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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. 10.0% 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%
11k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Topics
5
Growth, 2018-21 → 2022-25
+14%
the tick is no change
Largest producer
China
25% of the 10 largest, 2022-now
Algebra and Number Theory

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

By the world's output in 2021-25, 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 2021-25 in the topics tagged with each word; colour compares the word's share of this field with 2011-15. Each links to the topic it comes from most.

All 12 words, with their numbers
  1. Deformations6,822◆ 0.94×1 topic
  2. Hom-Lie Algebras6,822◆ 0.94×1 topic
  3. Modular Forms5,486◆ 1.06×2 topics
  4. Number Theory5,486◆ 1.06×2 topics
  5. Armendariz Rings3,243◆ 1.06×1 topic
  6. Zero-Divisor Graphs3,243◆ 1.06×1 topic
  7. L-Functions2,896◆ 1.04×1 topic
  8. Primes2,896◆ 1.04×1 topic
  9. Multiple Zeta Values2,590◆ 1.07×1 topic
  10. q-Series2,590◆ 1.07×1 topic
  11. Graded Betti Numbers1,727◆ 0.97×1 topic
  12. Monomial Ideals1,727◆ 0.97×1 topic

Which countries lead Algebra and Number Theory research?

On research quality in 2022-now, the United States, China and Germany rank highest in Algebra and Number Theory. By volume, China and the United States publish the most (2.3k and 2.1k works in 2022-now).

By research quality, 2022-now

  1. 1 United States #1 all time 1.04× citation excellence · 1.59× journals · 100% breadth 10.7% top 10% · 1.8k works
  2. 2 China #5 all time 1.07× citation excellence · 0.82× journals · 100% breadth 11.4% top 10% · 2k works
  3. 3 Germany #2 all time 1.17× citation excellence · 1.57× journals · 100% breadth 12.5% top 10% · 495 works
  4. 4 United Kingdom #4 all time 1.27× citation excellence · 1.63× journals · 100% breadth 13.1% top 10% · 387 works
  5. 5 France #3 all time 1.06× citation excellence · 1.32× journals · 100% breadth 9.4% top 10% · 532 works
  6. 6 South Korea #13 all time 1.47× citation excellence · 0.93× journals · 100% breadth 14.1% top 10% · 272 works
  7. 7 Italy #8 all time 1.54× citation excellence · 0.71× journals · 100% breadth 14.7% top 10% · 392 works
  8. 8 Japan #9 all time 0.89× citation excellence · 0.91× journals · 100% breadth 8.9% top 10% · 560 works
  9. 9 Canada #6 all time 0.88× citation excellence · 1.22× journals · 100% breadth 9.9% top 10% · 328 works
  10. 10 Spain #11 all time 1.15× citation excellence · 0.99× journals · 100% breadth 11.3% top 10% · 280 works

The track on each row is that row's top-10% rate. The ranking itself is the quality score, which compares the rate with what each place's own topics predict, adds its share of papers in the Nature Index journals, and counts output and breadth too.

Of 18 countries ranked in Algebra and Number Theory. Ranked on the quality score for 2022-now; the bracket is the all-time rank.

All countries ranked in Algebra and Number Theory

By volume, 2022-now

  1. 1 China 2.3k works
  2. 2 United States 2.1k works
  3. 3 India 1.4k works
  4. 4 Japan 615 works
  5. 5 France 584 works
  6. 6 Russia 550 works
  7. 7 Germany 549 works
  8. 8 Iran 485 works
  9. 9 Türkiye 474 works
  10. 10 Italy 430 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: 24.5%United States: 21.7%India: 15.0%Japan: 6.5%6 others listed: 32.3%25%largest
China2,327 · 24.5%United States2,058 · 21.7%India1,425 · 15.0%Japan615 · 6.5%6 others listed3,072 · 32.3%

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

Which institutions lead Algebra and Number Theory research?

Centre National de la Recherche Scientifique (France) ranks first in Algebra and Number Theory on research quality in 2022-now, followed by Aligarh Muslim University and Russian Academy of Sciences.

