Institutions

Where the abc 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; 40 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	University of Debrecen	HU	5	1.00	1.00
2	University of British Columbia	CA	2	0.68	0.29
3	Sorbonne Université	FR	1	0.32	0.57
4	University of Göttingen	DE	2	0.31	0.39
5	University of Salzburg	AT	3	-	0.70
6	University of Udine	IT	1	0.33	0.37
7	Royal Holloway University of London	GB	1	0.26	0.39
8	University of Oxford	GB	1	0.23	0.42
9	Birkbeck, University of London	GB	0	0.30	0.31
10	University of Waterloo	CA	4	0.08	0.52
11	Centre National de la Recherche Scientifique	FR	2	-	0.58
12	Imperial College London	GB	0	0.23	0.31
13	University of Granada	ES	3	-	0.54
14	Moscow State Pedagogical Institute	RU	0	0.29	0.22
15	University of California, Berkeley	US	0	0.50	0.00
16	Queen's University	CA	1	0.35	0.15
17	University of Würzburg	DE	2	-	0.47
18	University of Cambridge	GB	0	0.18	0.23
19	Institute of Fundamental Research	IN	0	0.25	0.15
20	Henan Academy of Sciences	CN	1	-	0.39
21	Johannes Gutenberg University Mainz	DE	1	-	0.39
22	University of Texas at Austin	US	1	-	0.39
23	University of Warwick	GB	1	-	0.39
24	North China University of Water Resources and Electric Power	CN	1	-	0.38
25	Texas State University	US	1	-	0.38
26	University of Graz	AT	0	0.20	0.18
27	University of Southern California	US	0	0.22	0.16
28	Institute of Technology	US	0	0.25	0.12
29	Universität Hamburg	DE	0	0.32	0.05
30	Pontifical Catholic University of Chile	CL	1	-	0.36
31	Pontificia Universidad Católica de Chile	CL	1	-	0.36
32	University of Alaska, Fairbanks	US	0	0.35	0.00
33	Utrecht University	NL	0	0.13	0.21
34	Scuola Normale Superiore	IT	1	-	0.31
35	Chinese Academy of Sciences	CN	0	0.30	0.00
36	Leiden University	NL	1	-	0.30
37	Purdue University Northwest	US	1	-	0.30
38	Université de Bordeaux	FR	0	0.29	0.00
39	Helmholtz-Institute Ulm	DE	1	-	0.30
40	Pennsylvania State University	US	1	-	0.29
41	Université Laval	CA	1	0.20	0.09
42	Université de Strasbourg	FR	1	-	0.28
43	Roma Tre University	IT	1	-	0.28
44	Stellenbosch University	ZA	1	-	0.27
45	University of Illinois Chicago	US	1	-	0.27
46	Waseda University	JP	2	-	0.26
47	Shandong University	CN	0	0.14	0.12
48	University of Michigan	US	0	0.16	0.09
49	Purdue University West Lafayette	US	1	-	0.25
50	Seikei University	JP	1	-	0.25
51	Vilnius University	LT	1	-	0.24
52	Dartmouth College	US	1	-	0.24
53	Lomonosov Moscow State University	RU	2	-	0.24
54	UNSW Sydney	AU	2	-	0.23
55	Brigham Young University	US	1	-	0.23
56	Northern Illinois University	US	1	-	0.23
57	University of Houston	US	1	-	0.22
58	Rice University	US	1	-	0.22
59	Academia Sinica	TW	1	-	0.22
60	University of Rochester	US	0	0.12	0.10
61	Freie Universität Berlin	DE	0	0.17	0.04
62	Queensland University of Technology	AU	1	-	0.20
63	Xian Polytechnic University	CN	1	-	0.20
64	Université Henri Poincaré Nancy 1	FR	0	0.03	0.16
65	University of Arizona	US	1	-	0.20
66	Center for Theoretical Physics	PL	1	-	0.20
67	Sofia University "St. Kliment Ohridski"	BG	1	-	0.20
68	California Institute of Technology	US	2	-	0.19
69	Universität Basel	CH	0	0.07	0.12
70	Graz University of Technology	AT	2	-	0.18
71	Koç University	TR	1	-	0.17
72	University of Lorraine	FR	1	-	0.16
73	UM-DAE Centre for Excellence in Basic Sciences	IN	1	-	0.16
74	Institute of Mathematics, National Academy of Sciences of Belarus	BY	1	-	0.16
75	University of Colorado Boulder	US	1	-	0.16
76	Michigan State University	US	1	-	0.15
77	Yale University	US	1	-	0.15
78	De La Salle University	PH	1	-	0.15
79	Cardiff University	GB	1	-	0.15
80	Fordham University	US	1	-	0.15
81	Hanoi National University of Education	VN	1	-	0.14
82	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	1	-	0.13
83	Universität Zürich	CH	0	0.01	0.12
84	Indian Institute of Technology Dharwad	IN	1	-	0.12
85	Shandong Normal University	CN	1	-	0.12
86	Massachusetts Institute of Technology	US	1	-	0.12
87	Boston University	US	1	-	0.12
88	University of Vienna	AT	0	0.02	0.09
89	University of Split	HR	1	-	0.11
90	Brown University	US	1	-	0.11
91	University of Science and Technology of China	CN	1	-	0.10
92	Tongji University	CN	1	-	0.08
93	Washington University in St. Louis	US	1	-	0.05
94	Universität Berlin	DE	0	0.01	0.04
95	Australian National University	AU	1	-	0.04
96	Kyoto University	JP	1	-	0.02
97	University of Basel	CH	1	-	-