Science Explorer Interactive view Map
Subfield · Mathematics

Algebra and Number Theory research

Algebra and Number Theory is a subfield of Mathematics. Science Explorer counts 106k research works in it since 1950. 13.5% of them reached the world's top 10% most cited for their field and year.

In short: part of mathematics in which letters and other symbols are used to represent numbers and quantities in formulae and equation.

Research works
106k
fractional, since 1950
In the world top 10%
14k
per year above
Top-10% rate
13.5%
share of its works in the world top 10%
Topics
5
Growth, 2013–17 → 2018–22
+4%
the tick is no change

What is Algebra and Number Theory research about, and what is growing?

By the world's output in 2019–23, its most used keywords are Deformations, Hom-Lie Algebras, Modular Forms, Number Theory, Armendariz Rings, Zero-Divisor Graphs.

▲ gaining share of this field◆ holding its share▼ losing share

Size is the world's fractional works in 2019–23 in the topics tagged with each word; colour compares the word's share of this field with 2009–13. Each links to the topic it comes from most.

All 12 words, with their numbers
  1. Deformations6,518◆ 0.92×1 topic
  2. Hom-Lie Algebras6,518◆ 0.92×1 topic
  3. Modular Forms5,168◆ 1.08×2 topics
  4. Number Theory5,168◆ 1.08×2 topics
  5. Armendariz Rings3,040◆ 1.05×1 topic
  6. Zero-Divisor Graphs3,040◆ 1.05×1 topic
  7. L-Functions2,678◆ 1.04×1 topic
  8. Primes2,678◆ 1.04×1 topic
  9. Multiple Zeta Values2,490◆ 1.14×1 topic
  10. q-Series2,490◆ 1.14×1 topic
  11. Graded Betti Numbers1,652◆ 1.00×1 topic
  12. Monomial Ideals1,652◆ 1.00×1 topic

Which countries lead Algebra and Number Theory research?

On research quality in 2022–2025, China, the United States and India rank highest in Algebra and Number Theory. By volume, China and the United States publish the most (2k and 1.8k works in 2022–2025).

By research quality, 2022–2025

  1. 1 China · #2 all time 14.1% top 10% · 2k works
  2. 2 United States · #1 all time 12.2% top 10% · 1.8k works
  3. 3 India · #12 all time 9.6% top 10% · 1.3k works
  4. 4 Germany · #3 all time 14.4% top 10% · 495 works
  5. 5 South Korea · #8 all time 19.7% top 10% · 272 works
  6. 6 United Kingdom · #6 all time 13.8% top 10% · 387 works
  7. 7 Italy · #10 all time 16.9% top 10% · 392 works
  8. 8 France · #5 all time 11.8% top 10% · 532 works
  9. 9 Japan · #4 all time 10.4% top 10% · 560 works
  10. 10 Russia · #9 all time 11.4% top 10% · 512 works

The track on each row is that row’s top-10% rate. The ranking itself is the composite score, which the rate is only one part of.

Of 18 countries ranked in Algebra and Number Theory. Composite of field-normalised excellence (50%), output (30%) and citations (20%); the bracket is the all-time rank.

All countries ranked in Algebra and Number Theory

By volume, 2022–2025

  1. 1 China 2k works
  2. 2 United States 1.8k works
  3. 3 India 1.3k works
  4. 4 Japan 560 works
  5. 5 France 532 works
  6. 6 Russia 512 works
  7. 7 Germany 495 works
  8. 8 Iran 451 works
  9. 9 Türkiye 434 works
  10. 10 Italy 392 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.

China: 23.8%United States: 21.4%India: 14.8%Japan: 6.6%6 others listed: 33.3%24%largest
China2,009 · 23.8%United States1,807 · 21.4%India1,251 · 14.8%Japan560 · 6.6%6 others listed2,815 · 33.3%

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

Which institutions lead Algebra and Number Theory research?

Aligarh Muslim University (India) ranks first in Algebra and Number Theory on research quality in 2022–2025, followed by Centre National de la Recherche Scientifique and Sidi Mohamed Ben Abdellah University.

By research quality, 2022–2025

  1. 1 Aligarh Muslim University India · Aligarh · #79 all time 20.1% top 10% · 90 works
  2. 2 Centre National de la Recherche Scientifique France · Paris · #5 all time 13.6% top 10% · 88 works
  3. 3 Sidi Mohamed Ben Abdellah University Morocco · Fes · #93 all time 6.3% top 10% · 90 works
  4. 4 Lomonosov Moscow State University Russia · Moscow · #27 all time 8.7% top 10% · 66 works

The track on each row is that row’s top-10% rate. The ranking itself is the composite score, which the rate is only one part of.

Of 4 institutions above the floor of 40 fractional works in Algebra and Number Theory.

Top 100 Algebra and Number Theory institutions

By volume, 2022–2025

  1. 1 Aligarh Muslim UniversityIndia 90 works
  2. 2 Sidi Mohamed Ben Abdellah UniversityMorocco 89 works
  3. 3 Centre National de la Recherche ScientifiqueFrance 88 works
  4. 4 Lomonosov Moscow State UniversityRussia 66 works
  5. 5 Indian Institute of Technology KharagpurIndia 60 works
  6. 6 University of BaghdadIraq 59 works
  7. 7 Shandong UniversityChina 47 works
  8. 8 Nagoya UniversityJapan 41 works
  9. 9 Universidade de São PauloBrazil 41 works
  10. 10 University of OxfordUnited Kingdom 40 works

Who are the leading researchers in Algebra and Number Theory?

