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Topic · Geometry and Topology

Mathematics and Applications

Mathematics and Applications is a research topic within Geometry and Topology. Science Explorer counts 35k research works in it since 1950. 7.7% of them reached the world's top 10% most cited for their field and year.

This cluster of papers covers a wide range of topics in geometric mathematics, including hyperbolic geometry, loops, billiards in ellipses, Poncelet's theorem, Moufang loops, trigonometry, algebraic structures, and their applications in relativity and inversive geometry.

  • Geometry
  • Hyperbolic
  • Loops
  • Billiards
  • Poncelet
  • Moufang
  • Trigonometry
  • Algebraic
  • Relativity
  • Inversive
Research works
35k
fractional, since 1950
In the world top 10%
2.7k
per year above
Top-10% rate
7.7%
share of its works in the world top 10%
Growth, 2013–17 → 2018–22
+0%
the tick is no change

Which countries lead Mathematics and Applications research?

By volume, the United States and Germany publish the most (690 and 268 works in 2022–2025).

By volume, 2022–2025

  1. 1 United States 690 works
  2. 2 Germany 268 works
  3. 3 China 245 works
  4. 4 India 197 works
  5. 5 France 157 works
  6. 6 United Kingdom 154 works
  7. 7 Brazil 152 works
  8. 8 Russia 136 works
  9. 9 Italy 123 works
  10. 10 Türkiye 118 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.

United States: 30.8%Germany: 11.9%China: 11.0%India: 8.8%6 others listed: 37.5%31%largest
United States690 · 30.8%Germany268 · 11.9%China245 · 11.0%India197 · 8.8%6 others listed841 · 37.5%

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

Which institutions lead Mathematics and Applications research?

By volume in 2022–2025, Indian Institute of Technology Kharagpur publishes the most Mathematics and Applications research, followed by University of Cambridge and Technical University of Munich.

By volume, 2022–2025

  1. 1 Indian Institute of Technology KharagpurIndia 30 works
  2. 2 University of CambridgeUnited Kingdom 29 works
  3. 3 Technical University of MunichGermany 21 works
  4. 4 Centre National de la Recherche ScientifiqueFrance 18 works
  5. 5 Universidad Nacional Autónoma de MéxicoMexico 18 works
  6. 6 University of ZagrebCroatia 15 works
  7. 7 Lomonosov Moscow State UniversityRussia 14 works
  8. 8 University of AugsburgGermany 13 works
  9. 9 Sapienza University of RomeItaly 12 works
  10. 10 Universidade de São PauloBrazil 11 works

Who are the leading researchers in Mathematics and Applications?

The most-cited researchers publishing on Mathematics and Applications include Donald E. Knuth and Stephan Ramon Garcia.

  1. 1 Donald E. Knuth United States 4k citations
  2. 2 Stephan Ramon Garcia United States 4k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

Where is Mathematics and Applications research done?

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

Largest cities, 2022–2025

  1. 1 Moscow Russia 74 works
  2. 2 Paris France 46 works
  3. 3 Beijing China 39 works
  4. 4 Tokyo Japan 33 works
  5. 5 New York United States 31 works
  6. 6 Mexico City Mexico 31 works
  7. 7 Kharagpur India 30 works
  8. 8 Cambridge United Kingdom 30 works
  9. 9 Vienna Austria 29 works
  10. 10 Berlin Germany 26 works

Where it is the local speciality

  1. KharagpurIN · 30.2 works18×
← less than its size predicts1×more →

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

See Mathematics and Applications on the map

Where is the best place to study Mathematics and Applications?

Among universities, judged by research, Technical University of Munich, University of Vienna and TU Wien 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%10%20%mean 7.39%fractional works in this node (log) →share in the world top 10% →Technical University of Munich: 22, 13.3%University of Vienna: 10, 14.5%TU Wien: 11, 6.8%University of Augsburg: 13, 8.3%Weizmann Institute of Science: 11, 6.0%Lewis & Clark College: 9, 5.6%University of Cambridge: 29, 3.1%Indian Institute of Technology Kharagpur: 30, 0.0%Technische Universität Berlin: 11, 4.3%University of Oxford: 11, 12.0%University of ViennaTechnical University…University of AugsburgTU Wien
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 Technical University of MunichGermany 68.313.3%8.2×22 -38.7%
2 University of ViennaAustria 58.114.5%6.0×10 +49.8%
3 TU WienAustria 56.46.8%10.4×11 +53.3%
4 University of AugsburgGermany 55.38.3%29.9×13 -21.2%
5 Weizmann Institute of ScienceIsrael 53.46.0%23.5×11 +6.2%
6 Lewis & Clark CollegeUnited States 53.25.6%202.0×9 +394.7%
7 University of CambridgeUnited Kingdom 52.83.1%8.2×29 -57.5%
8 Indian Institute of Technology KharagpurIndia 51.10.0%17.9×30 —
9 Technische Universität BerlinGermany 46.14.3%9.7×11 +15.0%
10 University of OxfordUnited Kingdom 43.912.0%2.7×11 +17.4%

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 and Applications research growing?

Output in 2018–2022 was 0% higher than in 2013–2017, peaking in 2024. The fastest-growing topics are Mathematics and Applications.

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.