The Top 100
Researchers active on Goldbach and adjacent problems
Table Details
arXiv rank, OA rank, and zbMATH rank are the researcher's position in the full composite score for each of three pipelines. For arXiv and OpenAlex a keyword match in a paper title counts at full weight and an abstract-only mention at half (A=0.5), so papers that only cite Goldbach in passing are discounted; each composite is then 60% weighted paper count + 40% network or citation signal, over arXiv (137 qualifying authors across 17 search terms) and OpenAlex (572 authors across 13 phrase queries). zbMATH (495 authors) uses the three Goldbach-core MSC classes 11P32, 11P55 and 11N36. The overall rank combines the three with a weighted order statistic, 70/20/10 on each researcher's best, middle and worst of the three ranks, so lower is better in every column and a single dominant Goldbach pipeline can carry a researcher (the top weight only ever lands on a measured rank). A value in [square brackets] is interpolated: the researcher did not appear in that pipeline directly, so their rank there is estimated from their position in the others. See the methodology for how. A dash means no estimate was possible.
| Rank | Name | Institution | Country | arXiv rank | OA rank | zbMATH rank | h-index | Source | First year | Last year |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | Janos Pintz | Alfréd Rényi Institute of Mathematics | HU | 2 | [116] | 1 | 26 | arx+zb | 1985 | 1985 |
| 2 | Igor E. Shparlinski | UNSW Sydney | AU | 12 | 9 | [54] | 42 | arx+oa | 2000 | 2015 |
| 3 | Trevor D. Wooley | Purdue University West Lafayette | US | 1 | 110 | 12 | 28 | all_three | 1990 | 2026 |
| 4 | D. A. Goldston | San Jose State University | US | 3 | [116] | 10 | 21 | arx+zb | 1990 | 2023 |
| 5 | Jörg Brüdern | University of Göttingen | DE | [30] | 140 | 2 | 19 | oa+zb | 1991 | 2024 |
| 6 | Jianya Liu | Shandong University | CN | [36] | [122] | 3 | 14 | zb_only | 2007 | 2026 |
| 7 | Tianze Wang | Henan Academy of Sciences | CN | [36] | [122] | 4 | 2 | zb_only | 2021 | 2021 |
| 8 | Terence Tao | University of California, Los Angeles | US | 9 | 65 | 50 | 101 | all_three | 2025 | 2025 |
| 9 | R. C. Vaughan | Pennsylvania State University | US | [36] | [122] | 5 | 35 | zb_only | 1973 | 2022 |
| 10 | Angel Kumchev | Towson University | US | 14 | [109] | 20 | 12 | arx+zb | 2023 | 2023 |
| 11 | Jinjiang Li | China University of Mining and Technology (Beijing) | CN | 6 | [96] | [62] | 6 | arxiv_only | 2016 | 2026 |
| 12 | Min Zhang | Beijing Information Science and Technology University | CN | 7 | [96] | [61] | 44 | arxiv_only | 2016 | 2026 |
| 13 | Stephan Baier | Ramakrishna Mission Vivekananda Educational and Research Institute | IN | 8 | [96] | [58] | 14 | arxiv_only | 2004 | 2024 |
| 14 | Joni Teräväinen | University of Cambridge | GB | 4 | 133 | [56] | 9 | arx+oa | 2021 | 2021 |
| 15 | Alessandro Zaccagnini | University of Parma | IT | 15 | [109] | 30 | 14 | arx+zb | 2007 | 2026 |
| 16 | V. N. Chubarikov | Lomonosov Moscow State University | RU | [39] | [122] | 11 | - | zb_only | - | - |
