Science Explorer Interactive view Map
Field · Physical Sciences

Mathematics research

Mathematics is a field of the Physical Sciences. Science Explorer counts 1.6M research works in it since 1950. 15.6% of them reached the world's top 10% most cited for their field and year.

In short: area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes.

Research works
1.6M
fractional, since 1950
In the world top 10%
249k
per year above
Top-10% rate
15.6%
share of its works in the world top 10%
Topics
82
Growth, 2013–17 → 2018–22
+22%
the tick is no change

What is Mathematics research about, and what is growing?

By the world's output in 2019–23, its most used keywords are Modeling, COVID-19, transmission dynamics, Nonlinear Equations, Numerical Methods, Mathematical Literacy. Gaining share since 2009–13: PISA Assessment, Problem-Solving, Mathematical Literacy, COVID-19, transmission dynamics. Losing share: Representation Theory, Ergodic Theory, Deformations, Hom-Lie Algebras.

▲ 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 40 words, with their numbers
  1. Modeling25k▲ 7.3×2 topics
  2. COVID-1925k▲ 7.6×1 topic
  3. transmission dynamics25k▲ 7.6×1 topic
  4. Nonlinear Equations25k▲ 1.21×5 topics
  5. Numerical Methods21k▼ 0.85×4 topics
  6. Mathematical Literacy19k▲ 9.1×2 topics
  7. PISA Assessment19k▲ 16×1 topic
  8. Problem-Solving19k▲ 16×1 topic
  9. Fractional Calculus16k▲ 1.43×2 topics
  10. Boundary Value Problems14k◆ 0.91×3 topics
  11. Bayesian Methods13k◆ 0.92×2 topics
  12. Anomalous Diffusion12k▲ 1.71×1 topic
  13. Homotopy Analysis Method12k▲ 1.71×1 topic
  14. Cohomology11k▼ 0.77×2 topics
  15. Model Selection10k◆ 0.90×3 topics
  16. Regression Analysis9,968▼ 0.83×3 topics
  17. Quantum Groups9,526▼ 0.83×2 topics
  18. Modular Forms9,434▼ 0.84×3 topics
  19. Symplectic Geometry9,325▼ 0.80×2 topics
  20. Principal Component Analysis8,383▼ 0.81×3 topics
  21. Teaching Methods7,922◆ 0.89×2 topics
  22. Random Matrix Theory7,851◆ 0.90×3 topics
  23. Representation Theory7,766▼ 0.76×2 topics
  24. Banach Spaces7,728▼ 0.82×3 topics
  25. Regularization7,653◆ 0.91×1 topic
  26. Variable Selection7,653◆ 0.91×1 topic
  27. Cluster Algebras7,357▼ 0.86×1 topic
  28. Triangulated Categories7,357▼ 0.86×1 topic
  29. Convection-Diffusion Problems7,288◆ 0.93×1 topic
  30. Singular Perturbation7,288◆ 0.93×1 topic
  31. Inverse Problems7,224▼ 0.85×2 topics
  32. Numerical Integration7,164▼ 0.78×2 topics
  33. Ergodic Theory7,052▼ 0.76×2 topics
  34. L-Functions6,944▼ 0.81×2 topics
  35. Deformations6,518▼ 0.76×1 topic
  36. Hom-Lie Algebras6,518▼ 0.76×1 topic
  37. K-Theory6,422▼ 0.77×2 topics
  38. Fractional Differential Equations6,237◆ 0.90×1 topic
  39. Semilinear Differential Equations6,237◆ 0.90×1 topic
  40. Hypergeometric Functions6,044◆ 0.99×2 topics

Which countries lead Mathematics research?

On research quality in 2022–2025, China, the United States and India rank highest in Mathematics. By volume, China and the United States publish the most (37k and 36k works in 2022–2025).

By research quality, 2022–2025

  1. 1 China · #2 all time 14.7% top 10% · 37k works
  2. 2 United States · #1 all time 15.9% top 10% · 36k works
  3. 3 India · #9 all time 12.8% top 10% · 17k works
  4. 4 United Kingdom · #3 all time 18.2% top 10% · 7.6k works
  5. 5 Germany · #4 all time 15.7% top 10% · 9.1k works
  6. 6 Saudi Arabia · #18 all time 23.3% top 10% · 4.7k works
  7. 7 Italy · #8 all time 17.9% top 10% · 7.2k works
  8. 8 France · #5 all time 13.1% top 10% · 9.4k works
  9. 9 South Korea · #13 all time 15.9% top 10% · 3.2k works
  10. 10 Türkiye · #15 all time 13.7% top 10% · 6.2k 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 82 countries ranked in Mathematics. Composite of field-normalised excellence (50%), output (30%) and citations (20%); the bracket is the all-time rank.

