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Topic · Mathematical Physics

advanced mathematical theories

advanced mathematical theories is a research topic within Mathematical Physics. Science Explorer counts 18k research works in it since 1950. 10.1% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the application of p-adic numbers and ultrametric spaces in mathematical physics, particularly in areas such as string theory, dynamics, wavelets, nonlinear equations, and Gibbs measures. It explores the implications of p-adic models in understanding phenomena in ultrametric spaces and their relevance to mathematical physics.

  • p-adic
  • mathematical physics
  • ultrametric
  • dynamics
  • string theory
  • wavelets
  • nonlinear equations
  • Gibbs measures
  • quantization
  • ergodic theory
Research works
18k
fractional, since 1950
In the world top 10%
1.9k
per year above
Top-10% rate
10.1%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+27%
the tick is no change
Largest producer
Russia
24% of the 10 largest, 2022-now
advanced mathematical theories

Which countries lead advanced mathematical theories research?

By volume, Russia and the United States publish the most (403 and 318 works in 2022-now).

By volume, 2022-now

  1. 1 Russia 403 works
  2. 2 United States 318 works
  3. 3 China 283 works
  4. 4 India 139 works
  5. 5 France 118 works
  6. 6 Germany 91 works
  7. 7 Japan 91 works
  8. 8 Ukraine 78 works
  9. 9 Italy 78 works
  10. 10 United Kingdom 62 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.

Russia: 24.3%United States: 19.2%China: 17.0%India: 8.4%6 others listed: 31.2%24%largest
Russia403 · 24.3%United States318 · 19.2%China283 · 17.0%India139 · 8.4%6 others listed518 · 31.2%

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

Which institutions lead advanced mathematical theories research?

By volume in 2022-now, Russian Academy of Sciences publishes the most advanced mathematical theories research, followed by Centre National de la Recherche Scientifique and Lomonosov Moscow State University.

By volume, 2022-now

  1. 1 Russian Academy of SciencesRussia 112 works
  2. 2 Centre National de la Recherche ScientifiqueFrance 56 works
  3. 3 Lomonosov Moscow State UniversityRussia 48 works
  4. 4 National Academy of Sciences of UkraineUkraine 23 works
  5. 5 St Petersburg UniversityRussia 17 works
  6. 6 Q-Flex (United States)United States 17 works
  7. 7 Yerevan State UniversityArmenia 14 works
  8. 8 Academy of Sciences Republic of UzbekistanUzbekistan 12 works
  9. 9 National Research University Higher School of EconomicsRussia 11 works
  10. 10 Moscow State UniversityTajikistan 11 works

Who are the leading researchers in advanced mathematical theories?

The most-cited researchers publishing on advanced mathematical theories include Xiaogang Wang, Leo Breiman and A. Meyer.

  1. 1 Xiaogang Wang China 260k citations
  2. 2 Leo Breiman United States 243k citations
  3. 3 A. Meyer France 224k citations
  4. 4 R. W. L. Jones United Kingdom 189k citations
  5. 5 V. Sharma France 178k citations
  6. 6 Andrei V. Gritsan France 174k citations
  7. 7 Edward H. Witten United States 174k 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 advanced mathematical theories?

The most cited paper in advanced mathematical theories is "On the stability of the linear mapping in Banach spaces" (Themistocles M. Rassias, 1978), with 2,860 citations. Next come "ON A CLASS OF SKEW DISTRIBUTION FUNCTIONS" (2,524) and "Hypoelliptic second order differential equations" (2,458).

Most cited papers
#PaperReleasedCitations
1 On the stability of the linear mapping in Banach spaces Themistocles M. Rassias · Proceedings of the American Mathematical Society Open access Nov 1978 2,860
2 ON A CLASS OF SKEW DISTRIBUTION FUNCTIONS Herbert A. Simon · Biometrika 1955 2,524
3 Hypoelliptic second order differential equations Lars Hörmander · Acta Mathematica 1967 2,458
4 A Class of Statistics with Asymptotically Normal Distribution Wassily Hoeffding · Springer series in statistics Book chapter 1992 1,913
5 Weak solutions of nonlinear hyperbolic equations and their numerical computation Peter D. Lax · Communications on Pure and Applied Mathematics Feb 1954 1,851
All 98 most cited papers, with filters and sorting

Where is advanced mathematical theories research done?

The largest centres of advanced mathematical theories research in 2022-now are Moscow (Russia), Beijing (China), Paris (France) and Tashkent (Uzbekistan). Among places with at least 20 works in it, it is an unusually large share of all research in Yerevan.

Largest cities, 2022-now

  1. 1 MoscowRussia 183 works
  2. 2 BeijingChina 47 works
  3. 3 ParisFrance 41 works
  4. 4 TashkentUzbekistan 35 works
  5. 5 KyivUkraine 31 works
  6. 6 Saint PetersburgRussia 29 works
  7. 7 YerevanArmenia 29 works
  8. 8 TokyoJapan 27 works
  9. 9 NovosibirskRussia 20 works
  10. 10 NanjingChina 20 works

Where it is the local speciality

  1. YerevanAM · 28.8 works25×
← less than its size predicts1×more →

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

See advanced mathematical theories on the map

Where is the best place to study advanced mathematical theories?

Among universities, judged by research, Indian Institute of Technology Kharagpur, Lomonosov Moscow State University and Moscow State 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%10%20%mean 9.23%fractional works in this field (log) →share of work in the world top 10% →Indian Institute of …Moscow State Univers…Moscow Center For Co…Lomonosov Moscow Sta…
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 57.218.4%9.2×10 -
2Lomonosov Moscow State UniversityRussia 54.68.8%25.6×48 -16.9%
3Moscow State UniversityTajikistan 51.912.4%18.6×11 +11.0%
4Moscow Center For Continuous Mathematical EducationRussia 41.69.4%238.1×9 +135.3%
5National University of UzbekistanUzbekistan 39.59.8%27.0×9 -22.3%
6Indian Statistical InstituteIndia 33.66.4%46.8×9 +260.7%
7University of California San DiegoUnited States 33.26.2%5.0×11 +222.4%
8Yerevan State UniversityArmenia 32.25.2%55.9×14 +31.3%
9Saratov State UniversityRussia 28.37.2%48.3×9 +14.4%
10National Research University Higher School of EconomicsRussia 26.38.5%12.3×11 -28.9%

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 advanced mathematical theories, country by country

Is advanced mathematical theories research growing?

Output in 2022-2025 was 27% higher than in 2018-2021, peaking in 2024. The fastest-growing topics are advanced mathematical theories.

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 advanced mathematical theories as a percentage of every work published that year, 0.014% in 2024.

still counting0.025%0.050%0.075%advanced mathematical theories0.012% in 202519801990200020102020

Fractional works of advanced mathematical theories 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%advanced mathematical theories10.8% 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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