By research quality, 2022-now

  1. 1 Centre National de la Recherche Scientifique France · Paris · #1 all time 8.5% top 10% · 271 works
  2. 2 Aligarh Muslim University India · Aligarh 16.6% top 10% · 90 works
  3. 3 Russian Academy of Sciences Russia · Moscow 10.8% top 10% · 134 works
  4. 4 Lomonosov Moscow State University Russia · Moscow 8.5% top 10% · 66 works
  5. 5 Sidi Mohamed Ben Abdellah University Morocco · Fes 6.7% top 10% · 90 works

The track on each row is that row's top-10% rate. The ranking itself is the quality score, which compares the rate with what each place's own topics predict, adds its share of papers in the Nature Index journals, and counts output and breadth too.

Of 5 institutions above the floor of 40 fractional works in Algebra and Number Theory.

Top 100 Algebra and Number Theory institutions

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 291 works
  2. 2 Russian Academy of SciencesRussia 145 works
  3. 3 Sidi Mohamed Ben Abdellah UniversityMorocco 95 works
  4. 4 Aligarh Muslim UniversityIndia 95 works
  5. 5 Lomonosov Moscow State UniversityRussia 69 works
  6. 6 University of BaghdadIraq 68 works
  7. 7 Indian Institute of Technology KharagpurIndia 68 works
  8. 8 Max Planck SocietyGermany 56 works
  9. 9 Shandong UniversityChina 49 works
  10. 10 Polish Academy of SciencesPoland 45 works

Who are the leading researchers in Algebra and Number Theory?

Counting only their work in Algebra and Number Theory, George E. Andrews, Dae San Kim and Taekyun Kim have the most papers in the world top 10% for their subfield and year beyond the 10% expected.

  1. 1 George E. Andrews United States · #101,699 worldwide overall 39.4 of 133 papers here in the top 10%
  2. 2 Dae San Kim South Korea · #314,795 worldwide overall 52.2 of 152 papers here in the top 10%
  3. 3 Taekyun Kim South Korea · #605,474 worldwide overall 50.8 of 182 papers here in the top 10%
  4. 4 Ken Ono United States · #86,060 worldwide overall 27.9 of 73 papers here in the top 10%
  5. 5 Jürgen Herzog Germany · #106,725 worldwide overall 27.7 of 74 papers here in the top 10%
  6. 6 Craig L. Huneke United States · #120,854 worldwide overall 25.9 of 75 papers here in the top 10%
  7. 7 Victor Gershevich Kac United States · #41,553 worldwide overall 22.0 of 55 papers here in the top 10%
  8. 8 Feng Qi China · #773,991 worldwide overall 32.3 of 74 papers here in the top 10%
  9. 9 Bernd Sturmfels United States · #43,200 worldwide overall 19.7 of 40 papers here in the top 10%
  10. 10 Victor J. W. Guo China · #194,371 worldwide overall 25.2 of 70 papers here in the top 10%

Ranked on their work in Algebra and Number Theory alone: how many more of their papers here reached the world top 10% for their subfield and year than the 10% expected, among 84,760 ranked researchers with a paper here. Each paper counts once, so many strong papers outrank one famous one, and a long record of ordinary papers does not climb. Identities come from OpenAlex author disambiguation, which occasionally merges or splits people.

Top 100 Algebra and Number Theory researchers

What are the most cited papers in Algebra and Number Theory?

The most cited paper in Algebra and Number Theory is "The Magma Algebra System I: The User Language" (Wieb Bosma, John Cannon, Catherine Playoust, 1997), with 7,465 citations. Next come "Table of Integrals, Series, and Products" (4,749) and "Factoring polynomials with rational coefficients" (4,058).

Most cited papers
#PaperReleasedCitations
1 The Magma Algebra System I: The User Language Wieb Bosma, John Cannon, Catherine Playoust · Journal of Symbolic Computation Open access Sep 1997 7,465
2 Table of Integrals, Series, and Products I. S. Gradshteyn, I.M. RYZHIK, D. F. Hays · Journal of Lubrication Technology Open access Jul 1976 4,749
3 Factoring polynomials with rational coefficients A. K. Lenstra, Hendrik W. Lenstra, László Lovász · Mathematische Annalen Open access Dec 1982 4,058
4 Completely positive linear maps on complex matrices Man-Duen Choi · Linear Algebra and its Applications Open access Jun 1975 2,767
5 Aq-difference analogue of U(g) and the Yang-Baxter equation Michio Jimbo · Letters in Mathematical Physics Jul 1985 2,665
All 100 most cited papers, with filters and sorting

Where is Algebra and Number Theory research done?