All countries ranked in Mathematics

By volume, 2022–2025

  1. 1 China 37k works
  2. 2 United States 36k works
  3. 3 India 17k works
  4. 4 Indonesia 16k works
  5. 5 Russia 10k works
  6. 6 France 9.4k works
  7. 7 Germany 9.1k works
  8. 8 United Kingdom 7.6k works
  9. 9 Italy 7.2k works
  10. 10 Japan 6.9k 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: 23.7%United States: 22.9%India: 10.6%Indonesia: 10.5%6 others listed: 32.2%24%largest
China37k · 23.7%United States36k · 22.9%India17k · 10.6%Indonesia16k · 10.5%6 others listed50k · 32.2%

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

Which institutions lead Mathematics research?

University of Oxford (United Kingdom) ranks first in Mathematics on research quality in 2022–2025, followed by Sogang University and Centre National de la Recherche Scientifique.

By research quality, 2022–2025

  1. 1 University of Oxford United Kingdom · Oxford · #15 all time 20.6% top 10% · 641 works
  2. 2 Sogang University South Korea · Seoul · #45 all time 42.7% top 10% · 69 works
  3. 3 Centre National de la Recherche Scientifique France · Paris · #11 all time 14.5% top 10% · 1.3k works
  4. 4 Hunan University of Technology China · Jianning 56.4% top 10% · 63 works
  5. 5 Shanghai University China · Shanghai · #59 all time 21.9% top 10% · 329 works
  6. 6 Stanford University United States · Stanford · #3 all time 25.3% top 10% · 448 works
  7. 7 Massachusetts Institute of Technology United States · Cambridge · #1 all time 22.3% top 10% · 407 works
  8. 8 Vellore Institute of Technology University India · Vellore 30.4% top 10% · 429 works
  9. 9 Tsinghua University China · Beijing 17.9% top 10% · 575 works
  10. 10 Harvard University United States · Cambridge · #10 all time 27.8% top 10% · 365 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 1,053 institutions above the floor of 40 fractional works in Mathematics.

Top 100 Mathematics institutions

By volume, 2022–2025

  1. 1 Centre National de la Recherche ScientifiqueFrance 1.3k works
  2. 2 Lomonosov Moscow State UniversityRussia 963 works
  3. 3 University of OxfordUnited Kingdom 641 works
  4. 4 Indonesia University of EducationIndonesia 631 works
  5. 5 Tsinghua UniversityChina 575 works
  6. 6 Sapienza University of RomeItaly 519 works
  7. 7 University of North Carolina at Chapel HillUnited States 515 works
  8. 8 University of MichiganUnited States 508 works
  9. 9 National Research University Higher School of EconomicsRussia 496 works
  10. 10 Russian Academy of SciencesRussia 490 works

Who are the leading researchers in Mathematics?

Among the most productive authors in Mathematics, Robert Tibshirani, Stanley Osher and Edward Witten rank highest on the composite score.

  1. 1 Robert Tibshirani United States · #38 worldwide 13k citations · 155 works
  2. 2 Stanley Osher United States · #48 worldwide 8k citations · 207 works
  3. 3 Edward Witten United States · #88 worldwide 7.2k citations · 151 works
  4. 4 Stephan Ramon Garcia United States · #107 worldwide 4k citations · 136 works
  5. 5 George Em Karniadakis United States · #151 worldwide 6.3k citations · 268 works
  6. 6 Frederick Mosteller United States · #203 worldwide 2.3k citations · 145 works
  7. 7 Peter M. Bentler United States · #237 worldwide 16k citations · 107 works
  8. 8 Trevor Hastie United States · #274 worldwide 4.9k citations · 118 works
  9. 9 Steven J. Miller United States · #283 worldwide 3.8k citations · 110 works
  10. 10 Jerry M. Mendel United States · #306 worldwide 4k citations · 162 works

Re-ranked on the composite score from the 5,850 highest-output authors in Mathematics. Identities come from OpenAlex author disambiguation, which occasionally merges or splits people.

Top 100 Mathematics researchers

Where is Mathematics research done?

