The Top 100

Researchers active on abc conjecture and adjacent problems

Table Details

Columns

# overall rank (lower is better)
Name the researcher
Institution current affiliation
Ctry country
aX arXiv rank
OA OpenAlex rank
zM zbMATH rank
h h-index (citation impact)
Source databases that list them
YSP years since PhD (2026 minus the Math Genealogy PhD year; a dash when the PhD year is not known)

How it works. arXiv, OpenAlex and zbMATH each rank a researcher; the three ranks merge into one, weighted toward each person's strongest. Recent work counts more. Lower is better. Click any header to sort. A rank in [brackets] is an estimate, not measured. Full method.

#	Name	Institution		aX	OA	zM	h	Source	YSP
1	Kálmán Győry	University of Debrecen	HU	23	2	8	24	all_three	60
2	István Gaál	University of Debrecen	HU	2	3	40	19	all_three	39
3	Umberto Zannier	Scuola Normale Superiore	IT	24	5	6	33	all_three	-
4	Hector Pasten	Pontificia Universidad Católica de Chile	CL	1	4	62	8	all_three	16
5	Shabnam Akhtari	Pennsylvania State University	US	7	11	23	5	all_three	18
6	Florian Luca	Stellenbosch University	ZA	[26]	22	4	28	oa+zb	30
7	J. C. Rosales	University of Granada	ES	[24]	[46]	1	26	zb_only	35
8	Jan-Hendrik Evertse	Leiden University	NL	60	16	2	23	all_three	43
9	Tobias Hilgart	University of Salzburg	AT	3	15	[56]	1	arx+oa	-
10	Michael A. Bennett	University of British Columbia	CA	12	7	46	20	all_three	33
11	Amos Turchet	Roma Tre University	IT	9	8	[56]	4	arx+oa	12
12	Yann Bugeaud	Université de Strasbourg	FR	[27]	57	3	36	oa+zb	30
13	Pietro Corvaja	University of Udine	IT	55	24	7	21	all_three	31
14	Jörg Brüdern	University of Göttingen	DE	[24]	[46]	9	19	zb_only	38
15	Jeffrey D. Vaaler	University of Texas at Austin	US	[24]	[46]	10	21	zb_only	52
16	Ingrid Vukusic	University of Waterloo	CA	5	38	[54]	2	arx+oa	3
17	Tianze Wang	Henan Academy of Sciences	CN	[24]	[46]	11	2	zb_only	35
18	Samir Siksek	University of Warwick	GB	28	9	[56]	20	arx+oa	31
19	Roger C. Baker	Brigham Young University	US	[24]	[46]	12	34	zb_only	55
20	Michel Waldschmidt	Sorbonne Université	FR	16	12	68	23	all_three	54
21	Julie Tzu-Yueh Wang	Institute of Mathematics, Academia Sinica	TW	[24]	[46]	14	14	zb_only	31
22	Raimundas Vidunas	Vilnius University	LT	8	[54]	[43]	15	arxiv_only	27
23	Igor E. Shparlinski	UNSW Sydney	AU	[29]	10	[68]	42	oa_only	46
24	Wade Hindes	Texas State University	US	11	32	[56]	-	arx+oa	11
25	László Remete	University of Debrecen	HU	6	55	[56]	5	arx+oa	5
26	John Voight	University of Sydney	AU	4	75	[54]	17	arx+oa	21
27	Clemens Fuchs	University of Salzburg	AT	[27]	52	15	12	oa+zb	24
28	Glyn Harman	Royal Holloway University of London	GB	[24]	[46]	17	19	zb_only	44
29	Roger J. Cook	Queensland University of Technology	AU	[24]	[46]	18	15	zb_only	55
30	Ariyan Javanpeykar	Radboud University Nijmegen	NL	10	48	[56]	11	arx+oa	13
31	Kirti Joshi	University of Arizona	US	22	18	[56]	7	arx+oa	30
32	Quanwu Mu	Xian Polytechnic University	CN	[24]	[46]	19	5	zb_only	-
