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Subfield · Mathematics

Applied Mathematics research

Applied Mathematics is a subfield of Mathematics. Science Explorer counts 341k research works in it since 1950. 14.5% of them reached the world's top 10% most cited for their field and year.

In short: discipline of mathematics.

Research works
341k
fractional, since 1950
In the world top 10%
49k
per year above
Top-10% rate
14.5%
share of its works in the world top 10%
Topics
17
Growth, 2013–17 → 2018–22
+34%
the tick is no change

What is Applied Mathematics research about, and what is growing?

By the world's output in 2019–23, its most used keywords are Mathematical Literacy, Problem-Solving, Boundary Value Problems, Fractional Differential Equations, Semilinear Differential Equations, Fractional Laplacian. Gaining share since 2009–13: Mathematical Literacy, Problem-Solving. Losing share: Difference Equations, Meromorphic Functions, Frames, Wavelets.

▲ 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 36 words, with their numbers
  1. Mathematical Literacy19k▲ 14×1 topic
  2. Problem-Solving19k▲ 14×1 topic
  3. Boundary Value Problems14k▼ 0.80×3 topics
  4. Fractional Differential Equations6,237▼ 0.78×1 topic
  5. Semilinear Differential Equations6,237▼ 0.78×1 topic
  6. Fractional Laplacian5,662◆ 0.89×1 topic
  7. Sobolev Spaces5,662◆ 0.89×1 topic
  8. Optimal Transport5,309▼ 0.85×1 topic
  9. Ricci Curvature5,309▼ 0.85×1 topic
  10. Boltzmann Equation4,881▼ 0.67×1 topic
  11. Kinetic Theory4,881▼ 0.67×1 topic
  12. Nonlocal4,744▼ 0.76×1 topic
  13. Partial Differential Equations4,744▼ 0.76×1 topic
  14. Composition Operators3,724▼ 0.70×1 topic
  15. Weighted Spaces3,724▼ 0.70×1 topic
  16. Orthogonal Polynomials3,403▼ 0.85×1 topic
  17. Quadrature Methods3,403▼ 0.85×1 topic
  18. Linear Differential Equations3,358▼ 0.62×2 topics
  19. Geometric Algebra2,793▼ 0.68×1 topic
  20. Quaternionic Analysis2,793▼ 0.68×1 topic
  21. Compressible Flows2,696◆ 0.91×1 topic
  22. Navier-Stokes Equations2,696◆ 0.91×1 topic
  23. Calderón–Zygmund Theory2,546▼ 0.75×1 topic
  24. Fourier Multiplier Theorems2,546▼ 0.75×1 topic
  25. Frames2,546▼ 0.59×1 topic
  26. Wavelets2,546▼ 0.59×1 topic
  27. Geometric Means2,143◆ 0.98×1 topic
  28. Matrix Inequalities2,143◆ 0.98×1 topic
  29. Functional Equations2,008▼ 0.67×1 topic
  30. Hyers-Ulam Stability2,008▼ 0.67×1 topic
  31. Point Processes1,929▼ 0.68×1 topic
  32. Spatstat1,929▼ 0.68×1 topic
  33. Singular Spectrum Analysis1,810▼ 0.74×1 topic
  34. Total Least Squares1,810▼ 0.74×1 topic
  35. Difference Equations1,350▼ 0.56×1 topic
  36. Meromorphic Functions1,350▼ 0.56×1 topic

Which countries lead Applied Mathematics research?

On research quality in 2022–2025, China, the United States and Indonesia rank highest in Applied Mathematics. By volume, Indonesia and China publish the most (14k and 9.4k works in 2022–2025).

By research quality, 2022–2025

  1. 1 China · #2 all time 15.4% top 10% · 9.4k works
  2. 2 United States · #1 all time 15.5% top 10% · 4.7k works
  3. 3 Indonesia · #4 all time 6.4% top 10% · 14k works
  4. 4 India · #9 all time 13.5% top 10% · 3.2k works
  5. 5 Italy · #5 all time 20.1% top 10% · 1.6k works
  6. 6 Saudi Arabia · #14 all time 23.1% top 10% · 1.1k works
  7. 7 Türkiye · #11 all time 15.4% top 10% · 1.5k works
  8. 8 Germany · #6 all time 16.9% top 10% · 1.5k works
  9. 9 South Korea · #15 all time 17.5% top 10% · 742 works
  10. 10 France · #3 all time 13.5% top 10% · 1.7k 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 48 countries ranked in Applied Mathematics. Composite of field-normalised excellence (50%), output (30%) and citations (20%); the bracket is the all-time rank.