| 17 | Jared Duker Lichtman | Stanford University | US | 10 | [96] | [58] | 4 | arxiv_only | 2025 | 2025 |
| 18 | Will Sawin | Princeton University | US | 24 | 31 | [54] | 10 | arx+oa | 2018 | 2018 |
| 19 | Jan Moser | Comenius University Bratislava | SK | 11 | [96] | [58] | 10 | arxiv_only | 2015 | 2015 |
| 20 | Alessandro Languasco | University of Padua | IT | 20 | [109] | 23 | 12 | arx+zb | 1994 | 2024 |
| 21 | Alberto Perelli | University of Genoa | IT | [46] | [122] | 15 | 20 | zb_only | 2008 | 2008 |
| 22 | Kaisa Matomäki | University of Turku | FI | 13 | [109] | 61 | 16 | arx+zb | 2020 | 2020 |
| 23 | Mark Shusterman | University of Wisconsin-Madison | US | [24] | 32 | [50] | 4 | oa_only | 2018 | 2022 |
| 24 | S. I. Dimitrov | Sofia University "St. Kliment Ohridski" | BG | 17 | [96] | [58] | 6 | arxiv_only | 2017 | 2025 |
| 25 | William D. Banks | University of Missouri | US | 18 | [96] | [58] | 21 | arxiv_only | 2024 | 2024 |
| 26 | James Maynard | University of Oxford | GB | 19 | [96] | [58] | 11 | arxiv_only | 2012 | 2025 |
| 27 | Xuancheng Shao | University of Kentucky | US | 5 | 132 | 92 | 10 | all_three | 2020 | 2021 |
| 28 | Alexander P. Mangerel | Durham University | GB | 21 | [96] | [58] | 6 | arxiv_only | 2018 | 2018 |
| 29 | Zhefeng Xu | Northwest University | CN | [18] | 39 | [50] | 8 | oa_only | 2022 | 2024 |
| 30 | Glyn Harman | Royal Holloway University of London | GB | [46] | [122] | 21 | 19 | zb_only | 1991 | 1991 |
| 31 | Karin Halupczok | Heinrich Heine University Düsseldorf | DE | 22 | [96] | [58] | 5 | arxiv_only | 2005 | 2021 |
| 32 | Tao Zhan | Southwest University | CN | [46] | [122] | 22 | 17 | zb_only | 1993 | 2006 |
| 33 | Ben Green | University of Oxford | GB | 16 | [109] | 75 | 32 | arx+zb | 2004 | 2025 |
| 34 | Pan, Chengdong | Shandong University | CN | [46] | [122] | 25 | - | zb_only | - | - |
| 35 | Kevin Ford | University of Illinois Urbana-Champaign | US | 26 | [96] | [58] | - | arxiv_only | 2004 | 2024 |
| 36 | András Sárközy | Eötvös Loránd University | HU | [46] | [122] | 27 | 31 | zb_only | 1988 | 2023 |
| 37 | Doychin Tolev | Sofia University "St. Kliment Ohridski" | BG | 27 | [109] | 55 | 10 | arx+zb | 1998 | 2017 |
| 38 | Gautami Bhowmik | Université de Lille | FR | 29 | [109] | 52 | 9 | arx+zb | 2008 | 2024 |
| 39 | Matteo Bordignon | KTH Royal Institute of Technology | SE | 31 | [96] | [58] | 13 | arxiv_only | 2018 | 2022 |
| 40 | Jori Merikoski | University of Oxford | GB | 32 | [96] | [58] | 2 | arxiv_only | 2020 | 2024 |
| 41 | Andrew Granville | Université de Montréal | CA | 30 | [109] | 63 | 32 | arx+zb | 2000 | 2000 |
| 42 | H. J. Weber | University of Virginia | US | 34 | [96] | [58] | - | arxiv_only | 2011 | 2012 |
| 43 | Shuntaro Yamagishi | Institute of Science and Technology Austria | AT | 57 | 41 | [53] | 5 | arx+oa | 2018 | 2025 |
| 44 | H. A. Helfgott | Université Paris Cité | FR | 33 | [109] | 56 | 19 | arx+zb | 2018 | 2018 |
| 45 | Yong-Gao Chen | Nanjing Normal University | CN | [46] | [122] | 35 | - | zb_only | - | - |
| 46 | Alexandru Zaharescu | University of Illinois Urbana-Champaign | US | 35 | [96] | [61] | 24 | arxiv_only | 2012 | 2012 |