33	S. I. Dimitrov	Technical University of Sofia	BG	[24]	[46]	20	6	zb_only	-
34	Hartmut Monien	University of Bonn	DE	14	[54]	[43]	32	arxiv_only	39
35	Akinari Hoshi	Niigata University	JP	21	20	[56]	12	arx+oa	21
36	R. C. Vaughan	Pennsylvania State University	US	[24]	[46]	21	35	zb_only	56
37	Trevor D. Wooley	Purdue University West Lafayette	US	[24]	[46]	22	28	zb_only	36
38	Min Ru	University of Houston	US	[29]	113	13	21	oa+zb	36
39	Ruiwen Dong	University of Oxford	GB	18	[54]	[43]	-	arxiv_only	3
40	Wenxu Ge	North China University of Water Resources and Electric Power	CN	[24]	[52]	25	5	zb_only	-
41	J. M. Urbano-Blanco	University of Granada	ES	[24]	[46]	26	8	zb_only	21
42	Ozlem Ejder	Koç University	TR	13	83	[54]	3	arx+oa	9
43	Oleg N. German	Lomonosov Moscow State University	RU	[24]	[52]	28	11	zb_only	21
44	Alain Togbé	Purdue University Northwest	US	[26]	17	126	16	oa+zb	29
45	Wolfgang M. Schmidt	University of Colorado Boulder	US	[30]	127	16	36	oa+zb	71
46	Volker Ziegler	University of Salzburg	AT	[30]	25	[68]	12	oa_only	21
47	S. G. Dani	UM-DAE Centre for Excellence in Basic Sciences	IN	[24]	[52]	29	25	zb_only	51
48	Dominik Barth	University of Würzburg	DE	19	61	[56]	-	arx+oa	4
49	Maurice Mignotte	Université de Strasbourg	FR	[27]	30	44	24	oa+zb	52
50	Jose Arnaldo B. Dris	Independent	PH	[24]	[52]	30	5	zb_only	-
51	Andreas Wenz	University of Würzburg	DE	20	62	[56]	3	arx+oa	-
52	Si Duc Quang	Hanoi National University of Education	VN	[24]	[52]	31	13	zb_only	16
53	Cameron L. Stewart	University of Waterloo	CA	51	41	27	20	all_three	50
54	Jeffrey Lin Thunder	Northern Illinois University	US	[24]	[52]	32	11	zb_only	36
55	Stephan Baier	Ramakrishna Mission Vivekananda Educational and Research Institute	IN	[25]	[46]	33	14	zb_only	26
56	Michelle Manes	American Institute of Mathematics	US	27	43	[56]	9	arx+oa	19
57	D. Eric Freeman	Stanford University	US	[25]	[46]	34	5	zb_only	27
58	Veekesh Kumar	Indian Institute of Technology Dharwad	IN	[25]	[46]	35	2	zb_only	7
59	A. Pethö	University of Debrecen	HU	[22]	23	139	16	oa+zb	50
60	M. Ram Murty	Queen's University	CA	[30]	31	[68]	25	oa_only	46
61	È. I. Kovalevskaya	Institute of Mathematics, National Academy of Sciences of Belarus	BY	[25]	[46]	36	4	zb_only	51
62	Aaron Levin	Michigan State University	US	26	137	24	11	all_three	21
63	Attila Bérczes	University of Debrecen	HU	[30]	33	[68]	10	oa_only	26
64	Borka Jadrijević	University of Split	HR	[25]	19	177	7	oa+zb	25
65	Irene I. Bouw	University of Ulm	DE	25	77	[54]	10	arx+oa	28
66	Huafeng Liu	Shandong Normal University	CN	[25]	[52]	37	55	zb_only	9
67	P. A. García-Sánchez	University of Granada	ES	[25]	[52]	38	24	zb_only	30
68	J. Mueller	Fordham University	US	[25]	[46]	39	-	zb_only	49
69	Wayne Peng	University of Science and Technology of China	CN	33	[54]	[43]	3	arxiv_only	6
70	Claude Levesque	Université Laval	CA	15	45	187	10	all_three	50
