advanced mathematical theories
advanced mathematical theories is a research topic within Mathematical Physics. Science Explorer counts 18k research works in it since 1950. 10.0% of them reached the world's top 10% most cited for their field and year.
This cluster of papers focuses on the application of p-adic numbers and ultrametric spaces in mathematical physics, particularly in areas such as string theory, dynamics, wavelets, nonlinear equations, and Gibbs measures. It explores the implications of p-adic models in understanding phenomena in ultrametric spaces and their relevance to mathematical physics.
- p-adic
- mathematical physics
- ultrametric
- dynamics
- string theory
- wavelets
- nonlinear equations
- Gibbs measures
- quantization
- ergodic theory
- Research works
- 18k fractional, since 1950
- In the world top 10%
- 1.9k per year above
- Top-10% rate
- 10.0% share of its works in the world top 10%
- Growth, 2013–17 → 2018–22
- +14% the tick is no change
Which countries lead advanced mathematical theories research?
By volume, Russia and the United States publish the most (387 and 269 works in 2022–2025).
By volume, 2022–2025
- 1 Russia 387 works
- 2 United States 269 works
- 3 China 258 works
- 4 India 133 works
- 5 France 109 works
- 6 Germany 87 works
- 7 Japan 86 works
- 8 Ukraine 75 works
- 9 Italy 74 works
- 10 United Kingdom 58 works
How concentrated that is
The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.
Shares of the rows listed above, not of the whole node.
Which institutions lead advanced mathematical theories research?
By volume in 2022–2025, Lomonosov Moscow State University publishes the most advanced mathematical theories research, followed by Steklov Mathematical Institute and Russian Academy of Sciences.
By volume, 2022–2025
- 1 Lomonosov Moscow State UniversityRussia 47 works
- 2 Steklov Mathematical InstituteRussia 22 works
- 3 Russian Academy of SciencesRussia 18 works
- 4 St Petersburg UniversityRussia 17 works
- 5 Centre National de la Recherche ScientifiqueFrance 16 works
- 6 Yerevan State UniversityArmenia 12 works
- 7 University of California San DiegoUnited States 11 works
- 8 Sobolev Institute of MathematicsRussia 11 works
- 9 National Research University Higher School of EconomicsRussia 11 works
- 10 Moscow State UniversityTajikistan 10 works
Who are the leading researchers in advanced mathematical theories?
The most-cited researchers publishing on advanced mathematical theories include Κ. Peters, S. A. Çetin and A. Zhemchugov.
- 1 Κ. Peters United Kingdom 7.8k citations
- 2 S. A. Çetin China 7.2k citations
- 3 A. Zhemchugov China 7.2k citations
- 4 V. Kartvelishvili Israel 6.8k citations
Ranked by citations received across their whole record, among researchers with at least three works on this topic.
Where is advanced mathematical theories research done?
The largest centres of advanced mathematical theories research in 2022–2025 are Moscow (Russia), Beijing (China), Paris (France) and Tashkent (Uzbekistan). Among places with at least 20 works in it, it is an unusually large share of all research in Yerevan and Tashkent.
Largest cities, 2022–2025
- 1 Moscow Russia 175 works
- 2 Beijing China 42 works
- 3 Paris France 38 works
- 4 Tashkent Uzbekistan 32 works
- 5 Kyiv Ukraine 30 works
- 6 Saint Petersburg Russia 28 works
- 7 Yerevan Armenia 27 works
- 8 Tokyo Japan 27 works
- 9 Nanjing China 20 works
- 10 Novosibirsk Russia 20 works
Where it is the local speciality
- YerevanAM · 26.9 works25×
- TashkentUZ · 31.6 works10×
Location quotient: how much more of its research is in advanced mathematical theories than the world average.
Where is the best place to study advanced mathematical theories?
Among universities, judged by research, Lomonosov Moscow State University, Moscow Center For Continuous Mathematical Education and National University of Uzbekistan score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.
One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.
| # | University | Score | Top 10% | Specialisation | Works | Growth |
|---|---|---|---|---|---|---|
| 1 | Lomonosov Moscow State UniversityRussia | 82.8 | 11.3% | 23.2× | 47 | +40.0% |
| 2 | Moscow Center For Continuous Mathematical EducationRussia | 64.1 | 11.5% | 217.8× | 9 | — |
| 3 | National University of UzbekistanUzbekistan | 62.4 | 10.4% | 24.1× | 9 | +92.8% |
| 4 | Yerevan State UniversityArmenia | 55.4 | 3.8% | 53.2× | 12 | +238.6% |
| 5 | Indian Statistical InstituteIndia | 50.7 | 8.9% | 43.0× | 8 | -36.8% |
| 6 | Saratov State UniversityRussia | 48.1 | 7.6% | 43.7× | 9 | -4.7% |
| 7 | National Research University Higher School of EconomicsRussia | 43.8 | 2.9% | 10.9× | 10 | +72.5% |
| 8 | St Petersburg UniversityRussia | 43.7 | 1.5% | 14.8× | 17 | +48.8% |
| 9 | University of California San DiegoUnited States | 42.6 | 6.2% | 5.4× | 11 | +225.3% |
| 10 | University of SfaxTunisia | 42.1 | 1.7% | 16.8× | 10 | +69.7% |
Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.
Is advanced mathematical theories research growing?
Output in 2018–2022 was 14% higher than in 2013–2017, peaking in 2024. The fastest-growing topics are advanced mathematical theories.
The same series as a ribbon — one cell per year, darker for more. The line above answers how much; this answers when.
Which topics inside it are moving
Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.