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Mathematical and Theoretical Analysis

Mathematical and Theoretical Analysis is a research topic within Mathematical Physics. Science Explorer counts 12k 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 explores the applications of generalized functions, infinite and infinitesimal numbers, and non-Archimedean mathematics in various mathematical and physical contexts. It covers topics such as Colombeau algebras, numerical computations, nonlinear models, microlocal analysis, topological structures, algebraic theory, and nonstandard analysis.

  • Generalized Functions
  • Infinite and Infinitesimal Numbers
  • Non-Archimedean Mathematics
  • Colombeau Algebras
  • Numerical Computations
  • Nonlinear Models
  • Microlocal Analysis
  • Topological Structures
  • Algebraic Theory
  • Nonstandard Analysis
Research works
12k
fractional, since 1950
In the world top 10%
1.2k
per year above
Top-10% rate
10.1%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+11%
the tick is no change
Largest producer
United States
31% of the 10 largest, 2022-now
Mathematical and Theoretical Analysis

Which countries lead Mathematical and Theoretical Analysis research?

By volume, the United States and Germany publish the most (265 and 91 works in 2022-now).

By volume, 2022-now

  1. 1 United States 265 works
  2. 2 Germany 91 works
  3. 3 India 81 works
  4. 4 China 80 works
  5. 5 Italy 76 works
  6. 6 Russia 70 works
  7. 7 France 59 works
  8. 8 United Kingdom 56 works
  9. 9 Japan 41 works
  10. 10 Poland 37 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: 31.0%Germany: 10.6%India: 9.5%China: 9.4%6 others listed: 39.5%31%largest
United States265 · 31.0%Germany91 · 10.6%India81 · 9.5%China80 · 9.4%6 others listed338 · 39.5%

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

Which institutions lead Mathematical and Theoretical Analysis research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Mathematical and Theoretical Analysis research, followed by Russian Academy of Sciences and City University of New York.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 27 works
  2. 2 Russian Academy of SciencesRussia 15 works
  3. 3 City University of New YorkUnited States 9 works
  4. 4 Lomonosov Moscow State UniversityRussia 9 works
  5. 5 Sapienza University of RomeItaly 9 works
  6. 6 Tbilisi State UniversityGeorgia 8 works
  7. 7 Polish Academy of SciencesPoland 7 works
  8. 8 University of ViennaAustria 7 works
  9. 9 ETH ZurichSwitzerland 7 works
  10. 10 University of PisaItaly 6 works

What are the most cited papers in Mathematical and Theoretical Analysis?

The most cited paper in Mathematical and Theoretical Analysis is "Phenomenological Lagrangians" (Steven Weinberg, 1979), with 3,370 citations. Next come "Doctoral Dissertation" (2,609) and "A Course in Functional Analysis." (2,360).

Most cited papers
#PaperReleasedCitations
1 Phenomenological Lagrangians Steven Weinberg · Physica A Statistical Mechanics and its Applications Apr 1979 3,370
2 Doctoral Dissertation Michael Monastyrsky · Birkhäuser Boston eBooks Book chapter 1987 2,609
3 A Course in Functional Analysis. Theodore W. Gamelin, John B. Conway · American Mathematical Monthly Nov 1986 2,360
4 The Classical Theory of Fields L.D. LANDAU, E.M. LIFSHITZ, C. H. Holbrow · Physics Today Jun 1963 2,184
5 Analysis on Measure Chains — A Unified Approach to Continuous and Discrete Calculus Stefan Hilger · Results in Mathematics Aug 1990 2,009
All 98 most cited papers, with filters and sorting

Where is Mathematical and Theoretical Analysis research done?

The largest centres of Mathematical and Theoretical Analysis research in 2022-now are Moscow (Russia), Paris (France), New York (United States) and Beijing (China).

Largest cities, 2022-now

  1. 1 MoscowRussia 33 works
  2. 2 ParisFrance 27 works
  3. 3 New YorkUnited States 19 works
  4. 4 BeijingChina 18 works
  5. 5 RomeItaly 14 works
  6. 6 LondonUnited Kingdom 14 works
  7. 7 WarsawPoland 14 works
  8. 8 TokyoJapan 13 works
  9. 9 ViennaAustria 12 works
  10. 10 PragueCzechia 10 works
See Mathematical and Theoretical Analysis on the map

Where is the best place to study Mathematical and Theoretical Analysis?

Among universities, judged by research, Lomonosov Moscow State University, City University of New York and Sapienza University of Rome 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 7.6%fractional works in this field (log) →share of work in the world top 10% →Lomonosov Moscow Sta…City University of N…Sapienza University …Tbilisi State Univer…
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
1Lomonosov Moscow State UniversityRussia 95.815.0%9.1×9 +48.4%
2City University of New YorkUnited States 84.19.8%14.2×9 +100.0%
3Sapienza University of RomeItaly 52.05.6%6.1×9 +159.5%
4Tbilisi State UniversityGeorgia 15.00.0%68.5×8 -

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 Mathematical and Theoretical Analysis, country by country

Is Mathematical and Theoretical Analysis research growing?

Output in 2022-2025 was 11% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Mathematical and Theoretical Analysis.

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 Mathematical and Theoretical Analysis as a percentage of every work published that year, 0.0061% in 2024.

still counting0.020%0.040%0.060%Mathematical and Theoretical Analysis0.0060% in 202519801990200020102020

Fractional works of Mathematical and Theoretical Analysis 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%Mathematical and Theoretical Analysis11.9% 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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