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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. 9.9% 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%
3.5k
per year above
Top-10% rate
9.9%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+17%
the tick is no change
Largest producer
United States
32% of the 10 largest, 2022-now
Mathematics and Applications

Which countries lead Mathematics and Applications research?

By volume, the United States and Germany publish the most (777 and 290 works in 2022-now).

By volume, 2022-now

  1. 1 United States 777 works
  2. 2 Germany 290 works
  3. 3 China 269 works
  4. 4 India 214 works
  5. 5 France 167 works
  6. 6 Brazil 167 works
  7. 7 United Kingdom 166 works
  8. 8 Russia 145 works
  9. 9 Italy 138 works
  10. 10 Türkiye 128 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: 31.6%Germany: 11.8%China: 10.9%India: 8.7%6 others listed: 37.0%32%largest
United States777 · 31.6%Germany290 · 11.8%China269 · 10.9%India214 · 8.7%6 others listed910 · 37.0%

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

Which institutions lead Mathematics and Applications research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Mathematics and Applications research, followed by Russian Academy of Sciences and University of Cambridge.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 65 works
  2. 2 Russian Academy of SciencesRussia 37 works
  3. 3 University of CambridgeUnited Kingdom 31 works
  4. 4 Indian Institute of Technology KharagpurIndia 30 works
  5. 5 Technical University of MunichGermany 24 works
  6. 6 Universidad Nacional Autónoma de MéxicoMexico 18 works
  7. 7 University of ZagrebCroatia 16 works
  8. 8 Lomonosov Moscow State UniversityRussia 15 works
  9. 9 City University of New YorkUnited States 14 works
  10. 10 University of AugsburgGermany 14 works

Who are the leading researchers in Mathematics and Applications?

The most-cited researchers publishing on Mathematics and Applications include Amos Tversky and Stephen M. Smith.

  1. 1 Amos Tversky United States 327k citations
  2. 2 Stephen M. Smith United Kingdom 214k citations

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

What are the most cited papers in Mathematics and Applications?

The most cited paper in Mathematics and Applications is "LOSS OF RECENT MEMORY AFTER BILATERAL HIPPOCAMPAL LESIONS" (William Beecher Scoville, Brenda Atkinson Milner, 1957), with 7,447 citations. Next come "A Course in Functional Analysis." (2,360) and "Calibrated geometries" (1,721).

Most cited papers
#PaperReleasedCitations
1 LOSS OF RECENT MEMORY AFTER BILATERAL HIPPOCAMPAL LESIONS William Beecher Scoville, Brenda Atkinson Milner · Journal of Neurology Neurosurgery & Psychiatry Open access Feb 1957 7,447
2 A Course in Functional Analysis. Theodore W. Gamelin, John B. Conway · American Mathematical Monthly Nov 1986 2,360
3 Calibrated geometries Reese Harvey, H. Blaine Lawson · Acta Mathematica Open access 1982 1,721
4 On the foundations of combinatorial theory I. Theory of M�bius Functions Gian Carlo Rota · Probability Theory and Related Fields Open access 1964 1,501
5 On the method of bounded differences Colin McDiarmid · Cambridge University Press eBooks Book chapter 3 Aug 1989 1,466
All 100 most cited papers, with filters and sorting

Where is Mathematics and Applications research done?

The largest centres of Mathematics and Applications research in 2022-now 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-now

  1. 1 MoscowRussia 77 works
  2. 2 ParisFrance 48 works
  3. 3 BeijingChina 42 works
  4. 4 TokyoJapan 36 works
  5. 5 New YorkUnited States 34 works
  6. 6 Mexico CityMexico 32 works
  7. 7 ViennaAustria 32 works
  8. 8 CambridgeUnited Kingdom 31 works
  9. 9 KharagpurIndia 30 works
  10. 10 MunichGermany 29 works

Where it is the local speciality

  1. KharagpurIN · 30.2 works16×
← 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, Indian Institute of Technology Kharagpur, University of Cambridge and University of Zagreb 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 10.41%fractional works in this field (log) →share of work in the world top 10% →Indian Institute of …University of ZagrebTU WienUniversity of Cambri…
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Indian Institute of Technology KharagpurIndia 89.421.1%18.5×30 +869.6%
2University of CambridgeUnited Kingdom 70.24.2%8.0×31 +241.9%
3University of ZagrebCroatia 62.616.8%7.0×16 +47.0%
4TU WienAustria 61.616.6%10.9×11 +75.2%
5Technical University of MunichGermany 56.83.7%8.3×24 +264.2%
6University of OxfordUnited Kingdom 52.59.9%2.5×11 +96.0%
7Lomonosov Moscow State UniversityRussia 50.716.2%5.3×14 -18.0%
8Technische Universität BerlinGermany 49.55.3%10.1×11 +158.7%
9University of ViennaAustria 49.28.0%6.8×11 +22.9%
10Weizmann Institute of ScienceIsrael 48.82.3%24.1×11 +301.7%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Mathematics and Applications, country by country

Is Mathematics and Applications research growing?

Output in 2022-2025 was 17% higher than in 2018-2021, peaking in 2024. The fastest-growing topics are Mathematics and Applications.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Mathematics and Applications as a percentage of every work published that year, 0.018% in 2024.

still counting0.10%0.20%Mathematics and Applications0.016% in 202519801990200020102020

Fractional works of Mathematics and Applications over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Mathematics and Applications10.6% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

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.

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