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Advanced Mathematical Theories

Advanced Mathematical Theories is a research topic within Mathematical Physics. Science Explorer counts 5.6k research works in it since 1950. 9.8% 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 mathematics and mathematical physics, including advancements in the Smarandache function, neutrosophy, number theory, income distribution analysis, combinatorial manifolds, Newton mechanics, nonlinear equations, cosmology, and the intersection of mathematics with information technology.

  • Smarandache Function
  • Neutrosophy
  • Number Theory
  • Mathematical Physics
  • Income Distribution
  • Combinatorial Manifolds
  • Newton Mechanics
  • Nonlinear Equations
  • Cosmology
  • Information Technology
Research works
5.6k
fractional, since 1950
In the world top 10%
556
per year above
Top-10% rate
9.8%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+17%
the tick is no change
Largest producer
United States
28% of the 10 largest, 2022-now
Advanced Mathematical Theories

Which countries lead Advanced Mathematical Theories research?

By volume, the United States and India publish the most (152 and 91 works in 2022-now).

By volume, 2022-now

  1. 1 United States 152 works
  2. 2 India 91 works
  3. 3 Türkiye 73 works
  4. 4 China 59 works
  5. 5 Indonesia 48 works
  6. 6 Brazil 41 works
  7. 7 United Kingdom 26 works
  8. 8 Japan 25 works
  9. 9 Germany 19 works
  10. 10 Russia 18 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: 27.5%India: 16.5%Türkiye: 13.2%China: 10.7%6 others listed: 32.0%28%largest
United States152 · 27.5%India91 · 16.5%Türkiye73 · 13.2%China59 · 10.7%6 others listed177 · 32.0%

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

Which institutions lead Advanced Mathematical Theories research?

By volume in 2022-now, Indian Institute of Technology Kharagpur publishes the most Advanced Mathematical Theories research, followed by Eckerd College and Universidad Nacional Experimental de Guayana.

By volume, 2022-now

  1. 1 Indian Institute of Technology KharagpurIndia 18 works
  2. 2 Eckerd CollegeUnited States 11 works
  3. 3 Universidad Nacional Experimental de GuayanaVenezuela 7 works
  4. 4 Russian Academy of SciencesRussia 7 works
  5. 5 Zonguldak Bülent Ecevit UniversityTürkiye 6 works
  6. 6 University of New MexicoUnited States 6 works
  7. 7 Erzincan Binali Yıldırım UniversityTürkiye 6 works
  8. 8 Centre National de la Recherche ScientifiqueFrance 5 works
  9. 9 Pamukkale UniversityTürkiye 5 works
  10. 10 Tribhuvan UniversityNepal 5 works

What are the most cited papers in Advanced Mathematical Theories?

The most cited paper in Advanced Mathematical Theories is "Generalized Hypergeometric Functions" (Lucy Joan Slater, Werner C. Rheinboldt, 1967), with 1,659 citations. Next come "On the foundations of combinatorial theory I. Theory of M�bius Functions" (1,501) and "Mathematics and its applications" (1,491).

Most cited papers
#PaperReleasedCitations
1 Generalized Hypergeometric Functions Lucy Joan Slater, Werner C. Rheinboldt · Physics Today Mar 1967 1,659
2 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
3 Mathematics and its applications Shing Tung Yau Conference paper 24 Aug 2005 1,491
4 Introduction to Percolation Theory N. Rivier · Physics Bulletin Nov 1987 1,305
5 Conjectures and Refutations Karl Raimund Popper, George Elford Hudson · Physics Today Nov 1963 1,040
All 102 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 Kharagpur (India), Moscow (Russia), St. Petersburg (United States) and New York (United States).

Largest cities, 2022-now

  1. 1 KharagpurIndia 18 works
  2. 2 MoscowRussia 12 works
  3. 3 St. PetersburgUnited States 11 works
  4. 4 New YorkUnited States 9 works
  5. 5 BeijingChina 9 works
  6. 6 Ciudad GuayanaVenezuela 7 works
  7. 7 TokyoJapan 7 works
  8. 8 BandungIndonesia 7 works
  9. 9 IstanbulTürkiye 7 works
  10. 10 ZonguldakTürkiye 6 works
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 and Eckerd College 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.

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 75.022.8%50.3×18 -
2Eckerd CollegeUnited States 15.08.6%1766.1×11 -

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 17% higher than in 2018-2021, peaking in 2025. 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, 0.0033% in 2024.

still counting0.010%0.020%0.030%Advanced Mathematical Theories0.0032% 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 Theories12.3% 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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