All countries ranked in Applied Mathematics

By volume, 2022–2025

  1. 1 Indonesia 14k works
  2. 2 China 9.4k works
  3. 3 United States 4.7k works
  4. 4 India 3.2k works
  5. 5 Russia 2.8k works
  6. 6 France 1.7k works
  7. 7 Italy 1.6k works
  8. 8 Germany 1.5k works
  9. 9 Türkiye 1.5k works
  10. 10 Japan 1.2k 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.

Indonesia: 34.3%China: 22.3%United States: 11.2%India: 7.6%6 others listed: 24.6%34%largest
Indonesia14k · 34.3%China9,368 · 22.3%United States4,711 · 11.2%India3,194 · 7.6%6 others listed10k · 24.6%

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

Which institutions lead Applied Mathematics research?

Indonesia University of Education (Indonesia) ranks first in Applied Mathematics on research quality in 2022–2025, followed by Beijing Normal University and Vellore Institute of Technology University.

By research quality, 2022–2025

  1. 1 Indonesia University of Education Indonesia · Bandung · #16 all time 10.7% top 10% · 573 works
  2. 2 Beijing Normal University China · Beijing · #7 all time 29.3% top 10% · 162 works
  3. 3 Vellore Institute of Technology University India · Vellore · #51 all time 40.6% top 10% · 104 works
  4. 4 Düzce Üniversitesi Türkiye · Düzce · #19 all time 36.5% top 10% · 110 works
  5. 5 Université Sultan Moulay Slimane Morocco · Beni Mellal 29.7% top 10% · 160 works
  6. 6 COMSATS University Islamabad Pakistan · Islamabad · #41 all time 34.9% top 10% · 78 works
  7. 7 Politecnico di Milano Italy · Milan · #29 all time 30.2% top 10% · 100 works
  8. 8 Tsinghua University China · Beijing · #44 all time 20.7% top 10% · 141 works
  9. 9 Centre National de la Recherche Scientifique France · Paris · #5 all time 14.6% top 10% · 221 works
  10. 10 Universitas Negeri Surabaya Indonesia · Surabaya 8.9% top 10% · 325 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 137 institutions above the floor of 40 fractional works in Applied Mathematics.

Top 100 Applied Mathematics institutions

By volume, 2022–2025

  1. 1 Indonesia University of EducationIndonesia 573 works
  2. 2 State University of MedanIndonesia 411 works
  3. 3 Universitas Muhammadiyah Tapanuli SelatanIndonesia 408 works
  4. 4 Universitas PGRI SemarangIndonesia 398 works
  5. 5 State University of SemarangIndonesia 332 works
  6. 6 State University of PadangIndonesia 328 works
  7. 7 Universitas Negeri SurabayaIndonesia 325 works
  8. 8 State University of MalangIndonesia 311 works
  9. 9 Yogyakarta State UniversityIndonesia 293 works
  10. 10 State University of MakassarIndonesia 286 works

Who are the leading researchers in Applied Mathematics?

Among the most productive authors in Applied Mathematics, Stanley Osher, Stephan Ramon Garcia and Peter D. Lax 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 Peter D. Lax United States · #1,685 worldwide 2k citations · 82 works
  4. 4 Brian Street United Kingdom · #2,417 worldwide 1.9k citations · 74 works
  5. 5 Terence Tao United States · #2,469 worldwide 3.1k citations · 215 works
  6. 6 Bernt Øksendal Norway · #2,498 worldwide 2k citations · 82 works
  7. 7 G. H. Hardy United Kingdom · #2,515 worldwide 939 citations · 96 works
  8. 8 Ronald R. Coifman United States · #2,605 worldwide 2k citations · 74 works
  9. 9 Gilbert Strang United States · #2,821 worldwide 1k citations · 99 works
  10. 10 Lars Hörmander Sweden · #3,455 worldwide 1.6k citations · 66 works

Re-ranked on the composite score from the 4,929 highest-output authors in Applied Mathematics. Identities come from OpenAlex author disambiguation, which occasionally merges or splits people.

Top 100 Applied Mathematics researchers

Where is Applied Mathematics research done?