The largest centres of Mathematics research in 2022–2025 are Beijing (China), Moscow (Russia), Paris (France) and Shanghai (China). Among places with at least 20 works in it, it is an unusually large share of all research in Pisa, Lawton and Huairou.

Largest cities, 2022–2025

  1. 1 Beijing China 5.6k works
  2. 2 Moscow Russia 4.6k works
  3. 3 Paris France 3.1k works
  4. 4 Shanghai China 2.7k works
  5. 5 Tokyo Japan 2.4k works
  6. 6 Nanjing China 1.9k works
  7. 7 London United Kingdom 1.8k works
  8. 8 New York United States 1.6k works
  9. 9 Seoul South Korea 1.6k works
  10. 10 Guangzhou China 1.6k works

Where it is the local speciality

  1. Pisa20.2 works47×
  2. LawtonUS · 53.4 works28×
  3. Huairou71.8 works26×
  4. Bures-sur-YvetteFR · 73.0 works22×
  5. NewarkUS · 26.6 works22×
  6. BeachwoodUS · 47.5 works21×
  7. Guanajuato CityMX · 65.6 works17×
  8. Orléans29.5 works16×
← less than its size predicts1×more →

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

See Mathematics on the map

Mathematics research by country

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

Where is the best place to study Mathematics?

Among universities, judged by research, Université Sultan Moulay Slimane, Prince Sultan University and China Medical University 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 26.82%fractional works in this node (log) →share in the world top 10% →Université Sultan Moulay Slimane: 360, 25.6%Prince Sultan University: 185, 32.3%China Medical University: 217, 33.2%Prince Sattam Bin Abdulaziz University: 214, 33.2%Düzce Üniversitesi: 176, 32.0%Qassim University: 337, 21.6%Moscow Center For Continuous Mathematical Education: 180, 12.0%Imam Mohammad ibn Saud Islamic University: 260, 23.9%COMSATS University Islamabad: 254, 28.8%Princess Nourah bint Abdulrahman University: 237, 25.6%China Medical Univer…Prince Sattam Bin Ab…Prince Sultan Univer…Université Sultan Mo…
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 Université Sultan Moulay SlimaneMorocco 73.625.6%10.8×360 +325.7%
2 Prince Sultan UniversitySaudi Arabia 71.132.3%6.9×185 +469.8%
3 China Medical UniversityTaiwan 69.933.2%6.4×217 +1143.7%
4 Prince Sattam Bin Abdulaziz UniversitySaudi Arabia 63.633.2%3.4×214 +360.9%
5 Düzce ÜniversitesiTürkiye 57.932.0%4.5×176 +419.3%
6 Qassim UniversitySaudi Arabia 57.621.6%5.3×337 +149.6%
7 Moscow Center For Continuous Mathematical EducationRussia 57.012.0%43.9×180 +479.5%
8 Imam Mohammad ibn Saud Islamic UniversitySaudi Arabia 56.123.9%5.7×260 +92.3%
9 COMSATS University IslamabadPakistan 55.328.8%4.5×254 +67.8%
10 Princess Nourah bint Abdulrahman UniversitySaudi Arabia 53.125.6%3.8×237 +92.1%

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 Mathematics research growing?

Output in 2018–2022 was 22% higher than in 2013–2017, peaking in 2022. The fastest-growing topics are Mathematics Education and Pedagogy, Fractional Differential Equations Solutions and COVID-19 epidemiological studies.

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. Mathematics Education and Pedagogy+3040%
  2. Fractional Differential Equations Solutions+176%
  3. COVID-19 epidemiological studies+173%
  4. Statistical Methods and Inference+56%
  5. Statistical Methods in Clinical Trials+55%
  6. Geometric Analysis and Curvature Flows+51%
← shrinkingno changegrowing →

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

What does Mathematics include?

Advanced Topics in Algebra: 46k fractional worksAlgebraic structures and combinatorial models: 42k fractional worksCOVID-19 epidemiological studies: 40k fractional worksAdvanced Statistical Methods and Models: 39k fractional worksStatistical Methods and Inference: 39k fractional worksGas Dynamics and Kinetic…38kGas Dynamics and Kinetic Theory: 38k fractional worksNumerical methods for differential equations: 37k fractional worksFractional Differential Equations Solutions: 37k fractional worksDifferential Equations a…36kDifferential Equations and Numerical Methods: 36k fractional worksMathematics Education and Pedagogy: 36k fractional worksMathematics and Applications: 35k fractional worksHistory and Theory of Ma…34kHistory and Theory of Mathematics: 34k fractional works

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