| 47 | Hongze Li | Shanghai Jiao Tong University | CN | 66 | [116] | 31 | - | arx+zb | 2007 | 2019 |
| 48 | Chaohua Jia | Academy of Mathematics and Systems Science, Chinese Academy of Sciences | CN | [46] | [122] | 36 | 11 | zb_only | 1995 | 2020 |
| 49 | Tim Browning | Institute of Science and Technology Austria | AT | 23 | 200 | [54] | 19 | arx+oa | 2005 | 2025 |
| 50 | Daniel R. Johnston | Australian National University | AU | 36 | [96] | [61] | 4 | arxiv_only | 2021 | 2026 |
| 51 | G. I. Arkhipov | Steklov Institute of Mathematics | RU | [46] | [122] | 37 | - | zb_only | - | - |
| 52 | Bryce Kerr | UNSW Sydney | AU | 37 | [96] | [61] | 7 | arxiv_only | 2017 | 2025 |
| 53 | Hugh Lowell Montgomery | University of Michigan | US | [46] | [122] | 38 | 32 | zb_only | 1971 | 2026 |
| 54 | Lasse Grimmelt | University of Oxford | GB | 38 | [96] | [61] | 2 | arxiv_only | 2018 | 2024 |
| 55 | Hao Pan | Nanjing University of Finance and Economics | CN | 28 | [109] | 90 | 17 | arx+zb | 2007 | 2025 |
| 56 | Marek Wolf | University of Wrocław | PL | 41 | [96] | [58] | 11 | arxiv_only | 2001 | 2011 |
| 57 | Kevin Hughes | Edinburgh Napier University | GB | 42 | [96] | [58] | 8 | arxiv_only | 2015 | 2021 |
| 58 | Victor Z. Guo | Xi'an Jiaotong University | CN | 43 | [96] | [58] | 4 | arxiv_only | 2017 | 2026 |
| 59 | Greg Martin | University of British Columbia | CA | 44 | [96] | [58] | 16 | arxiv_only | 1998 | 2025 |
| 60 | Jan-Christoph Schlage-Puchta | University of Rostock | DE | [46] | [122] | 44 | 11 | zb_only | 2008 | 2019 |
| 61 | Akshat Mudgal | University of Bristol | GB | 45 | [96] | [58] | 3 | arxiv_only | 2020 | 2023 |
| 62 | Helmut Maier | Universität Ulm | DE | 64 | [116] | 41 | 18 | arx+zb | 2006 | 2006 |
| 63 | Koichi Kawada | Iwate University | JP | [46] | [122] | 46 | 9 | zb_only | 1993 | 2019 |
| 64 | Jesse Thorner | University of Illinois Urbana-Champaign | US | 47 | [96] | [58] | 9 | arxiv_only | 2013 | 2025 |
| 65 | Jean‐Marc Deshouillers | Centre National de la Recherche Scientifique | FR | [46] | [122] | 47 | 16 | zb_only | 2012 | 2012 |
| 66 | Adrian Dudek | The University of Queensland | AU | 48 | [96] | [58] | 5 | arxiv_only | 2014 | 2025 |
| 67 | Kai-Man Tsang | University of Hong Kong | HK | [46] | [122] | 48 | 8 | zb_only | 1982 | 2017 |
| 68 | Matt Visser | Victoria University of Wellington | NZ | 49 | [96] | [58] | - | arxiv_only | 1981 | 2026 |
| 69 | Chantal David | Concordia University | CA | 50 | [96] | [58] | 14 | arxiv_only | 2010 | 2010 |
| 70 | K. Soundararajan | Stanford University | US | 51 | [96] | [58] | 33 | arxiv_only | 2006 | 2026 |
| 71 | Cameron L. Stewart | University of Waterloo | CA | [46] | [122] | 51 | 20 | zb_only | 1991 | 2001 |
| 72 | Stephan Ramon Garcia | Pomona College | US | 52 | [96] | [58] | 27 | arxiv_only | 2011 | 2024 |
| 73 | Emmanuel Kowalski | CCI Reprographics (United States) | US | 53 | [96] | [58] | 29 | arxiv_only | 2000 | 2012 |
| 74 | Ade Irma Suriajaya | Kyushu University | JP | 46 | [109] | 79 | 4 | arx+zb | 2021 | 2025 |
| 75 | Roger C. Baker | Brigham Young University | US | 55 | [109] | 53 | 34 | arx+zb | 2017 | 2017 |