71	Boris Adamczewski	Centre National de la Recherche Scientifique	FR	[25]	[46]	41	19	zb_only	24
72	Natalia Garcia-Fritz	Pontifical Catholic University of Chile	CL	29	74	[54]	-	arx+oa	11
73	Gregory Margulis	Yale University	US	[25]	[46]	42	42	zb_only	56
74	David McKinnon	University of Waterloo	CA	36	[54]	[43]	-	arxiv_only	27
75	QiMing Yan	Tongji University	CN	[25]	[46]	43	-	zb_only	-
76	Vesselin Dimitrov	California Institute of Technology	US	32	78	[54]	-	arx+oa	9
77	Evelina Viada	University of Göttingen	DE	39	42	[56]	-	arx+oa	25
78	Nikolai G. Moshchevitin	Lomonosov Moscow State University	RU	[25]	[52]	45	12	zb_only	32
79	Nicole Looper	University of Illinois Chicago	US	34	84	[54]	3	arx+oa	8
80	Philipp Habegger	University of Basel	CH	35	80	[54]	12	arx+oa	19
81	Matthew Satriano	University of Waterloo	CA	43	[54]	[43]	9	arxiv_only	16
82	Isao Wakabayashi	Seikei University	JP	[25]	[52]	49	6	zb_only	-
83	Paul Vojta	University of California, Berkeley	US	31	85	73	18	all_three	43
84	Bjorn Poonen	Massachusetts Institute of Technology	US	44	[54]	[43]	34	arxiv_only	32
85	Paul M. Voutier	Independent	GB	41	53	[56]	12	arx+oa	33
86	Prajeet Bajpai	University of British Columbia	CA	40	64	[54]	-	arx+oa	2
87	Yu Yasufuku	Waseda University	JP	30	105	69	4	all_three	18
88	P. Vasco	-	PT	[25]	[52]	51	-	zb_only	-
89	Frédéric Campana	University of Lorraine	FR	38	89	[54]	18	arx+oa	46
90	Sebastian Heintze	Graz University of Technology	AT	[25]	[52]	52	-	zb_only	-
91	Dan Abramovich	Brown University	US	47	[54]	[43]	32	arxiv_only	35
92	Robert F. Tichy	Graz University of Technology	AT	[27]	94	47	26	oa+zb	47
93	Kurt Mahler	Australian National University	AU	[26]	[54]	53	28	zb_only	99
94	Shinichi Mochizuki	Kyoto University	JP	[30]	50	[68]	20	oa_only	34
95	Benjamin Matschke	Boston University	US	46	51	[56]	8	arx+oa	15
96	Alina Ostafe	UNSW Sydney	AU	45	56	[56]	14	arx+oa	-
97	Anthony Várilly-Alvarado	Rice University	US	49	[54]	[43]	14	arxiv_only	17
98	M. N. Huxley	Cardiff University	GB	[26]	[54]	54	23	zb_only	56
99	Constantin M. Petridi	Independent	-	42	87	[54]	2	arx+oa	-
100	T. N. Shorey	Indian Institute of Technology Bombay	IN	[30]	40	155	22	oa+zb	51

Source column legend

The Source column records which of the pipelines ranked each researcher directly.

all_three: ranked directly by arXiv, OpenAlex, and zbMATH. The unanimous core.
arx+oa: ranked by arXiv and OpenAlex, but not zbMATH.
arx+zb: ranked by arXiv and zbMATH, but not OpenAlex.
oa+zb: ranked by OpenAlex and zbMATH, but not arXiv.
arxiv_only: ranked only by the arXiv pipeline.
oa_only: ranked only by OpenAlex. Often senior figures who publish in journals and do not post preprints.
zb_only: ranked only by zbMATH. Often pre-1995 Russian and Chinese number theorists.

Source	Count
`zb_only`	35
`arx+oa`	26
`all_three`	14
`oa+zb`	11
`arxiv_only`	9
`oa_only`	5

Limitations

This list reflects publication output and citation network density, not subjective importance. A starting point, not a verdict.