US	0	0.26	0.00
78	University of Hong Kong	HK	2	-	0.26
79	KTH Royal Institute of Technology	SE	1	-	0.26
80	Baltazar Zaprešić University of Applied Sciences	HR	1	-	0.25
81	ETH Zurich	CH	1	0.11	0.13
82	Tel Aviv University	IL	0	0.16	0.08
83	Pennsylvania State University	US	0	0.15	0.09
84	University of Rostock	DE	1	-	0.23
85	Victoria University of Wellington	NZ	1	-	0.23
86	Shanghai Jiao Tong University	CN	1	-	0.23
87	Universität Zürich	CH	0	0.09	0.13
88	Indiana University Bloomington	US	1	-	0.22
89	University of California, Davis	US	1	-	0.22
90	University of Virginia	US	1	-	0.20
91	University of Minnesota - Twin Cities	US	0	0.19	0.00
92	Sogang University	KR	1	-	0.18
93	Technion - Israel Institute of Technology	IL	1	-	0.17
94	Chalmers University of Technology	SE	1	-	0.15
95	South China University of Technology	CN	1	-	0.15
96	University of Rochester	US	0	0.06	0.08
97	Massachusetts Institute of Technology	US	1	-	0.13
98	University of British Columbia	CA	1	0.08	0.05
99	Hellenic Military Academy	GR	1	-	0.13
100	University of Wrocław	PL	1	-	0.12
101	Universiteit van Amsterdam		0	0.12	-
102	Virginia Tech	US	1	-	0.12
103	Xi'an Jiaotong University	CN	1	0.05	0.06
104	Skidmore College	US	1	-	0.11
105	Emory University	US	0	0.11	0.00
106	Brigham Young University	US	1	-	0.11
107	Williams College	US	1	-	0.11
108	Université Grenoble Alpes	FR	0	0.07	0.03
109	Université Laval	CA	1	-	0.10
110	Pennsylvania State University, Beaver	US	1	-	0.10
111	University of Wisconsin-Madison	US	0	0.05	0.03
112	Uniwersytet Warszawski		0	0.07	-
113	University of Wisconsin-Whitewater	US	1	-	0.06
114	Château Gombert	FR	1	-	0.05
115	Université de Bordeaux	FR	0	0.04	0.00
116	University of Arizona	US	0	0.03	0.00
117	University of Massachusetts Amherst		0	0.02	-
118	Tashkent State University	UZ	1	-	0.02
119	Stellenbosch University	ZA	1	-	0.01
120	University of Alaska, Fairbanks	US	0	0.01	0.00
121	Lehman College, CUNY	US	1	-	-