The largest centres of Algebra and Number Theory research in 2022-now are Moscow (Russia), Beijing (China), Paris (France) 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-now

  1. 1 MoscowRussia 298 works
  2. 2 BeijingChina 210 works
  3. 3 ParisFrance 201 works
  4. 4 TokyoJapan 188 works
  5. 5 ShanghaiChina 187 works
  6. 6 NanjingChina 167 works
  7. 7 TehranIran 147 works
  8. 8 SeoulSouth Korea 140 works
  9. 9 BaghdadIraq 113 works
  10. 10 Xi'anChina 113 works

Where it is the local speciality

  1. ZhoukouCN · 27.0 works40×
← 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, Massachusetts Institute of Technology, ETH Zurich and University of California, Berkeley score highest, combining standing in the field's ranking, citation 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 15.73%fractional works in this field (log) →share of work in the world top 10% →ETH ZurichMassachusetts Instit…University of Califo…Princeton University
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.

Standingthis field's institution ranking, three quarters all time and a quarter 2022-now
50%
Citation excellenceshare of its work in the world top 10%, 2022-now and all time averaged
20%
Specialisationhow much of its work is in this field, counted up to 10× the world share
5%
Sizeits output in this field, on a log scale
15%
Growthoutput growth, counted from -20% to +20%
5%
Internationalshare of its work with a co-author abroad
5%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreRank in field (all time)Top 10%SpecialisationWorksGrowth
1Massachusetts Institute of TechnologyUnited States 81.7- (#2)19.4%4.4×40 +34.3%
2ETH ZurichSwitzerland 70.3- (#3)19.9%2.6×23 +8.8%
3University of California, BerkeleyUnited States 62.1- (#4)16.8%1.9×24 -24.0%
4Princeton UniversityUnited States 61.5- (#6)16.3%3.5×20 +9.2%
5Stanford UniversityUnited States 60.0- (#5)11.9%1.0×20 +10.5%
6University of California, Los AngelesUnited States 59.4- (#8)17.2%1.6×23 +38.5%
7Harvard UniversityUnited States 58.7- (#7)21.6%0.3×14 +78.1%
8California Institute of TechnologyUnited States 54.5- (#10)15.8%3.5×17 +28.0%
9University of MichiganUnited States 53.7- (#12)8.3%1.7×33 +35.5%
10University of California San DiegoUnited States 51.7- (#13)10.1%2.1×27 +71.8%

Universities only. The score blends standing (50%), citation excellence (20%), size (15%), specialisation (5%), growth (5%), international reach (5%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise. Standing is the score in this field's institution ranking, three quarters over all time and a quarter 2022-now; excellence averages the two windows too. Four years alone undercount fields such as AI, where many conference and arXiv papers from 2022 on carry no affiliation in the data.

Every institution in Algebra and Number Theory, country by country

Is Algebra and Number Theory research growing?

Output in 2022-2025 was 14% higher than in 2018-2021, peaking in 2024. The fastest-growing topics are Analytic Number Theory Research, Advanced Topics in Algebra and Rings, Modules, and Algebras.

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 Algebra and Number Theory as a percentage of every work published that year, 0.065% in 2024.

still counting0.10%0.20%0.30%Algebra and Number Theory0.060% in 202519801990200020102020

Fractional works of Algebra and Number Theory 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%Algebra and Number Theory10.2% 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.

  1. Analytic Number Theory Research+19%
  2. Advanced Topics in Algebra+14%
  3. Rings, Modules, and Algebras+13%
  4. Commutative Algebra and Its Applications+13%
  5. Advanced Mathematical Identities+13%
← shrinkingno changegrowing →

Growth in output from 2018-21 to 2022-25. 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.

Share who leads Algebra and Number Theory

Who leads Algebra and Number Theory, on Science Explorer

A card with the countries and institutions that lead Algebra and Number Theory, for a post or a slide.

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1200 × 630 PNG, sized for social posts, drawn from the latest snapshot.

The leading institutions' badges5Each links to that institution's page and updates with every snapshot

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