Among the most productive authors in Algebra and Number Theory, Stephan Ramon Garcia, Steven J. Miller and Donald E. Knuth rank highest on the composite score.

  1. 1 Stephan Ramon Garcia United States · #107 worldwide 4k citations · 136 works
  2. 2 Steven J. Miller United States · #283 worldwide 3.8k citations · 110 works
  3. 3 Donald E. Knuth United States · #357 worldwide 4k citations · 107 works
  4. 4 N. J. A. Sloane United States · #887 worldwide 2.8k citations · 116 works
  5. 5 Hywel C Williams United Kingdom · #1,208 worldwide 1.9k citations · 173 works
  6. 6 Jeffrey C. Lagarias United States · #2,191 worldwide 1.9k citations · 76 works
  7. 7 Michael Atiyah United Kingdom · #2,229 worldwide 1.4k citations · 87 works
  8. 8 Terence Tao United States · #2,469 worldwide 3.1k citations · 215 works
  9. 9 G. H. Hardy United Kingdom · #2,515 worldwide 939 citations · 96 works
  10. 10 David J. Benson United States · #2,816 worldwide 1.5k citations · 75 works

Re-ranked on the composite score from the 3,887 highest-output authors in Algebra and Number Theory. Identities come from OpenAlex author disambiguation, which occasionally merges or splits people.

Top 100 Algebra and Number Theory researchers

Where is Algebra and Number Theory research done?

The largest centres of Algebra and Number Theory 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 Zhoukou.

Largest cities, 2022–2025

  1. 1 Moscow Russia 275 works
  2. 2 Paris France 183 works
  3. 3 Beijing China 180 works
  4. 4 Tokyo Japan 170 works
  5. 5 Shanghai China 167 works
  6. 6 Nanjing China 148 works
  7. 7 Tehran Iran 132 works
  8. 8 Seoul South Korea 130 works
  9. 9 Baghdad Iraq 100 works
  10. 10 Xi'an China 100 works

Where it is the local speciality

  1. ZhoukouCN · 26.7 works46×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Algebra and Number Theory than the world average.

See Algebra and Number Theory on the map

Algebra and Number Theory research by country

The best places for Algebra and Number Theory research inside each country, with that country's researchers and world standing.

Where is the best place to study Algebra and Number Theory?

Among universities, judged by research, Kwangwoon University, Aligarh Muslim University and Hasan Kalyoncu 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%25%50%75%mean 37.86%fractional works in this node (log) →share in the world top 10% →Kwangwoon University: 16, 71.1%Aligarh Muslim University: 90, 20.1%Hasan Kalyoncu University: 9, 51.2%Sogang University: 14, 66.7%Sidi Mohamed Ben Abdellah University: 90, 6.3%Huaiyin Normal University: 12, 52.9%Prince Mohammad bin Fahd University: 18, 34.0%Indian Institute of Technology Gandhinagar: 22, 36.2%Cukurova University: 26, 31.2%University of Sfax: 37, 8.9%Kwangwoon UniversitySogang UniversityHasan Kalyoncu Unive…Aligarh Muslim Unive…
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 Kwangwoon UniversitySouth Korea 63.871.1%17.1×16 -11.3%
2 Aligarh Muslim UniversityIndia 62.620.1%25.4×90 +71.9%
3 Hasan Kalyoncu UniversityTürkiye 62.651.2%18.9×9 +327.1%
4 Sogang UniversitySouth Korea 60.966.7%13.3×14 -13.8%
5 Sidi Mohamed Ben Abdellah UniversityMorocco 57.96.3%24.9×90 +101.4%
6 Huaiyin Normal UniversityChina 57.452.9%25.7×12 +56.6%
7 Prince Mohammad bin Fahd UniversitySaudi Arabia 57.134.0%21.3×18 —
8 Indian Institute of Technology GandhinagarIndia 55.236.2%17.5×22 —
9 Cukurova UniversityTürkiye 53.931.2%7.8×26 +145.1%
10 University of SfaxTunisia 53.78.9%11.2×37 +102.3%

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 Algebra and Number Theory research growing?

Output in 2018–2022 was 4% higher than in 2013–2017, peaking in 2024. The fastest-growing topics are Advanced Mathematical Identities, Analytic Number Theory Research and Commutative Algebra and Its 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.

  1. Advanced Mathematical Identities+50%
  2. Analytic Number Theory Research+37%
  3. Commutative Algebra and Its Applications+32%
  4. Rings, Modules, and Algebras+22%
  5. Advanced Topics in Algebra+13%
← shrinkingno changegrowing →

Growth in output from 2005–09 to 2015–19. Every topic is a page of its own.

What does Algebra and Number Theory include?

Advanced Topics in Algebra46kAdvanced Topics in Algebra: 46k fractional worksRings, Modules, and Algebras: 21k fractional worksAnalytic Number Theory R…15kAnalytic Number Theory Research: 15k fractional worksAdvanced Mathematical Id…13kAdvanced Mathematical Identities: 13k fractional worksCommutative Algebra and Its Applications: 10k fractional works

Area is fractional works in that topic. Every name below is a page of its own.