| 76 | Ofir Gorodetsky | Technion - Israel Institute of Technology | IL | 54 | [96] | [58] | 5 | arxiv_only | 2018 | 2024 |
| 77 | Akio Fujii | Rikkyo University | JP | [46] | [122] | 54 | 14 | zb_only | 1968 | 2018 |
| 78 | Zhi-Wei Sun | Nanjing University | CN | 157 | [116] | 29 | 31 | arx+zb | 2012 | 2014 |
| 79 | John B. Friedlander | University of Toronto | CA | 107 | [98] | 42 | 34 | arx+zb | 2009 | 2009 |
| 80 | J. P. Keating | University of Oxford | GB | 56 | [96] | [58] | 40 | arxiv_only | 2004 | 2004 |
| 81 | Li Ma | Sun Yat-sen University | CN | [18] | 74 | [50] | 22 | oa_only | 2004 | 2016 |
| 82 | Henryk Iwaniec | Rutgers University | US | 108 | [98] | 43 | 50 | arx+zb | 1975 | 2010 |
| 83 | Christian Elsholtz | Graz University of Technology | AT | [46] | [122] | 57 | 13 | zb_only | 2001 | 2026 |
| 84 | Xiumin Ren | Shandong University | CN | [46] | [122] | 58 | 11 | zb_only | 2022 | 2024 |
| 85 | Ciprian Demeter | Indiana University Bloomington | US | 58 | [110] | [56] | 15 | arxiv_only | 2014 | 2016 |
| 86 | Michele Piconi | University of Perugia | IT | [18] | 78 | [50] | 4 | oa_only | 2024 | 2026 |
| 87 | Fei Xue | Université du Québec à Montréal | CA | 59 | [110] | [56] | 6 | arxiv_only | 2020 | 2024 |
| 88 | Ping Xi | Xi'an Jiaotong University | CN | 60 | [110] | [56] | 9 | arxiv_only | 2010 | 2025 |
| 89 | Julia Brandes | Chalmers University of Technology | SE | 61 | [110] | [56] | 4 | arxiv_only | 2012 | 2024 |
| 90 | Leo Goldmakher | Williams College | US | 62 | [110] | [56] | 5 | arxiv_only | 2009 | 2025 |
| 91 | H. J. J. te Riele | Centrum Wiskunde & Informatica | NL | [46] | [122] | 64 | - | zb_only | - | - |
| 92 | Jiseong Kim | Sogang University | KR | 63 | [110] | [56] | 20 | arxiv_only | 2020 | 2025 |
| 93 | Antal Balog | Baltazar Zaprešić University of Applied Sciences | HR | [46] | [122] | 65 | 18 | zb_only | 1985 | 2013 |
| 94 | Tikao Tatuzawa | Saitama University | JP | [46] | [122] | 67 | - | zb_only | - | - |
| 95 | Imre Z. Ruzsa | Alfréd Rényi Institute of Mathematics | HU | 140 | [116] | 45 | 33 | arx+zb | 2003 | 2026 |
| 96 | Dieter Wolke | University of Freiburg | DE | [46] | [122] | 68 | - | zb_only | - | - |
| 97 | Alexei Kourbatov | Allscripts (United States) | US | 67 | [110] | [56] | 4 | arxiv_only | 2014 | 2015 |
| 98 | P. F. Kelly | Texas A&M University | US | 68 | [110] | [56] | - | arxiv_only | 2001 | 2001 |
| 99 | Weiping Li | - | CN | [46] | [122] | 70 | - | zb_only | - | - |
| 100 | Terry Pilling | NA | NA | 69 | [110] | [56] | 2 | arxiv_only | 2001 | 2001 |
Source column legend
The Source column records which of the three pipelines ranked each researcher directly. Where a pipeline did not rank someone, the rank shown for that pipeline is an interpolated estimate (in [square brackets]).
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 that arXiv and OpenAlex under-index.
| Source | Count |
|---|---|
arxiv_only | 41 |
zb_only | 26 |
arx+zb | 20 |
arx+oa | 5 |
oa_only | 4 |
all_three | 3 |
oa+zb | 1 |
Limitations
This list reflects publication output and citation network density, not subjective importance. A starting point, not a verdict.