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Subfield · Mathematics

Mathematical Physics research

Mathematical Physics is a subfield of Mathematics. Science Explorer counts 257k research works in it since 1950. 15.0% of them reached the world's top 10% most cited for their field and year.

In short: use of mathematics to solve physics problems.

Research works
257k
fractional, since 1950
In the world top 10%
38k
per year above
Top-10% rate
15.0%
share of its works in the world top 10%
Topics
12
Growth, 2013–17 → 2018–22
+3%
the tick is no change

What is Mathematical Physics research about, and what is growing?

By the world's output in 2019–23, its most used keywords are Ergodic Theory, K-Theory, Inverse Problems, Regularization Methods, Global Well-Posedness, Nonlinear Schrödinger Equation. Gaining share since 2009–13: Global Well-Posedness, Nonlinear Schrödinger Equation. Losing share: Interacting Particle Systems, Scaling Limits.

▲ gaining share of this field◆ holding its share▼ losing share

Size is the world's fractional works in 2019–23 in the topics tagged with each word; colour compares the word's share of this field with 2009–13. Each links to the topic it comes from most.

All 28 words, with their numbers
  1. Ergodic Theory7,052◆ 0.96×2 topics
  2. K-Theory6,422◆ 0.98×2 topics
  3. Inverse Problems5,186◆ 1.05×1 topic
  4. Regularization Methods5,186◆ 1.05×1 topic
  5. Global Well-Posedness5,175▲ 1.36×1 topic
  6. Nonlinear Schrödinger Equation5,175▲ 1.36×1 topic
  7. Chaos4,529◆ 0.91×1 topic
  8. Dynamical Systems4,529◆ 0.91×1 topic
  9. Automorphic Forms4,266◆ 1.00×1 topic
  10. Langlands Conjectures4,266◆ 1.00×1 topic
  11. Deformation Quantization4,253◆ 0.99×1 topic
  12. Poisson Manifolds4,253◆ 0.99×1 topic
  13. Interacting Particle Systems3,432▼ 0.84×1 topic
  14. Scaling Limits3,432▼ 0.84×1 topic
  15. Differential Operators3,376◆ 1.00×1 topic
  16. Spectral Theory3,376◆ 1.00×1 topic
  17. Mathematical Physics3,317◆ 1.02×2 topics
  18. Nonlinear Equations3,317◆ 1.02×2 topics
  19. p-adic2,523◆ 1.05×1 topic
  20. ultrametric2,523◆ 1.05×1 topic
  21. Banach Spaces2,259◆ 0.88×1 topic
  22. Operators2,259◆ 0.88×1 topic
  23. C*-Algebras2,169◆ 0.96×1 topic
  24. Quantum Groups2,169◆ 0.96×1 topic
  25. Generalized Functions1,445◆ 0.90×1 topic
  26. Infinite and Infinitesimal Numbers1,445◆ 0.90×1 topic
  27. Neutrosophy793◆ 0.92×1 topic
  28. Smarandache Function793◆ 0.92×1 topic

Which countries lead Mathematical Physics research?

On research quality in 2022–2025, China, the United States and Germany rank highest in Mathematical Physics. By volume, China and the United States publish the most (5.8k and 4.7k works in 2022–2025).

By research quality, 2022–2025

  1. 1 China · #3 all time 13.3% top 10% · 5.8k works
  2. 2 United States · #1 all time 13.4% top 10% · 4.7k works
  3. 3 Germany · #4 all time 14.7% top 10% · 1.5k works
  4. 4 France · #2 all time 12.0% top 10% · 2.2k works
  5. 5 Italy · #7 all time 16.8% top 10% · 1.2k works
  6. 6 India · #13 all time 12.2% top 10% · 1.5k works
  7. 7 United Kingdom · #5 all time 15.1% top 10% · 1.2k works
  8. 8 Russia · #8 all time 8.8% top 10% · 2.3k works
  9. 9 Spain · #11 all time 12.7% top 10% · 710 works
  10. 10 Japan · #6 all time 8.4% top 10% · 1.4k works

The track on each row is that row’s top-10% rate. The ranking itself is the composite score, which the rate is only one part of.

Of 32 countries ranked in Mathematical Physics. Composite of field-normalised excellence (50%), output (30%) and citations (20%); the bracket is the all-time rank.

