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Subfield · Computer Science

Computational Theory and Mathematics research

Computational Theory and Mathematics is a subfield of Computer Science. Science Explorer counts 616k research works in it since 1950. 16.9% of them reached the world's top 10% most cited for their field and year.

In short: area of mathematics.

Research works
616k
fractional, since 1950
In the world top 10%
104k
per year above
Top-10% rate
16.9%
share of its works in the world top 10%
Topics
24
Growth, 2013–17 → 2018–22
+7%
the tick is no change

What is Computational Theory and Mathematics research about, and what is growing?

By the world's output in 2019–23, its most used keywords are Machine Learning, Molecular Docking, Virtual Screening, Finite Element, Heterogeneous, Multiscale Methods. Gaining share since 2009–13: Adaptive Dynamic Programming, Reinforcement Learning, Molecular Docking, Virtual Screening, Machine Learning. Losing share: Granular Computing, Rough Sets, Model Checking, Symbolic Model Checker.

▲ 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. Machine Learning24k▲ 1.79×2 topics
  2. Molecular Docking22k▲ 1.85×1 topic
  3. Virtual Screening22k▲ 1.85×1 topic
  4. Finite Element11k◆ 1.05×2 topics
  5. Heterogeneous9,967◆ 1.09×1 topic
  6. Multiscale Methods9,967◆ 1.09×1 topic
  7. Algorithmic Applications9,446◆ 0.95×2 topics
  8. Approximation Algorithms9,446◆ 0.95×2 topics
  9. Evolutionary Algorithms8,290▲ 1.36×1 topic
  10. Multiobjective Optimization8,290▲ 1.36×1 topic
  11. Automata7,831▼ 0.65×2 topics
  12. Matrix Computations6,386▼ 0.82×1 topic
  13. Numerical Linear Algebra6,386▼ 0.82×1 topic
  14. Graph Theory5,555◆ 0.94×1 topic
  15. Parameterized Complexity5,555◆ 0.94×1 topic
  16. Variational Inequalities5,426▼ 0.86×2 topics
  17. Granular Computing5,414▼ 0.55×1 topic
  18. Rough Sets5,414▼ 0.55×1 topic
  19. Model Checking5,026▼ 0.63×1 topic
  20. Symbolic Model Checker5,026▼ 0.63×1 topic
  21. Fuzzy Logic4,389◆ 0.88×1 topic
  22. Residuated Lattices4,389◆ 0.88×1 topic
  23. Complexity Theory4,290◆ 0.92×2 topics
  24. Iterative Algorithms4,044◆ 0.87×1 topic
  25. Nonlinear Operators4,044◆ 0.87×1 topic
  26. Simulation4,007▼ 0.73×2 topics
  27. Combinatorial Optimization3,891◆ 0.96×1 topic
  28. Graph Algorithms3,891◆ 0.96×1 topic
  29. Algorithmic Information Theory3,853◆ 0.88×1 topic
  30. Computability3,853◆ 0.88×1 topic
  31. Graph Labeling3,557▲ 1.28×1 topic
  32. Metric Dimension3,557▲ 1.28×1 topic
  33. Emergence3,517▼ 0.70×2 topics
  34. Cellular Automata3,118▼ 0.71×1 topic
  35. Computation3,118▼ 0.71×1 topic
  36. Adaptive Dynamic Programming2,859▲ 4.3×1 topic
  37. Reinforcement Learning2,859▲ 4.3×1 topic
  38. Formal Languages2,804▼ 0.70×1 topic
  39. Regular Expressions2,804▼ 0.70×1 topic
  40. Gröbner Bases2,756◆ 0.89×1 topic

Which countries lead Computational Theory and Mathematics research?

On research quality in 2022–2025, China, the United States and India rank highest in Computational Theory and Mathematics. By volume, China and the United States publish the most (19k and 12k works in 2022–2025).

By research quality, 2022–2025

  1. 1 China · #2 all time 19.3% top 10% · 19k works
  2. 2 United States · #1 all time 14.8% top 10% · 12k works
  3. 3 India · #7 all time 13.1% top 10% · 8.8k works
  4. 4 Germany · #4 all time 13.8% top 10% · 4.2k works
  5. 5 United Kingdom · #3 all time 16.7% top 10% · 2.9k works
  6. 6 Italy · #8 all time 15.1% top 10% · 2.6k works
  7. 7 France · #5 all time 10.0% top 10% · 3.5k works
  8. 8 Canada · #6 all time 13.0% top 10% · 1.6k works
  9. 9 Saudi Arabia · #28 all time 21.2% top 10% · 1.2k works
  10. 10 South Korea · #16 all time 19.8% top 10% · 1.3k 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 59 countries ranked in Computational Theory and Mathematics. Composite of field-normalised excellence (50%), output (30%) and citations (20%); the bracket is the all-time rank.

