Institutions

Where the abc 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; 63 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 (hover rows for details)		Top 100	Training	Environment
1	University of Debrecen	HU	4	0.82	0.88
2	Harvard University	US	2	1.00	0.68
3	Sorbonne University	FR	2	0.28	1.00
4	Brown University	US	2	0.57	0.61
5	University of Paris-Saclay	FR	0	0.33	0.83
6	Leiden University	NL	3	0.33	0.73
7	Collège de France	FR	1	-	1.00
8	Université Paris Cité	FR	1	-	0.98
9	Centre National de la Recherche Scientifique	FR	1	-	0.96
10	University of Cambridge	GB	0	0.59	0.34
11	Massachusetts Institute of Technology	US	1	0.26	0.67
12	University of California, Berkeley	US	2	0.63	0.28
13	University of Oxford	GB	2	0.20	0.64
14	Royal Holloway University of London	GB	1	0.24	0.53
15	University of Waterloo	CA	4	-	0.72
16	University of British Columbia	CA	2	0.31	0.37
17	University of London	GB	0	0.22	0.44
18	Queen's University	CA	2	0.31	0.34
19	University of Udine	IT	1	0.31	0.32
20	Princeton University	US	0	0.23	0.39
21	Radboud University Nijmegen	NL	1	0.08	0.52
22	University of Strasbourg	FR	3	-	0.57
23	University of Vienna	AT	0	0.43	0.09
24	University of Warwick	GB	1	-	0.51
25	Graz University of Technology	AT	1	0.26	0.24
26	Université Henri Poincaré Nancy 1	FR	0	0.12	0.36
27	Max Planck Institute for Mathematics	DE	2	-	0.44
28	Pontifical Catholic University of Chile	CL	2	-	0.44
29	Columbia University	US	1	0.06	0.37
30	Université de Montréal	CA	1	-	0.42
31	McGill University	CA	1	-	0.42
32	University of Bordeaux	FR	1	0.27	0.13
33	Yale University	US	0	0.13	0.27
34	Heidelberg University	DE	0	0.13	0.26
35	University of Exeter	GB	0	0.28	0.11
36	Institute for Advanced Study	US	1	-	0.39
37	Fordham University	US	1	-	0.39
38	Rutgers University	US	1	-	0.38
39	Illinois Institute of Technology	US	0	0.21	0.15
40	University of Lorraine	FR	1	-	0.36
41	University of Rochester	US	1	0.14	0.22
42	Universität Basel	CH	0	0.14	0.21
43	University of Salzburg	AT	1	-	0.34
44	American Institute of Mathematics	US	1	-	0.33
45	California Institute of Technology	US	1	-	0.33
46	University of Concepción	CL	0	0.32	0.01
47	Scuola Normale Superiore	IT	1	-	0.32
48	Université Louis Pasteur - Strasbourg I		0	0.32	-
49	University of Milan	IT	0	0.25	0.07
50	University of New South Wales	AU	2	-	0.31
51	Roma Tre University	IT	1	-	0.29
52	Universiteit van Amsterdam		0	0.29	-
53	University of Houston	US	1	-	0.29
54	Rice University	US	1	-	0.29
55	University of California, Los Angeles	US	1	-	0.28
56	University of Regensburg	DE	1	-	0.27
57	Moscow State Pedagogical University	RU	0	0.27	0.00
58	University of Göttingen	DE	2	-	0.27
59	University of Notre Dame		0	0.26	-
60	Dartmouth College	US	1	-	0.26
61	Pennsylvania State University	US	1	-	0.25
62	Universität Zürich	CH	0	0.08	0.16
63	Institute of Mathematics, Academia Sinica	TW	1	-	0.23
64	Université Laval	CA	1	-	0.23
65	Texas State University	US	1	-	0.22
66	Tata Institute of Fundamental Research	IN	0	0.22	0.00
67	University of Colorado Boulder	US	1	-	0.22
68	University of California, San Diego	US	1	-	0.20
69	Hong Kong University of Science and Technology	HK	1	-	0.20
70	University of Mumbai	IN	0	0.20	0.00
71	University of Arizona	US	1	-	0.20
72	Aristotle University of Thessaloniki	GR	2	-	0.19
73	Michigan State University	US	1	-	0.18
74	ETH Zurich	CH	0	0.01	0.16
75	Hanoi National University of Education	VN	1	-	0.17
76	Kyoto University	JP	1	-	0.16
77	University of Illinois Chicago	US	1	-	0.16
78	Université de la Méditerranée		0	0.15	-
79	Waseda University	JP	1	-	0.14
80	University of Bucharest	RO	0	0.11	0.01
81	University of Illinois Urbana-Champaign	US	1	-	0.12
82	Tongji University	CN	1	-	0.10
83	Freie Universität Berlin	DE	0	0.07	0.03
84	University of Colorado at Boulder		0	0.10	-
85	Chalmers University of Technology	SE	1	-	0.09
86	Utah Valley University	US	1	-	0.07
87	University of Warsaw	PL	0	0.05	0.01
88	Universiteit Leiden and Université Paris-Sud XI - Orsay		0	0.05	-
89	University of Wrocław	PL	1	-	0.05
90	Universidade de São Paulo	BR	0	0.03	0.00
91	The Ohio State University	US	0	0.01	0.02
92	Tsinghua University	CN	1	-	0.02
93	Beijing Institute of Mathematical Sciences and Applications	US	1	-	0.02
94	Carleton University	CA	1	-	-
95	Gonville and Caius College, University of Cambridge	GB	1	-	-
96	National Central University	TW	1	-	-
97	National Institute of Advanced Studies	IN	1	-	-
98	University of Basel	CH	2	-	-
99	University of Bayreuth	DE	1	-	-
100	University of Caen Normandy	FR	2	-	-
101	University of Duisburg-Essen	DE	1	-	-
102	University of Zagreb	HR	1	-	-