All countries ranked in Mathematical Physics

By volume, 2022–2025

  1. 1 China 5.8k works
  2. 2 United States 4.7k works
  3. 3 Russia 2.3k works
  4. 4 France 2.2k works
  5. 5 Germany 1.5k works
  6. 6 India 1.5k works
  7. 7 Japan 1.4k works
  8. 8 Italy 1.2k works
  9. 9 United Kingdom 1.2k works
  10. 10 Brazil 828 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.

China: 25.7%United States: 20.6%Russia: 10.0%France: 9.6%6 others listed: 34.1%26%largest
China5,816 · 25.7%United States4,650 · 20.6%Russia2,269 · 10.0%France2,172 · 9.6%6 others listed7,704 · 34.1%

Shares of the rows listed above, not of the whole node.

Which institutions lead Mathematical Physics research?

Centre National de la Recherche Scientifique (France) ranks first in Mathematical Physics on research quality in 2022–2025, followed by University of Oxford and Tsinghua University.

By research quality, 2022–2025

  1. 1 Centre National de la Recherche Scientifique France · Paris · #3 all time 14.1% top 10% · 326 works
  2. 2 University of Oxford United Kingdom · Oxford · #19 all time 21.3% top 10% · 113 works
  3. 3 Tsinghua University China · Beijing · #72 all time 18.6% top 10% · 116 works
  4. 4 Beijing Normal University China · Beijing · #52 all time 21.5% top 10% · 90 works
  5. 5 Lomonosov Moscow State University Russia · Moscow · #40 all time 10.7% top 10% · 251 works
  6. 6 University of Bonn Germany · Bonn · #27 all time 18.4% top 10% · 80 works
  7. 7 Central South University China · Changsha 19.1% top 10% · 87 works
  8. 8 ETH Zurich Switzerland · Zurich · #13 all time 22.4% top 10% · 84 works
  9. 9 Princeton University United States · Princeton · #1 all time 24.2% top 10% · 64 works
  10. 10 University of Cambridge United Kingdom · Cambridge · #11 all time 19.7% top 10% · 85 works

The track on each row is that row’s top-10% rate. The ranking itself is the composite score, which the rate is only one part of.

Of 58 institutions above the floor of 40 fractional works in Mathematical Physics.

Top 100 Mathematical Physics institutions

By volume, 2022–2025

  1. 1 Centre National de la Recherche ScientifiqueFrance 326 works
  2. 2 Lomonosov Moscow State UniversityRussia 251 works
  3. 3 National Research University Higher School of EconomicsRussia 143 works
  4. 4 St Petersburg UniversityRussia 128 works
  5. 5 Steklov Mathematical InstituteRussia 124 works
  6. 6 Kyoto UniversityJapan 120 works
  7. 7 Russian Academy of SciencesRussia 118 works
  8. 8 Tsinghua UniversityChina 116 works
  9. 9 University of OxfordUnited Kingdom 113 works
  10. 10 University of ViennaAustria 103 works

Who are the leading researchers in Mathematical Physics?

Among the most productive authors in Mathematical Physics, Stanley Osher, Stephan Ramon Garcia and Steven J. Miller rank highest on the composite score.

  1. 1 Stanley Osher United States · #48 worldwide 8k citations · 207 works
  2. 2 Stephan Ramon Garcia United States · #107 worldwide 4k citations · 136 works
  3. 3 Steven J. Miller United States · #283 worldwide 3.8k citations · 110 works
  4. 4 Benoît B. Mandelbrot United States · #426 worldwide 4.2k citations · 109 works
  5. 5 H. S. M. Coxeter Canada · #1,398 worldwide 1.3k citations · 115 works
  6. 6 Peter D. Lax United States · #1,685 worldwide 2k citations · 82 works
  7. 7 Marc Lambert France · #1,779 worldwide 2.1k citations · 83 works
  8. 8 Leo P. Kadanoff United States · #2,164 worldwide 2.2k citations · 81 works
  9. 9 Jeffrey C. Lagarias United States · #2,191 worldwide 1.9k citations · 76 works
  10. 10 Michael Atiyah United Kingdom · #2,229 worldwide 1.4k citations · 87 works

Re-ranked on the composite score from the 5,257 highest-output authors in Mathematical Physics. Identities come from OpenAlex author disambiguation, which occasionally merges or splits people.

Top 100 Mathematical Physics researchers

Where is Mathematical Physics research done?

The largest centres of Mathematical Physics research in 2022–2025 are Moscow (Russia), Beijing (China), Paris (France) and Tokyo (Japan). Among places with at least 20 works in it, it is an unusually large share of all research in Bures-sur-Yvette, Vladikavkaz and Guarulhos.