All countries ranked in Computational Theory and Mathematics

By volume, 2022–2025

  1. 1 China 19k works
  2. 2 United States 12k works
  3. 3 India 8.8k works
  4. 4 Germany 4.2k works
  5. 5 France 3.5k works
  6. 6 United Kingdom 2.9k works
  7. 7 Russia 2.6k works
  8. 8 Italy 2.6k works
  9. 9 Japan 2.5k works
  10. 10 Brazil 1.7k 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: 31.8%United States: 20.4%India: 14.5%Germany: 7.0%6 others listed: 26.3%32%largest
China19k · 31.8%United States12k · 20.4%India8,770 · 14.5%Germany4,204 · 7.0%6 others listed16k · 26.3%

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

Which institutions lead Computational Theory and Mathematics research?

Tsinghua University (China) ranks first in Computational Theory and Mathematics on research quality in 2022–2025, followed by Vellore Institute of Technology University and Centre National de la Recherche Scientifique.

By research quality, 2022–2025

  1. 1 Tsinghua University China · Beijing · #41 all time 21.3% top 10% · 239 works
  2. 2 Vellore Institute of Technology University India · Vellore 21.5% top 10% · 244 works
  3. 3 Centre National de la Recherche Scientifique France · Paris · #7 all time 11.2% top 10% · 499 works
  4. 4 Northwestern Polytechnical University China · Xi'an · #79 all time 24.3% top 10% · 219 works
  5. 5 Central South University China · Changsha · #57 all time 26.5% top 10% · 202 works
  6. 6 Zhejiang University China · Hangzhou 24.2% top 10% · 170 works
  7. 7 Dalian University of Technology China · Dalian · #77 all time 24.2% top 10% · 162 works
  8. 8 Massachusetts Institute of Technology United States · Cambridge · #4 all time 20.1% top 10% · 202 works
  9. 9 Chinese Academy of Sciences China · Beijing · #37 all time 20.7% top 10% · 195 works
  10. 10 University of Electronic Science and Technology of China China · Chengdu · #73 all time 21.5% top 10% · 185 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 277 institutions above the floor of 40 fractional works in Computational Theory and Mathematics.

Top 100 Computational Theory and Mathematics institutions

By volume, 2022–2025

  1. 1 Centre National de la Recherche ScientifiqueFrance 499 works
  2. 2 University of OxfordUnited Kingdom 254 works
  3. 3 Vellore Institute of Technology UniversityIndia 244 works
  4. 4 Lomonosov Moscow State UniversityRussia 240 works
  5. 5 Shanghai Jiao Tong UniversityChina 240 works
  6. 6 Tsinghua UniversityChina 239 works
  7. 7 Northwestern Polytechnical UniversityChina 219 works
  8. 8 ETH ZurichSwitzerland 217 works
  9. 9 Technical University of MunichGermany 205 works
  10. 10 Xidian UniversityChina 204 works

Who are the leading researchers in Computational Theory and Mathematics?

Among the most productive authors in Computational Theory and Mathematics, Stanley Osher, Dan Boneh and Seyedali Mirjalili rank highest on the composite score.

  1. 1 Stanley Osher United States · #48 worldwide 8k citations · 207 works
  2. 2 Dan Boneh United States · #95 worldwide 7.5k citations · 143 works
  3. 3 Seyedali Mirjalili Australia · #98 worldwide 7.6k citations · 164 works
  4. 4 Stephan Ramon Garcia United States · #107 worldwide 4k citations · 136 works
  5. 5 Robert E. Tarjan United States · #193 worldwide 3.9k citations · 141 works
  6. 6 Steven J. Miller United States · #283 worldwide 3.8k citations · 110 works
  7. 7 Kalyanmoy Deb United States · #287 worldwide 6.7k citations · 218 works
  8. 8 Ted Belytschko United States · #315 worldwide 4.1k citations · 139 works
  9. 9 Donald E. Knuth United States · #357 worldwide 4k citations · 107 works
  10. 10 Ronald L. Rivest United States · #425 worldwide 7.3k citations · 103 works

Re-ranked on the composite score from the 5,683 highest-output authors in Computational Theory and Mathematics. Identities come from OpenAlex author disambiguation, which occasionally merges or splits people.