The largest centres of Applied Mathematics research in 2022–2025 are Beijing (China), Moscow (Russia), Medan (Indonesia) and Jakarta (Indonesia). Among places with at least 20 works in it, it is an unusually large share of all research in Kairouan, Beni Mellal and Tiaret.

Largest cities, 2022–2025

  1. 1 Beijing China 1.4k works
  2. 2 Moscow Russia 1.2k works
  3. 3 Medan Indonesia 1k works
  4. 4 Jakarta Indonesia 957 works
  5. 5 Semarang Indonesia 877 works
  6. 6 Bandung Indonesia 844 works
  7. 7 Yogyakarta Indonesia 676 works
  8. 8 Shanghai China 580 works
  9. 9 Malang Indonesia 576 works
  10. 10 Makassar Indonesia 563 works

Where it is the local speciality

  1. KairouanTN · 32.8 works22×
  2. Beni MellalMA · 160.3 works20×
  3. TiaretDZ · 30.2 works19×
  4. MostaganemDZ · 34.8 works17×
  5. GuelmaDZ · 33.1 works16×
← less than its size predicts1×more →

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

See Applied Mathematics on the map

Applied Mathematics research by country

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

Where is the best place to study Applied Mathematics?

Among universities, judged by research, Düzce Üniversitesi, Université Sultan Moulay Slimane and Indonesia University of Education 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 20.4%fractional works in this node (log) →share in the world top 10% →Düzce Üniversitesi: 110, 36.5%Université Sultan Moulay Slimane: 160, 29.7%Indonesia University of Education: 573, 10.7%China Medical University: 58, 33.0%COMSATS University Islamabad: 78, 34.9%Universitas Muhammadiyah Tapanuli Selatan: 408, 5.1%Universitas PGRI Semarang: 398, 5.6%Prince Sultan University: 41, 33.0%Yogyakarta State University: 294, 10.7%State University of Medan: 411, 4.8%Düzce ÜniversitesiChina Medical Univer…Université Sultan Mo…Indonesia University…
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 Düzce ÜniversitesiTürkiye 73.836.5%11.6×110 +277.4%
2 Université Sultan Moulay SlimaneMorocco 72.529.7%19.7×160 +237.1%
3 Indonesia University of EducationIndonesia 66.210.7%9.6×573 +1687.2%
4 China Medical UniversityTaiwan 62.933.0%7.0×58 +2038.1%
5 COMSATS University IslamabadPakistan 62.334.9%5.6×78 +178.4%
6 Universitas Muhammadiyah Tapanuli SelatanIndonesia 60.95.1%15.8×408 +1599.5%
7 Universitas PGRI SemarangIndonesia 60.95.6%14.5×398 +1170.9%
8 Prince Sultan UniversitySaudi Arabia 60.833.0%6.3×41 +488.1%
9 Yogyakarta State UniversityIndonesia 59.110.7%8.6×294 +419.3%
10 State University of MedanIndonesia 59.04.8%9.4×411 +1371.8%

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 Applied Mathematics research growing?

Output in 2018–2022 was 34% higher than in 2013–2017, peaking in 2025. The fastest-growing topics are Mathematics Education and Pedagogy, Mathematical Inequalities and Applications and Navier-Stokes equation solutions.

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. Mathematical Inequalities and Applications+68%
  3. Navier-Stokes equation solutions+56%
  4. Nonlinear Partial Differential Equations+52%
  5. Geometric Analysis and Curvature Flows+51%
  6. Advanced Harmonic Analysis Research+40%
  7. Meromorphic and Entire Functions-1%
← shrinkingno changegrowing →

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

What does Applied Mathematics include?

Gas Dynamics and Kinetic…38kGas Dynamics and Kinetic Theory: 38k fractional worksMathematics Education an…36kMathematics Education and Pedagogy: 36k fractional worksNonlinear Differential Equations Analysis: 28k fractional worksDifferential Equations and Boundary Problems: 26k fractional worksGeometric Analysis and Curvature Flows: 26k fractional worksNonlinear Partial Differential Equations: 25k fractional worksHolomorphic and Operator Theory: 23k fractional worksAlgebraic and Geometric …21kAlgebraic and Geometric Analysis: 21k fractional worksMathematical functions and polynomials: 19k fractional worksMathematical Analysis and Transform Methods: 16k fractional worksAdvanced Harmonic Analysis Research: 13k fractional worksFunctional Equations Stability Results: 13k fractional works

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