Largest cities, 2022–2025

  1. 1 Moscow Russia 1.1k works
  2. 2 Beijing China 934 works
  3. 3 Paris France 725 works
  4. 4 Tokyo Japan 441 works
  5. 5 Shanghai China 428 works
  6. 6 Nanjing China 331 works
  7. 7 Guangzhou China 258 works
  8. 8 London United Kingdom 252 works
  9. 9 New York United States 238 works
  10. 10 Wuhan China 230 works

Where it is the local speciality

  1. Bures-sur-YvetteFR · 25.0 works57×
  2. VladikavkazRU · 45.5 works25×
  3. GuarulhosBR · 82.5 works25×
  4. KlosterneuburgAT · 30.0 works22×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Mathematical Physics than the world average.

See Mathematical Physics on the map

Mathematical Physics research by country

The best places for Mathematical Physics research inside each country, with that country's researchers and world standing.

Where is the best place to study Mathematical Physics?

Among universities, judged by research, University of Monastir, Université Sultan Moulay Slimane and National Research University Higher School of Economics 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.

0%20%40%mean 20.49%fractional works in this node (log) →share in the world top 10% →University of Monastir: 54, 26.4%Université Sultan Moulay Slimane: 42, 28.8%National Research University Higher School of Economics: 143, 8.4%Institute of Science and Technology Austria: 30, 17.5%Scuola Internazionale Superiore di Studi Avanzati: 45, 18.7%Lomonosov Moscow State University: 251, 10.7%Université Paris-Saclay: 92, 11.5%Courant Institute of Mathematical Sciences: 26, 28.0%Scuola Normale Superiore: 23, 31.3%Saratov State University: 40, 23.6%Université Sultan Mo…University of MonastirInstitute of Science…National Research Un…
above the meannear itbelow it

One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.

#UniversityScoreTop 10%SpecialisationWorksGrowth
1 University of MonastirTunisia 70.326.4%11.2×54 +108.7%
2 Université Sultan Moulay SlimaneMorocco 63.728.8%9.5×42 +58.4%
3 National Research University Higher School of EconomicsRussia 61.88.4%10.7×143 +173.3%
4 Institute of Science and Technology AustriaAustria 60.117.5%25.3×30 +124.1%
5 Scuola Internazionale Superiore di Studi AvanzatiItaly 60.018.7%33.0×45 +67.4%
6 Lomonosov Moscow State UniversityRussia 59.410.7%9.0×251 +35.8%
7 Université Paris-SaclayFrance 59.211.5%7.4×92 +348.4%
8 Courant Institute of Mathematical SciencesUnited States 59.128.0%34.9×26 -7.0%
9 Scuola Normale SuperioreItaly 58.931.3%12.1×23 -29.9%
10 Saratov State UniversityRussia 56.723.6%14.3×40 +21.9%

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 Mathematical Physics research growing?

Output in 2018–2022 was 3% higher than in 2013–2017, peaking in 2024. The fastest-growing topics are Advanced Mathematical Physics Problems, Numerical methods in inverse problems and Mathematical and Theoretical Analysis.

19801990200020102020
grewheldshrank

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.

  1. Advanced Mathematical Physics Problems+54%
  2. Numerical methods in inverse problems+29%
  3. Mathematical and Theoretical Analysis+26%
  4. Advanced Algebra and Geometry+24%
  5. Advanced Operator Algebra Research+22%
  6. Spectral Theory in Mathematical Physics+21%
  7. Advanced Mathematical Theories-8%
← shrinkingno changegrowing →

Growth in output from 2005–09 to 2015–19. Every topic is a page of its own.

What does Mathematical Physics include?

Mathematical Dynamics an…31kMathematical Dynamics and Fractals: 31k fractional worksNumerical methods in inv…31kNumerical methods in inverse problems: 31k fractional worksHomotopy and Cohomology in Algebraic Topology: 28k fractional worksAdvanced Algebra and Geo…27kAdvanced Algebra and Geometry: 27k fractional worksStochastic processes and…26kStochastic processes and statistical mechanics: 26k fractional worksSpectral Theory in Mathematical Physics: 23k fractional worksAdvanced Mathematical Physics Problems: 22k fractional worksadvanced mathematical th…18kadvanced mathematical theories: 18k fractional worksAdvanced Banach Space Theory: 18k fractional worksAdvanced Operator Algebra Research: 15k fractional worksMathematical and Theoretical Analysis: 12k fractional worksAdvanced Mathematical Theories: 5,642 fractional works

Area is fractional works in that topic. Every name below is a page of its own.