Top 100 Computational Theory and Mathematics researchers

Where is Computational Theory and Mathematics research done?

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

Largest cities, 2022–2025

  1. 1 Beijing China 2.8k works
  2. 2 Shanghai China 1.4k works
  3. 3 Moscow Russia 1.1k works
  4. 4 Paris France 1.1k works
  5. 5 Xi'an China 1k works
  6. 6 Nanjing China 1k works
  7. 7 Tokyo Japan 871 works
  8. 8 Guangzhou China 787 works
  9. 9 Chennai India 741 works
  10. 10 Chengdu China 702 works

Where it is the local speciality

  1. MaramagPH · 29.5 works23×
  2. Iligan CityPH · 53.3 works14×
  3. KatraIN · 47.0 works12×
  4. KlosterneuburgAT · 44.1 works12×
← less than its size predicts1×more →

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

See Computational Theory and Mathematics on the map

Computational Theory and Mathematics research by country

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

Where is the best place to study Computational Theory and Mathematics?

Among universities, judged by research, Université Sultan Moulay Slimane, Macau University of Science and Technology and Bohai 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 22.61%fractional works in this node (log) →share in the world top 10% →Université Sultan Moulay Slimane: 72, 27.2%Macau University of Science and Technology: 67, 24.7%Bohai University: 59, 36.9%Prince Sattam Bin Abdulaziz University: 52, 27.4%Vellore Institute of Technology University: 244, 21.5%Southern University of Science and Technology: 107, 23.2%COMSATS University Islamabad: 88, 23.8%Mindanao State University – Iligan Institute of Technology: 53, 3.6%Shri Mata Vaishno Devi University: 47, 18.2%ETH Zurich: 217, 19.6%Bohai UniversityPrince Sattam Bin Ab…Université Sultan Mo…Macau University of …
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 57.027.2%6.0×72 +259.6%
2 Macau University of Science and TechnologyMacau 54.824.7%3.5×67 +217.8%
3 Bohai UniversityChina 51.536.9%6.6×59 +3.9%
4 Prince Sattam Bin Abdulaziz UniversitySaudi Arabia 51.527.4%2.3×52 +243.8%
5 Vellore Institute of Technology UniversityIndia 50.521.5%2.8×244 +149.8%
6 Southern University of Science and TechnologyChina 49.423.2%2.3×107 +2088.8%
7 COMSATS University IslamabadPakistan 47.023.8%4.2×88 +31.4%
8 Mindanao State University – Iligan Institute of TechnologyPhilippines 47.03.6%14.6×53 +290.0%
9 Shri Mata Vaishno Devi UniversityIndia 46.718.2%12.2×47 +38.7%
10 ETH ZurichSwitzerland 46.319.6%3.7×217 -2.7%

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 Computational Theory and Mathematics research growing?

Output in 2018–2022 was 7% higher than in 2013–2017, peaking in 2025. The fastest-growing topics are Adaptive Dynamic Programming Control, Computational Drug Discovery Methods and Advanced Multi-Objective Optimization Algorithms.

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. Adaptive Dynamic Programming Control+257%
  2. Computational Drug Discovery Methods+80%
  3. Advanced Multi-Objective Optimization Algorithms+73%
  4. Quantum-Dot Cellular Automata+68%
  5. Topological and Geometric Data Analysis+59%
  6. Graph Labeling and Dimension Problems+53%
  7. semigroups and automata theory-11%
  8. Formal Methods in Verification-15%
  9. Rough Sets and Fuzzy Logic-28%
  10. Petri Nets in System Modeling-28%
← shrinkingno changegrowing →

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

What does Computational Theory and Mathematics include?

Computational Drug Discovery Methods: 78k fractional worksAdvanced Mathematical Modeling in Engineering: 56k fractional worksMatrix Theory and Algorithms: 50k fractional worksFormal Methods in Verification: 43k fractional worksRough Sets and Fuzzy Logic: 36k fractional worksAdvanced Graph Theory Research: 33k fractional worksAdvanced Algebra and Logic: 33k fractional worksAdvanced Multi-Objective Optimization Algorithms: 32k fractional worksComputability, Logic, AI Algorithms: 29k fractional worksOptimization and Variational Analysis: 25k fractional workssemigroups and automata theory: 25k fractional worksCellular Automata and Applications: 24k fractional works

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